Improved quartz oscillator

Abstract

Disclosed is a quartz oscillator system comprising: a quartz oscillator comprising a quartz crystal and an oscillator circuit whose frequency is based on a resonant frequency of the quartz crystal; a monitoring module for monitoring an output frequency of the quartz oscillator; a control system external to the quartz oscillator, and configured to compare the output frequency with a setpoint frequency, and apply an adjustment signal to an electronic circuit of the quartz oscillator to adjust a frequency of the quartz oscillator based on the comparison with the reference frequency.

Description

[0001] IMPROVED QUARTZ OSCILLATOR

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to the field of quartz oscillators and the like in which their resonant frequency is utilised to provide or regulate an oscillator frequency.

[0004] BACKGROUND ART

[0005] Some time keeping devices rely on periodically oscillating systems to measure the passage of time. A second is counted by measuring a fixed number of periods of oscillation that add together to define said second. Different natural phenomena can be used to provide this periodic oscillation; for example, the resonant oscillation of a pendulum, the mechanical resonance of a crystalline structure such as a quartz crystal, or the resonant oscillation of atoms. In order to excite these systems such that they can resonate, energy needs to be added to the system. In the case of a pendulum the energy is provided by the gravitational acceleration of the Earth, whereas in a quartz crystal the piezoelectric effect allows for the use of an electrical signal to ‘excite’ resonance in the crystalline structure. For an atomic clock, electromagnetic waves such as microwaves or visible light are used to ‘excite’ atomic resonances.

[0006] Quartz clocks leverage the piezoelectric properties of quartz crystals to achieve consistent timekeeping. A quartz crystal's resonance frequency, carefully tailored during its design and cutting phases, dictates the clock's primary, or operating, frequency. An electronic circuit of the quartz clock is engineered to sustain oscillation at this primary frequency, ensuring uniform timekeeping. Should the electronic signal used to ‘excite’ the resonance in the quartz crystal fail to match this primary frequency, timekeeping accuracy is compromised, leading to deviations over time. Such a misalignment, besides causing temporal inaccuracies, can stress the oscillator components, particularly the quartz crystal. Over time, this strain can lead to quicker wear and potentially, crystal failure, impacting the clock's longevity.

[0007] Due to the relativistic effects of Einstein’s theories of special relativity and general relativity, objects in different inertial frames of reference (FoR) travelling at different

[0008] I speeds, as well as objects subject to different gravitational potentials, experience the passage of time at different rates. In relatively simple terms, special relativity dictates that objects travelling at a higher velocity will experience a time dilation effect relative to objects travelling at a slower velocity. For example, an observer A travelling in a first FoR, who measures an observer B travelling in a second FoR with a greater velocity, would measure observer B as having experienced less time for a set period of observer A’s time. Furthermore, an observer A in a weaker gravitational potential would measure an observer B in a stronger gravitation potential as having experienced less time for a set period of observer A’s time.

[0009] These relativistic effects are real and measurable, and their effects need to be accounted for in real world scenarios. For example, atomic clocks in low earth orbit travel at high velocities relative to observers on the ground, therefore resulting in a dilation of the ticking rate of the onboard clocks relative to ground-based observers. Furthermore, these satellites are in a lower gravitational potential relative to ground-based observers as their distance from the Earth’s centre of mass is greater, thereby resulting in less dilation of the ticking rate of the onboard clocks relative to the ground-based observers.

[0010] These relativistic effects affect everything uniformly, regardless the method of time recordal utilised. It is the actual passage of time that is different relative to a different frame of reference. As such, adjustments for the relativistic effects on the ticking rate of clocks, whether in varying FoR’s or under different gravitational potentials, are considered in a uniform manner across different types of clocks, including both atomic clocks and quartz oscillators. However, emerging observations of certain temporal anomalies associated with quartz oscillator-based clocks hint that there may be other external factors that affect quartz oscillators in a manner distinct from atomic clocks. These discrepancies suggest that quartz oscillators, due to their mechanical nature and sensitivity to minor gravitational variations, might be subject to changes of the resonant frequency of the quartz crystal, resulting in mismatches between the circuit frequency and crystal resonant frequency which ultimately results in inaccurate time recordal. A 2009 paper published by E. Fischbach and J. H. Jenkins, titled "Perturbation of Nuclear Decay Rates During the Solar Flare of 13 December 2006," Astroparticle Physics, vol. 31, no. 6, pp. 407-411, 2009, outlines seasonal shifts in the measured nuclear decay rates of certain atomic isotopes. This study, along with two further papers by E. Fischbach et al ("Analysis of environmental influences in nuclear half-life measurements exhibiting timedependent decay rates.," Nuclear Instruments and Methods, vol. A620, p. 330, 2010; and "Concerning the Phase of the Time-Variation in the 32C1 decay Rate," arXiv: 1210.3334 [nucl-ex], Oct 2012) further detail these apparent fluctuations in nuclear decay rates, and reaffirm that these fluctuations are not a result of environmental factors such as humidity, temperature, and background, or any systematic effects.

[0011] To date the scientific community has yet to reach a consensus that adequately explains the observed anomalies in decay rates. The dominant view leans towards potential experimental errors or unaccounted environmental variables, such as temperature, humidity, or pressure, causing these anomalies. However, the increasing global reports of decay rate variations signal a need for more examination and understanding.

[0012] Another example is the Pioneer anomaly from the Pioneer 10 and 11 data sets. Navigational tracking data of the Pioneer 10 and 11 spacecraft indicates the presence of a small anomalous Doppler frequency drift in their radio-metric observables. This drift has been interpreted as an anomalous constant acceleration acting on both these spacecraft in the sunward direction. This acceleration of unknown origin is now known as the Pioneer anomaly. Fig. 3 illustrates the anomaly. See Turyshev, Slava G., et al. “Support for Temporally Varying Behaviour of the Pioneer Anomaly from the Extended Pioneer 10 and 11 Doppler Data Sets.” Physical Review Letters, vol. 107, no. 8, 19 Aug. 2011, https: / / doi.org / 10.1103 / physrevlett.107.081103. Accessed 10 Oct. 2021. The timekeeping devices utilised in the Pioneer 10 and 11 spacecrafts are quartz oscillator based instruments. As such, it is likely that the same unaccounted for variance in quartz crystal resonant frequency as a result of changes to the experienced gravitational potential onboard the spacecraft are the result for the unaccounted acceleration (Pioneer Anomaly). It is to be understood that, if any prior art is referred to herein, such reference does not constitute an admission that the prior art forms a part of the common general knowledge in the art, in Australia or any other country.

[0013] SUMMARY

[0014] Disclosed is a quartz oscillator system comprising: a quartz oscillator comprising a quartz crystal and an oscillator circuit whose frequency is based on a resonant frequency of the quartz crystal; a monitoring module for monitoring an output frequency of the quartz oscillator; a control system external to the quartz oscillator, and configured to compare the output frequency with a setpoint frequency, and apply an adjustment signal to an electronic circuit of the quartz oscillator to adjust a frequency of the quartz oscillator based on the comparison with the reference frequency.

[0015] In some forms, the controller comprises a setpoint determination module configured to determine the setpoint frequency.

[0016] In some forms, the setpoint frequency is determined based on at least the resonant frequency of the quartz crystal, and an adjustment data in relation to an orbital position of the earth around the sun.

[0017] In some forms, the system comprises data storage to store the adjustment data, the control system having access to the data storage.

[0018] In some forms, the system comprises a communication module for querying the setpoint frequency from a data source.

[0019] In some forms, the control system comprises a phase locked loop (PLL), wherein a signal at the setpoint frequency is provided as a reference input for the PLL, and wherein a signal at the output frequency determined by the frequency monitor is at an output for the PLL.

[0020] In some forms, the controller is configured to generate control signals based on the comparison between the output frequency determined by the frequency monitor and the setpoint frequency, wherein the control signals are provided as input to an adjustment module configured to generate adjustment signals to adjust the output frequency of the quartz oscillator.

[0021] In some forms, the controller comprises a synchronisation module, configured to synchronise the setpoint frequency with frequency determined based on an external time source.

[0022] In some forms, the external time source comprises an atomic clock or a time source in a global positioning system.

[0023] In some forms, the monitoring module is configured to use the output frequency of the system as a base frequency for monitoring a ticking rate of the quartz crystal.

[0024] In some forms, the monitoring module is configured to provide a data generated based on an output signal from the quartz oscillator, to the controller. The output signal from the quartz oscillator may be indicative of a ticking rate (resonant frequency) of the quartz oscillator.

[0025] In some forms, the quartz oscillator is a temperature-compensated quartz crystal oscillator or oven-controlled crystal oscillator.

[0026] In some forms, the controller is configured to receive user input for system calibration and / or setting data.

[0027] In some forms, the controller is configured to provide a user interface displayable on a display screen, the user interface being configured to enable the user input to be provided.

[0028] The present disclosure also describes an apparatus providing three quartz oscillator systems, each system being in accordance with the above, wherein the quartz oscillators for the three systems are respectively mounted along three orthogonal axes.

[0029] The present disclosure also provides a timing device comprising the quartz oscillator system, or the apparatus mentioned above.

[0030] The present disclosure also provides a method for improving accuracy of a quartz oscillator clock, comprising: monitoring an output frequency of a quartz oscillator of the quartz oscillator clock; comparing the output frequency with a setpoint frequency to determine an error between the output frequency and the setpoint frequency; providing a voltage adjustment signal to the quartz oscillator, the voltage adjustment signal being determined on the basis of the error, to adjust the output frequency of the quartz oscillator.

[0031] The above summary is not intended to describe each embodiment or every implementation of the clock feedback loop system as described herein. Rather, a more complete understanding of the invention will become apparent and appreciated by reference to the following Brief Description of the Drawings and claims in view of the accompanying figures of the drawing.

[0032] BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Non-exhaustive and non-limiting embodiments of the invention are described herein below, with reference to exemplary configurations illustrated in the accompanying drawings, in which:

[0034] Fig- 1 is a graph plotting the shift in quartz resonant frequency over an anomalistic year.

[0035] Fig- 2 is a graph plotting experimental results of isotope214Po decay rate over an anomalist year, compared to theoretically calculated decay rates.

[0036] Fig- 3 is a graph depicting the Pioneer 10 anomaly.

[0037] Fig. 4 is a block diagram illustrating an embodiment of the oscillator system

[0038] Fig. 5 is a block diagram illustrating an embodiment of a controller of an improved oscillator system.

[0039] Fig. 6 is a block diagram illustrating an example operation of a controller of the oscillator system in accordance with an embodiment.

[0040] Fig. 7 is a block diagram illustrating a synchronisation process for adjusting the quartz frequency parameter.

[0041] Fig. 8 is a block diagram illustrating another embodiment of an oscillator system. Fig- 9 is a block diagram illustrating another embodiment of the controller.

[0042] Fig. 10 is a flow charge depicting a control process in one embodiment.

[0043] Fig- 11 is a frequency versus time plot depicting the different frequency shift effects attributable to acceleration and temperature.

[0044] DETAILED DESCRIPTION

[0045] In the following detailed description, reference is made to accompanying drawings which form a part of the detailed description. The illustrative embodiments described in the detailed description, depicted in the drawings and defined in the claims, are not intended to be limiting. Other embodiments may be utilised and other changes may be made without departing from the spirit or scope of the subject matter presented. It will be readily understood that the aspects of the present disclosure, as generally described herein and illustrated in the drawings can be arranged, substituted, combined, separated and designed in a wide variety of different configurations, all of which are contemplated in this disclosure.

[0046] A potentially overlooked phenomenon that may be the underlying cause of at least some of the temporal anomalies that result from the use of quartz oscillators (e.g. anomalies in measured nuclear isotope decay rates and the Pioneer anomaly), is that the resonant frequency of a quartz crystal is susceptible to changes in gravitational potential by a factor of 10'9per unit gravitational acceleration (g). This shift in resonant frequency of the quartz crystal, if unaccounted for, can result in time recordal errors.

[0047] The design to correct for the Earths orbital acceleration effect in advanced quartz clocks holds significant promise for the telecommunications industry, particularly with the advent of 5G technology. As 5G networks require exceptionally high precision in timing to handle the increased data rates, lower latency, and more extensive network coverage, even minor timing inaccuracies can lead to substantial performance degradation. By addressing the subtle frequency variations induced by Earth's orbital dynamics, the present application ensures that quartz clocks maintain their accuracy under these dynamic conditions. This improvement in timing precision directly translates to more reliable synchronisation across 5G networks, reducing the likelihood of data packet loss, improving signal integrity, and enhancing overall network efficiency. Moreover, as 5G technology enables new applications such as autonomous vehicles, remote surgery, and advanced loT devices, the need for precise and stable timing becomes even more critical.

[0048] Herein described is a clock design, to provide an improved precision in performing timing. This improved precision can be beneficial for radar systems, which rely on accurate time measurements for determining distance and speed. By maintaining stable and precise timing through compensation for gravitational effects, crystal aging, and other environmental factors, the clock design enhances radar performance. The improved precision may be particularly valuable for applications requiring high range resolution and Doppler accuracy. As will be described, the clock's dynamic adjustment capabilities ensure continuous accuracy in varying environmental conditions, making it suited for radar systems on moving platforms such as aircraft, ships, and satellites. Additionally, the synchronisation, more closely aligned with atomic time standards, improves the overall reliability and coordination of radar systems. Such improvement may be advantageous in both civilian and defence applications.

[0049] Stability of Quartz Oscillators

[0050] Quartz crystal oscillators are recognized for their stability and precision in timekeeping applications. These oscillators rely on the mechanical resonance of quartz crystals to generate accurate and consistent frequencies. The stability of quartz oscillators is primarily due to their inherent insensitivity to various environmental factors, including pressure fluctuations. However, temperature fluctuations can still affect their performance to some extent.

[0051] A quartz oscillator's stability arises from the resonance properties of quartz crystals. When subjected to an electrical voltage, quartz crystals vibrate at a well-defined natural frequency, determined by their physical dimensions and crystalline structure. This inherent resonance frequency is highly stable, making quartz crystals suited for precise timekeeping.

[0052] Quartz oscillators often incorporate temperature compensation mechanisms, such as compensation circuits, to mitigate frequency variations caused by temperature fluctuations. These compensation circuits adjust the drive voltage to counteract the temperature-induced frequency shifts, ensuring consistent performance over a wide temperature range.

[0053] Additionally, whilst quartz crystals do exhibit minimal aging effects, particularly in the first year, these effects significantly diminish over time, resulting in their resonant frequencies remaining stable over extended periods.

[0054] Quartz oscillators exhibit a high degree of insensitivity to external environmental factors, such as changes in air pressure and humidity. This characteristic makes them suitable for diverse applications, from consumer electronics to scientific instruments, where stable and reliable timekeeping is crucial.

[0055] Quartz Relevance to Gravitation Effects

[0056] Even though quartz crystals are generally considered to be stable, quartz oscillators exhibit a sensitivity to changes in gravitational acceleration on the order of 10'9hertz per unit gravitational acceleration (g). Consequently, quartz-based clocks may exhibit frequency variations in response to stresses induced by Earth’s orbital dynamics, a result of Einstein’s Equivalence Principle, which states that inertial acceleration is equivalent to gravitation acceleration. This may become consequential in precision timing applications.

[0057] For example, in precision timing experiments, such as those involving the measurement of radioactive isotope decay rates, the electronic circuit of a quartz oscillator records a discernible variation in the resonant frequency of the quartz crystal. This phenomenon arises from the slight variability of the quartz crystal's resonant frequency due to changes in Earth’s orbital dynamics, a result of the Equivalency Principal. The perceived gravitational potential is the net gravitational potential experienced by the quartz crystal as a result of its motion relative to the sun (the quartz crystal located on Earth and matching that motion), and the crystals position relative to large gravitational wells (e.g. the Sun, Earth, and Moon).

[0058] Hence, the rate at which the electronic circuit of the quartz oscillator ‘counts’ these resonances may be affected. This is because changes in the gravitational potential experienced by the quartz crystal, primarily from Earth’s radial accelerations throughout its orbit, affect the resonant frequency of the quartz crystal. This results in a mismatch between the time measured by the electronic circuit of a quartz oscillator clock and the actual resonant frequency of the quartz crystal.

[0059] Examples of the factors influencing gravitational changes include the Earth’s orbit around the Sun, and the position of the Moon relative to the Earth. The Earth’s orbit around the Sun is not perfectly circular, and therefore during an anomalistic year the Earth may be closer to or further away from the Sun depending on its location along its orbital path, thereby either increasing or decreasing the strength of the gravitational potential experienced on or around the Earth. The orbit of the Moon around the Earth is also non-circular, and so depending on where the Moon is in its orbital path around the Earth, the position affects the gravitational potential experienced on or around the Earth. Furthermore, the rotation of the Earth underneath the Moon also affects the gravitational potential experienced on or around the Earth, i.e. depending on if the Moon is overhead or on the other side of the Earth, and whether that aligns with the gravitational acceleration of the Sun, or acts against it.

[0060] To ensure precise timekeeping, the present disclosure provides a quartz oscillator system which has a control module and feedback loop system to account for deviation of the quartz crystal’s resonant frequency.

[0061] Frequency stability is a fundamental requirement for quartz oscillators, impacting the accuracy and resolution of radar and radio navigation systems, measurement precision in various applications, and the quality and reliability of communication systems. The ability to address or mitigate the time recordal errors therefore has utility in myriad applications, including but not limited to, radar, radio, navigation systems, astronomy calculations, space application, telecommunications, network synchronisation, critical infrastructure (such as energy grids), aviation and aerospace, military and defense, financial markets (including high-frequency trading), Global Positioning Systems (GPS), space navigation, astronomy, scientific research, radar, radio navigation, etc.

[0062] As will be described, the system in accordance with the present disclosure monitors the quartz crystal’s frequency. If any drift is detected - whether higher or lower than the desired frequency - it calculates an offset frequency to counteract this drift in the opposite direction. By applying this correction, the system ensures that the quartz oscillator remains at the correct frequency. This process involves frequency monitoring, drift detection and analysis, calculating the necessary correction, and dynamically applying the correction through a feedback control mechanism such as a Phase-Locked Loop (PLL). The system is configured to have access to information regarding the drift which is within the calculated range derived from orbital dynamics; deviations outside this range may indicate the influence of other external factors such as temperature or aging. In some embodiments, regular synchronisation with atomic clocks and adjustments for environmental factors further enhance the accuracy, ensuring precise timekeeping.

[0063] Measuring Nuclear Decay Rates

[0064] An example of a use of a system described herein is to measure nuclear decay rates. Recent years have seen growing evidence from various studies reporting anomalies including annual variations in nuclear decay rates, with the periodicities aligning with the Sun’s rotational phases on its axis and suggesting a possible relation to the Sun. Radioactive decay is viewed as a stochastic self-governed process and a constant of nature. The discovery of nuclear decay rate variation in any unstable isotope would challenge this view, prompting a re-evaluation of the perceived constancy of decay rates.

[0065] Studies conducted over the last 20 years have revealed consistent annual variations in the decay rates of various nuclear isotopes. One ongoing potential explanation for these variations is the presence of neutrinos or antineutrinos from the Sun, and their subsequent interaction with the atomic nuclei. However, a 2022 [1] study provides substantial evidence that neutrino or antineutrino interactions are not the source of these observed decay rate variations. Conducted just 6.53 metres from the High Flux Isotope Reactor (HFIR) core at Oak Ridge National Laboratory, the study was ideally positioned to test the hypothesis regarding neutrino interactions due to the high neutrino flux near the reactor core.

[0066] To date, the scientific community has yet to reach a consensus that adequately explains the observed anomalies in decay rates. The prevailing view attributes these anomalies to potential experimental errors or unaccounted environmental variables such as temperature, humidity, or pressure. However, increasing global reports of decay rate variations underscore the need for further examination and understanding. When using a quartz oscillator clock to measure nuclear decay rates, different positions of the Earth’s and the Moon’s orbits introduce variation in the experienced gravitational effects on or around the Earth. The quartz crystal’s sensitivity to minor gravitational changes becomes evident during these measurements as it results in the discussed shift of the resonant frequency of the quartz crystal, causing a mismatch between the quartz crystal’s resonant frequency and the electronic circuit of the quartz oscillator clock used to measure the crystal.

[0067] The sensitivity of quartz crystals to gravitational potentials provides one possible explanation for measured temporal variations in nuclear decay rates, suggesting that these variations may be artifacts arising from quartz crystal’s response to minor acceleration changes, rather than from intrinsic alterations in the decay processes. Therefore, measurements performed using the present system may be more accurate.

[0068] Earth’s Orbital Effects on Resonant Frequency of Quartz

[0069] The Earth’s orbital dynamics on quartz oscillator measurements may be determined using a mathematical model that represents the orbital dynamics experienced by these oscillators. Such a model is useful for quantifying the specific effects of Earth’s motion on the frequency variations observed in decay rate experiments.

[0070] Earth’s orbital effects can be broken down into two constituent parts, Earth’s radial acceleration and its tangential acceleration. Firstly, the radial acceleration accounts for the gravitational influence of the Sun as Earth’s radial distance from the Sun changes throughout an anomalistic year, Earth’s tilt and its rotation.

[0071] Earth’s Tangential acceleration component is orthogonal to the radial acceleration and provides insight into the dynamic changes in velocity as an object moves along its orbital path, i.e. the Earth’s velocity vector’s direction. The magnitude of tangential acceleration on quartz resonant frequency is an order of magnitude smaller than Earth’s radial acceleration imparts on the quartz. In some embodiments, the adjustments take the radial acceleration into account. In preferred embodiments, the adjustments further take the radial acceleration, into account. Derivation of a final radial equation and final tangential equation, both with latitude and hemisphere adjustment factors, are detailed in accompanying paper “Impact of Gravitational Fields and Earth’s Orbital Dynamics on Quartz Oscillators: Insights into Temporal Variations in Nuclear Decay Rates”. Final Radial Equation

[0072] Wherein:

[0073] (fo) = base frequency of the quartz oscillator

[0074] (k) = Sensitivity to gravitational acceleration factor - constant specific to the material properties of the quartz crystal

[0075] A( , (|), v) = radial force component projection in the direction perpendicular to the Earth’s surface at the specified location, and adjusted for the true anomaly.

[0076] (g) = 9.81ms"2; acceleration due to Earth’s gravity

[0077] (r(i'))=rate °f change of the radial distance (r(v)) = radial distance as a function of (v)

[0078] (G) = 6.7430 * 10"11m3kg"1s"2- gravitational constant

[0079] (M) = 1.989 * 1030Kg - mass of the Sun

[0080] (a) = 145.598* 106km - semi-major axis of Earth’s orbit

[0081] (vi) and (V2) = limits of integration over the relevant period Final tangential equation

[0082] Wherein:

[0083] (fo) = base frequency of the quartz oscillator (k) = Sensitivity to gravitational acceleration factor - constant specific to the material properties of the quartz crystal

[0084] A( , (j), v) = radial force component projection in the direction perpendicular to the Earth’s surface at the specified location, and adjusted for the true anomaly.

[0085] (g) = 9.81ms"2- acceleration due to Earth’s gravity (G) = 6.7430 * 10"11m3kg"1s"2- gravitational constant

[0086] (M) = 1.989 * 1030Kg - mass of the Sun

[0087] (a) = 145.598* 106km - semi-major axis of Earth’s orbit

[0088] (vi) = starting value of the true anomaly for the integration

[0089] (V2) = ending value of the true anomaly Figure l is a graph which depicts a combination of the results from both the radial and tangential acceleration calculations to demonstrate how these combined forces influence the resonant frequency of a quartz crystal over an annual cycle. It should be noted however, that the radial component of acceleration is more than an order of magnitude larger than the tangential component, and hence it’s the radial component that plays the major role. Quartz Oscillator Measurement of Nuclear Decay Rates

[0090] When measuring the decay rate of an isotope, the accuracy of the clock frequency is crucial. An increase in the clock frequency will result in a measured half-life that appears shorter than the actual half-life, while a decrease in the clock frequency will cause the measured half-life to appear longer. This is because the timing mechanism speeds up or slows down, respectively, affecting the rate at which decay events are counted. To predict the expected half-life measurement based on the frequency shift in the clock, we can use the formula:

[0091] Expected Half — Lif Measurement

[0092] — Known Half Life X (1 — Frequency Shift) (1)

[0093] This formula allows us to adjust the known half-life of the isotopes by accounting for the deviation in the clock’s frequency, providing a theoretical measurement that matches the observed frequency shift.

[0094] Figure 2 illustrates the annual variation of214Po half-life as measured in "Results of a search for daily and annual variations of the 214Po half-life at the two-year observation period.," sourced from conference paper: Cl 5-02-01, 2nd International Workshop on Prospects of Particle Physics and Astrophysics., Vols. arXiv: 1505.01752v 1 [nucl-ex] 7 May 2015, 2015. Also plotted here is the curve showing the theoretical half-life deviations based on the shift in quartz resonant frequency over an anomalistic year.

[0095] The sinusoidal pattern observed in the plot reveals the periodic nature of the frequency shifts and their direct correlation with the documented variations in isotope decay rates. These results support the hypothesis that subtle changes in Earth's orbital dynamics can have measurable impacts on high-precision measurements. The matching phases and amplitudes between the clock frequency shifts and the decay rate variations underscore the interconnectedness of dynamic astronomical factors and terrestrial quantum phenomena.

[0096] These results highlight the importance of considering orbital dynamics in the design and interpretation of experiments involving precision timekeeping and radioisotope measurements. This also reveals that short term measurements might not see large variations compared to long term measurements as the quartz frequency shift due to Earth’s orbital dynamics is a cumulative effect. It also depends to some degree when the measurements are made, for instance in late March to early April and late September to early October will show the largest variations in clock frequency, whereas early January and July have the smallest variations.

[0097] Effects to Quartz Oscillators On-Board Spacecraft

[0098] As discussed in the background, the Pioneer Anomaly presents a case study concerning the unexplained deviations observed in the trajectories of the Pioneer 10 and Pioneer 11 spacecraft. Initial analyses pointed towards an apparent sunward acceleration, which conventional models of celestial mechanics could not fully explain. Similar to the measurement of nuclear decay rates using quartz oscillators, it is hypothesised that variations in the resonant frequency of quartz crystals used on board the Pioneer 10 and 11 spacecrafts, induced by changes in gravitational acceleration as the spacecraft traverse the solar system, could account for the observed discrepancies.

[0099] A mathematical model that accurately represents the orbital dynamics is useful for the understanding of the effects on a quartz oscillator onboard a spacecraft. The inverse square law of gravitational force can be used to estimate the gravitational acceleration experienced by the spacecraft as it moves away from the Sun. Given the sensitivity of quartz oscillators to gravitational variations, even minute changes in the gravitational field can induce measurable frequency shifts. These shifts accumulate over time, affecting the spacecraft's onboard timekeeping systems and, consequently, navigational data. By integrating the gravitational effects over the trajectory of the spacecraft, the equation aims to quantify the resultant frequency shift in terms that relate directly to observable anomalies.

[0100] This model assumes that the primary source of the anomaly is the gravitational sensitivity of the quartz oscillator, distinct from other proposed explanations such as thermal forces or observational errors. This exploration provides a novel perspective on the Pioneer Anomaly.

[0101] The model accounts for the direction of the spacecraft's movement relative to the Sun with a variable termed 'direction Factor (h)' . This factor adjusts the sign of the calculations to reflect the physical dynamics accurately: it is set to one value, e.g., '-1' when the spacecraft is moving away from the Sun, reflecting a decreasing gravitational influence, and another value e.g., '+1' when moving towards the Sun, indicating increasing gravitational effects. The different signs help to correctly model the gravitational stresses on the quartz oscillator and their impact on frequency response.

[0102] NASA typically employs a two-way Doppler shift method for enhanced accuracy in signals sent from Earth and reflected back, to calculate navigational accuracy or to track spacecrafts This approach assumes symmetric conditions on the path of the signal. In contrast, the present application focuses on the increase in frequency, (A ), generated by the onboard clock as a result of gravitational changes, which inherently involves a one-way transmission from the spacecraft to Earth. Embodiments disclosed herein use a one-way Doppler shift on the frequency change (A ) to reflect the frequency changes as they are observed directly on Earth, without the reciprocal influence typical of two-way measurements. The one-way consideration is designed to interpret the specific gravitational effects on the oscillator’s frequency.

[0103] Final Equation for the Pioneer Anomaly

[0104] Wherein:

[0105] F(T) = cumulative frequency shift of the quartz oscillator over time (t)

[0106] (ns) = Sensitivity of quartz to acceleration, measured as a fractional frequency shift of (10‘9). This parameter quantifies how susceptible the frequency of the quartz oscillator is to changes in acceleration due to gravitational effects or other forces. rcnvarXs the Sun - ; - ; - mwy / orm txv Swt base frequency for Pioneer IQ & H acceleration due to Earth’s gravity

[0107] (6) “ 6.67430 X lQ~22m2&|?~i£“s- gravitational constant

[0108] (M) — 1.989 X 10ssA^ -mass of the Sun

[0109] (v) - 12200 w’x•- radial velocity of the spacecraft relative to the Sun

[0110] Oh) “ 1«496 X 10^ On. — initial, distance from Qte Sun at time (t-0)

[0111] (T) “Total elapsed tune m seconds (s)

[0112] Figure 3 illustrates the changes in quartz frequency relative to distance from the Sun. This plot represents the change in the quarts frequency of Pioneer 10’s onboard clock, measured in hertz (Hz), as a function of its distance from the Sun, expressed in astronomical units (AU). The above equation, which incorporates the effects of gravitational anomalies and one-way Doppler shifts, demonstrates a close alignment with NASA's documented measurements. Notably, at the 8-year mark, our model aligns with NASA’s observations, showing a steady frequency drift of approximately -1.5 Hz over 8 years, which corresponds to a frequency change rate of about -6.4 x 10-9 Hz / s. This drift translates to a clock acceleration of -2.9 x 10-18 s / s2. This underscores the critical impact of subtle gravitational effects on spacecraft timekeeping systems over extended periods.

[0113] Fig. 4 illustrates an embodiment of a quartz oscillator system 100 according to the present disclosure, which has a modified design compared with a conventional quartz oscillator system. As quartz oscillators (or “oscillators” for short) are often used in time-keeping (i.e., “clock”) systems where the oscillator’s output frequency is used to keep time, the modified quartz oscillator system 100 can also be considered a clock feedback system 100 (herein interchangeably referred to as the feedback loop, clock feedback loop, feedback loop system, or feedback system without departing from its meaning or scope), designed to at least partially mitigate the issue with the mismatch between the effects of gravitational changes on the quartz oscillator and on the circuitry of the quartz clock, in conventional quartz oscillator clocks. The system 100 operates a feed-back loop external to the quartz oscillator of the system 100, preferably continuously, aiming to keep a ticking rate of a quartz oscillator used in the system 100 in alignment with a desired setpoint, accounting for relativistic variation. This design aims to allow the system 100 to automatically adjust its ticking rate in real-time or close to real-time, to optimise accuracy.

[0114] As shown in Figure 4, the system 100 includes a quartz oscillator 108 which provides the ticking rate of the overall system 100, a monitoring module 106 which monitors an output frequency of the quartz oscillator 108, and a controller 104 which adjusts the output frequency of the quartz oscillator 108 on the basis of a current setpoint for the system frequency. The monitoring module 106, quartz oscillator 108, and controller 104 therefore form a feedback loop 110. The output frequency of the quartz oscillator 108 is what the feedback loop 110 within the system 100 is designed to monitor and adjust, ensuring that it aligns with the predetermined set point.

[0115] The determination of the setpoint is made on the basis of data comprising at least adjustment data. In Figure 4, the system includes a memory or data storage 102 configured to store precalculated adjustment data. The pre-calculated adjustment data comprises data based on established data concerning Earth's orbital mechanics and known relativistic effects, and are set in accordance with an orbital position of the Earth, or a date (which corresponds to an orbital position). This ensures that the adjustments to the frequency of the quartz oscillator 108 in the system 100 reflect relativistic variations throughout the anomalistic year. The adjustment data are used to determine the desired setpoints for the operation of the system 100 at different days throughout the anomalistic year. In alternative embodiments, rather than storing this information onboard, the system 100 may include a communications module for receiving the current adjustment data. The communications module can provide updated adjustments, ensuring the system remains accurate in response to the latest orbital and relativistic data. Additionally or alternatively, the system 100 may be equipped with the capability to dynamically calculate these values. The calculations may be performed in real time. This feature allows the system to adapt to current gravitational and relativistic conditions, providing even more precise timekeeping by continuously updating its adjustments based on real-time data.

[0116] The controller 104 is configured for generating adjustment signals for adjusting the system frequency based on the aforementioned setpoint. The controller 104 is configured to calculate an error between an actual output frequency of the quartz oscillator 108 (as measured by a monitoring module 106) and the desired setpoint as determined from the adjustment data 102. This error calculation may be done continuously.

[0117] The controller 104 is configured to execute control algorithm(s) to analyse the discrepancy between the actual ticking rate (i.e., output frequency) of the quartz oscillator 108 and the desired setpoint based on the adjustment data. The control algorithm may be configured to analyse the discrepancy to obtain different characteristics of the discrepancy, including but not limited to the magnitude of discrepancy, the sign of the discrepancy. The algorithm may be configured to calculate the magnitude and direction of adjustment needed to minimize this error using this information. The control algorithm may also be configured to obtain further characteristics such as a rate of change in the output frequency, or a rate of change in the discrepancy relative to the set points.

[0118] The analysis implemented by the control algorithm may take into account environmental conditions, or historical data to predict and pre-emptively correct future discrepancies. The adjustment could involve increasing the frequency if it is found to be lower than the desired setpoint, decreasing it if it is higher, or making more complex adjustments based on the nature of the discrepancy. For example, if temperature fluctuations are causing periodic variations in frequency, the algorithm might adjust the temperature compensation settings. If gravitational influences are detected, it might apply corrections based on the predicted gravitational impact. Additionally, if long-term aging effects are identified, the algorithm could implement gradual compensations to counteract these changes. Furthermore, the algorithm employed by controller 104 may be adaptive. It may be configured to learn from past adjustments and improve its accuracy over time, ensuring that the system becomes more efficient and precise in maintaining the oscillator's frequency at the desired setpoint.

[0119] Figure 5 depicts an embodiment of the controller 104. Algorithmic or processing modules provided by controller 104 may be implemented by a microcontroller or a digital controller with processing capabilities. The controller 104 is adapted to generate control signals, such as voltage control signals, or precursors thereof, to implement control logic and setpoint adjustments. It may provide control signals to external circuitries for generating the required voltages, or the controller 104 may be provided in the same module as the required circuitries.

[0120] In this embodiment, the controller 104 includes a setpoint frequency determination module 112, configured to determine the setpoint frequency for the system on the basis of at least the adjustment data 102. A Phase-Locked Loop (PLL) 114 is provided to synchronize the frequency of the quartz oscillator 108 with the setpoint frequency. That is, the reference frequency used by the PLL will be based on the setpoint frequency. The PLL may be implemented as a PLL circuit. It may include a phase detector, loop filter, and Voltage- Controlled Oscillator (VCO).

[0121] For example, when the PLL detects a phase discrepancy between the oscillator's frequency and the reference frequency for the PLL, it generates an error signal. This error signal is proportional to the difference in phase and is used by the control algorithm to adjust the oscillator's frequency. The adaptive nature of the control algorithm, combined with the precision of the PLL, help to align the quartz oscillator's frequency with the setpoint, thus helping to minimize errors and enhance the overall stability and accuracy of the system, and maintaining a frequency that is more in line with atomic time standards.

[0122] In some embodiments, the system 100 includes a frequency synthesizer 116, which may be located as part of the controller 104 as shown in Figure 5. However it may be separate to the controller 104 in other embodiments. It is configured to synthesize a reference frequency signal for the PLL The reference frequency signal is used by the Phase-Locked Loop (PLL) to compare with the system’s current output frequency and determine a frequency error.

[0123] The controller 104 further includes an adjustment module 118. The adjustment module 118 is configured to generate a feedback adjustment signal. The adjustment module 118 includes, or provides the feedback adjustment signal to, circuitry for translating the feedback adjustment signals into voltage-controlled oscillator (VCO) adjustments required by the VCO within the PLL circuit. For example, if the electronic circuit's output frequency becomes out of phase with the frequency synthesized based on information taking into account relativistic and gravitational variations, this is detected by the PLL 114 and the adjustment module 118 modulates the VCO signal so as to maintain frequency alignment. This fine-tunes the system’s output frequency, ensuring it stays aligned with the synthesized reference frequency and maintains the desired ticking rate with a precision akin to atomic time standards. The quartz oscillator 108 (interchangeably referred to as a quartz oscillator or a quartz crystal oscillator circuit, without departing from its meaning or scope), may be a temperature-compensated quartz crystal oscillator (TCXOs) or oven-controlled crystal oscillator (OCXOs), to provide the best stability and thus accuracy, under different environmental conditions such as varying temperatures. However other types of oscillators may be used.

[0124] Referring again to Figure 4, the monitoring module 106 is configured to measure and monitor a frequency of the quartz crystal oscillator 108. The monitoring module 106 comprises measurement components to ensure the real-time operational integrity of the quartz oscillator 108. These may include a frequency counter to monitor the frequency stability, or it may receive a phase detector output from the phase detector as part of the PLL. The components may include temperature sensors, in embodiments using temperature- compensated or oven-controlled oscillators. Voltage and current sensors may be provided to maintain oversight of power supply conditions. It may include a data acquisition system (DAQ) to facilitate accurate and real-time data capture from the quartz oscillator 108. The DAQ converts analogue signals from the oscillator into digital data, which is processed and transmitted to the controller 104. This monitoring and feedback within the control system enables dynamic adjustments to the oscillator's frequency, to maintain alignment with pre- determined setpoints for optimal timekeeping accuracy. The monitoring may be done continuously to provide real-time data on the quartz oscillator's performance. This information enables the control system to dynamically adjust the electronic circuit's frequency. The monitoring system 106 may be further configured to monitor the stability of the quartz crystal oscillator 108 by assessing whether the frequency values are stable. For example, the frequency may be considered stable, if it stays within a particular range. It may need to stay within the range for at least a minimum percentage of the time, or all the time. This can provide real-time data on the clock’s actual performance.

[0125] The monitoring system may be further configured to measure the resonant frequency of the quartz crystal oscillator 108 through a frequency counter mechanism. As will be explained below with reference to Figure 6, this may be used, in conjunction with adjustment data, to determine the system’s setpoint frequency. The frequency counter determines the number of oscillations (or "ticks") generated by the quartz crystal within a given timeframe. Preferably, the frequency counter utilizes the system's electronic circuit output frequency (i.e., the system output frequency) as its base frequency for measurement, rather than the internal quartz usually included in an available frequency counter. A typical frequency counter would be expected to also suffer from gravitational effects of a typical quartz oscillator. Therefore, configuring the frequency counter to count the “ticks” with the system’s output frequency, which is being aligned with the determined setpoint as described above, as the baseline frequency for measuring the “ticks”, will help to mitigate or avoid these effects. This approach also helps to align the measurements with the expected atomic time standards. The baseline frequency may be updated regularly or irregularly, where the updating is performed based on the most recent output frequency.

[0126] Variations resulting from the Earth’s orbit around the Sun or the Moon’s orbit around Earth can impact the crystal’s resonant frequency. This characteristic means that both the quartz crystal and the electronic circuit in the oscillator are susceptible to these gravitational variations. The inventor considers that this susceptibility causes slight changes in quartz crystal frequency and phase as perceived by the electronic circuit. Therefore, adjustments are required based on, at least, one or more of the current date, the orbital position of the Moon, the orbital position of the Earth, and the latitude at which the clock is positioned, as gravitational effects can vary with latitude. The controller may be designed to daily adjust the circuit frequency by a pre-calculated amount (e.g., by reading the pre-stored or dynamically calculated adjustment data 102), ensuring accurate compensation for Earth’s time dilation and precise timekeeping.

[0127] The goal of the feedback included in the system 100 is to maintain an accurate resonant frequency of the quartz. The challenge lies in adjusting the circuit to account for the true length of a unit of time (such as a second), ensuring the resonant frequency is counted correctly. This is where the setpoint frequency comes into play. It is a pre-calculated frequency adjustment that offsets the current frequency, effectively aligning the output circuit with atomic time as closely as possible. Gravitational changes, Earth's orbital position, latitude, time of day, and the duration for which the clock has been energized all affect the quartz crystal's resonant frequency, leading to discrepancies between the measured frequency and the desired setpoint. The clock determines the expected amount of change to the quartz frequency based on one or more of these factors. Any deviations from the expected changes signal that other factors, such as aging, temperature, or elevation, may be involved. Therefore, the control system 104 adjusts the circuit frequency to compensate for these variations. For example, the system may output the required VCO signal to correct the electronic circuit's frequency based on the detected changes in the quartz frequency due to gravitational effects and other environmental influences. This approach further ensures that the system maintains the output frequency at the determined setpoint, effectively accounting for the apparent frequency deviation of the quartz as perceived by the electronic circuitry. Updates to the baseline frequency based on recent output frequency measurements help to maintain precise timekeeping despite the quartz crystal's natural frequency changes.

[0128] Adjusting the output circuit frequency to account for the known effects of gravitational dynamics ensures that a clock or timer which uses the oscillator system 100 measures time accurately within the clock or timer’s own frame of reference. The electronic circuit perceives the variations in the quartz crystal’s resonant frequency caused by gravitation changes due to the Earth’s orbit. The feedback loop adjusts the circuit frequency accordingly. Calculations show that Earth's orbital dynamics increase the quartz's frequency during the first half of the year and decrease it during the second half. Furthermore, due to special and general relativity, an atomic clock on Earth relative to an observer in the ephemerides in a non-accelerated frame will run slower in the first half of the year and faster in the second half. This difference exacerbates the quartz clock error, but the monitoring system is designed to bring the quartz frequency back in line as nearly as possible. For instance, if gravitational effects cause an increase in the quartz crystal’s resonant frequency, the feedback system lowers the circuit frequency to maintain alignment with an atomic clock’s frequency. Conversely, if the electronic circuit detects a decrease in the resonant frequency of the crystal due to other environmental influences such as temperature or elevation, it adjusts the circuit frequency upward to compensate. This continuous correction process aligns the clock’s ticking rate with the desired setpoint, ensuring accuracy in the presence of gravitational and other environmental effects, thereby maintaining synchronicity with atomic clock frequencies.

[0129] As explained above, the inventor has designed the oscillator system 100 by considering the effects of gravitational changes on the quartz resonant frequency. Adjusting the output circuit frequency to match the frequency that an observer in the ephemerides, in a non-accelerated frame, would perceive for an atomic clock. By understanding these influences, we can adjust the circuit frequency up or down to match our setpoint frequency, aligning it as closely as possible to that of an atomic clock.

[0130] Continuous monitoring and feedback provided by embodiments of the system allows a dynamic adjustment to be made. This can help to result in a smooth transition between setpoint changes and maintaining the desired ticking rate with high precision. Further, the dynamic adjustments may be set to gradually increase or decrease the measured frequency of the quartz oscillator over specified time periods. One way of implementing is to limit the rate of increase or decrease. The prestored adjustment data may also be pre-configured so as to implement a smooth transition between setpoint changes, e.g., by setting a maximum rate of change between different set points.

[0131] An example control process 400 implemented by a controller 104 incorporating a phase- locked loop (PLL) is described with reference to Figure 7. If the current setpoint frequency (which accounts for the adjustment for gravitational effects) is lower than the natural resonance frequency of the quartz crystal (as measured by the monitoring module 106), then the PLL will work to maintain the system’s output frequency at that lower setpoint. In this circumstance, it works in the following manner:

[0132] -Quartz frequency determination: At step 202, the system determines the resonant frequency of the quartz crystal (also known as the fundamental frequency) utilised within the quartz oscillator. To ensure the high resolution and sensitivity required for detecting subtle variations due to gravitational effects (and preferably, other environmental influences), the system may employ the third overtone frequency of the quartz or higher. This overtone frequency is a higher harmonic of the fundamental frequency (e.g., 3x) and is applied to the circuit’s output frequency to enhance the measurement precision. By using the output frequency’s overtone frequency as the baseline, the system achieves a higher precision in measuring and adjusting the resonant frequency of the quartz crystal, to help accurately determine the fundamental frequency.

[0133] Frequency measurement'. The frequency measurement is carried out using the current adjusted circuit frequency, i.e., the current output frequency of the quartz oscillator circuit 108 (see Fig. 4) as measured at the monitoring system 106 is used as the base frequency. In the processing flow in Figure 7, the “adjustment” here occurs at step 214, and the adjustment is determined at step 210 by comparing the determined setpoint frequency of step 206 to the current output frequency. Therefore, where the term “adjusted circuit frequency” is used refers to the output frequency that has been aligned with the setpoint frequency based on the adjustments made in step 214.

[0134] Unlike typical systems, the configuration of the present system does not utilize a separate quartz-based frequency counter to measure the resonant frequency and hence overtone frequency. Rather, the adjusted circuit frequency will be used as the base frequency for a frequency counter provided for measuring the resonant frequency. The currently available adjusted circuit frequency will be used as the base frequency for the measurement, e.g., at step 202. This is advantageous because unlike a frequency counter based on quartz which would itself be susceptible to gravitational acceleration, leading to compounded errors, the adjusted circuit frequency provides a more stable reference, ensuring that measurements reflect true changes in the quartz oscillator due to Earth's orbital dynamics without interference from similar gravitational biases.

[0135] The resolution of frequency measurements generally depends on the stability and quality of the quartz oscillator, as well as the precision of the frequency counter or measurement system employed. Using a higher overtone improves the signal-to-noise ratio and may enhance resolution for detecting any deviations to the setpoint because higher frequencies can be measured more precisely under the same conditions. Higher frequencies provide higher temporal precision because the period of the oscillation (1 / f) is smaller. This means that any given time interval contains more cycles of the signal, allowing for finer measurement and detection of small frequency changes.

[0136] The accuracy of the measurement of the fundamental or overtone frequency may be dependent on various factors, for example one or more of the following. A factor is the oscillator Stability and Quality. High-quality oscillators with good stability (low phase noise and jitter) will inherently offer better resolution. The stability is often characterized by the oscillator’s Allan deviation, which indicates how stable the frequency is over a certain period. Another factor is the measurement duration. The resolution of frequency measurements also depends on the measurement integration time, which can be varied by the user or pre-set to a setting. Longer integration times can improve resolution by averaging out noise. Another factor is the measurement equipment sensitivity. The precision of the frequency counter or measurement device directly affects the resolution. Modern frequency counters can achieve very high resolution under optimal conditions. A typical advanced frequency counter can resolve changes in frequency to within a small fraction of a hertz, often down to microhertz (10‘6Hz) under stable conditions with sufficient measurement time. For a 98304 Hz signal (third overtone of 32768 Hz), assuming high-quality measurement equipment and conditions, achieving a resolution of 0.00001 Hz (10 microhertz) is realistic. This level of resolution allows for detecting very minute changes in the oscillator frequency, which can be crucial for applications sensitive to gravitational effects or other minute environmental influences. - Referring back to Figure 7, the setpoint frequency is determined (step 206). The setpoint frequency may be pre-calculated, stored in the system memory, or downloaded from another source, as mentioned before. It may be further adjusted on the basis of other factors such as crystal aging, or on the basis of external data as discussed in relation to the synchronisation module. The system stores these pre-calculated setpoint frequencies within the adjustment data module 102.

[0137] - PLL Frequency Lock (step 208): The PLL locks onto the setpoint frequency as the reference, rather than directly locking onto the quartz oscillator's natural resonant frequency. A reference signal at the setpoint frequency may be generated by a frequency synthesizer and provided to the PLL for this purpose.

[0138] - Provide the current oscillator frequency to PLL (step 210): the PLL takes the current oscillator frequency as an input and compares with the reference frequency. Both the input variable (oscillator frequency) and the reference variable (reference frequency) may be provided to the PLL at the same time, or the PLL may lock onto the oscillator frequency first. That is, the order for steps 208 and 210 as depicted in Figure 7 may be changed.

[0139] - The PLL determines whether the oscillator frequency matches the reference frequency (box 212). The match could mean a match with a tolerance level or a threshold.

[0140] - Voltage-controlled oscillator (VCO) adjustment: If there is a match 204 between the frequencies, the system goes back to step 202. If the frequencies do not match, then a control signal to instruct the VCO to make an adjustment to the voltage is provided (step 214). The PLL adjusts the voltage applied to the VCO at step 216 to fine-tune its achieved output frequency in alignment with the reference frequency of the synthesized reference signal, rather than directly matching the quartz crystal's resonance. Once the voltage adjustment is applied, the system loops back to again (i.e. to box 212) to compare the adjusted oscillator frequency with the setpoint frequency. This process allows the system to maintain accurate timekeeping by dynamically adapting to relativistic and gravitational effects. To implement this, the system compares the reference frequency with the current system output frequency (212), and based on the comparison generates a VCO adjustment signal (214). The VCO adjustment signal is provided to the quartz oscillator circuitry for dynamic real-time adjustment (216).

[0141] - system synchronisation check: the system 100 continues to monitor the system output frequency and compares it with the desired frequency (212) to see whether the VCO adjustment has resulted in the output frequency aligning with the desired setpoint frequency which is used to generate the reference frequency. If there is an alignment, then the system operation returns to step 202 and continues to monitor the output frequency. If there is no alignment, the system again instructs the adjustment module to make the VCO adjustment signal (212). Here, an alignment between the system output frequency and the reference frequency may mean that the output frequency is within a predefined range from the reference frequency. The range may be tuneable to define the amount of deviation that can be tolerated. E.g., if it is tuned to zero-range this means no deviation is tolerated.

[0142] An example of the application of the aforementioned process is discussed below. In the discussed example the setpoint is slightly lower than the quartz resonance frequency.

[0143] - Phase Difference detection (i.e. comparison of frequencies; refer to step 212 of Figure 7): The PLL may compare the reference and oscillator frequencies by determining an amount of phase difference between the synthesized reference signal and the oscillator signal. The oscillator frequency may be taken as the VCO output frequency from the monitoring module 106.

[0144] - Error Signal Generation (refer to step 214 of Figure 7): a detection of a sufficient amount of phase difference may indicate that the oscillator and reference frequencies do not match. The controller 104 generates an error signal based on this phase difference. If the VCO output frequency is too high, the error signal will indicate that the output frequency needs to be decreased.

[0145] - Feedback Adjustment (refer to step 216 of Figure 7): The error signal is fed through the loop filter of the PLL and used to adjust the voltage applied to the VCO. In this example, the error signal indicates that the frequency is too high, the VCO's frequency will decrease in response. Thus the adjustments made to the VCO’s control voltage are made in real time. - Steady-State Operation: As long as a sufficient amount (which could be any non-zero amount) phase difference exists, indicating that oscillator frequency is not at the setpoint, the system will continue to adjust the VCO voltage, to synchronize it with the setpoint. The PLL will maintain this steady state, effectively locking the VCO's frequency slightly below the natural resonance frequency of the quartz crystal, in this example.

[0146] By operating the PLL in this manner, it is possible to effectively offset the errors resulting from the difference resulting from the gravitational effects on the natural resonance frequency of the quartz crystal of the oscillator and on the electronics of the oscillator, creating a stable output frequency that is set to the desired setpoint frequency. The adjustments may be performed continuously, daily, or at a schedule which may be determined by the pre-stored adjustment data, or may be separately tuned by the user. This approach allows a fine-tuning and control of the frequency output of the oscillator system, even if it means operating it at a frequency slightly diverging from its natural resonance frequency. This enables adjustments to be made to counteract the effects of gravitational acceleration.

[0147] In a clock system which comprises the oscillator system 100 as described above, the clock’s ticking rate is controlled by the frequency of the oscillator system 100. Therefore, the control system feedback loop 110 is responsible for maintaining the clock's accuracy and synchronisation with the desired setpoint, particularly when compensating for gravitational effects. The feedback loop 110 ensures that the clock's ticking rate remains stable and aligned with the reference. It allows for dynamic frequency adjustments in response to the pre-determined changing setpoints over time, accommodating the gravitational effects that influence the quartz crystals and the electronic circuitry.

[0148] In some embodiments, the controller may be configured to allow different amounts of deviation from the set point variable, depending on the precision requirements of the application. The requirements may be user specified, e.g., smaller deviations may be allowed for applications requiring high accuracy clocks. This may be set via the user interface. In the described and other embodiments, the controller for the oscillator system 100 may be configured to provide one or more optional features. Examples include but are not limited to:

[0149] Data Logging and Analysis, to record historical performance data for analysis and optimization.

[0150] User Security measures to restrict unauthorized access to control functions and data.

[0151] Remote Access option for remote access and control of the system.

[0152] Calibration and Maintenance provisions to ensure long-term accuracy and reliability. These functions may be accessed remotely if the remote access option is available.

[0153] Data storage on or accessible by the controller, for storing data regarding system architecture, control algorithms, or user instructions. The controller may enable these to be navigated and displayed on a user interface.

[0154] Optionally, the controller may be configured to provide a user interface which may be displayable on an onboard display device, or on a display area of a separate device (such as a user mobile device or a remote computer) which is paired with the controller or otherwise in wireless or wired communication therewith, to facilitate a monitoring and / or controlling of the system 100. Additionally or alternatively, a user interface may be provided by a remote system which has access to the system 100, for a user to interact with the system 100. As non-limiting examples, the interface may enable a user to do one or more of: view a realtime clock performance data, perform system calibration, initiate manual adjustments or corrections, change environmental compensation settings, make time zone and / or daylight saving adjustments, change or set alarm settings, input data logging preferences, enter or change access control and security settings, enter or change network and connectivity settings, configure software updates and system upgrades or access historical data for analysis.

[0155] As non-limiting examples, one or more of the below may be enabled via the user interface: manual frequency adjustments, whereby users adjust the frequency directly, temporarily overriding automatic adjustments to test specific conditions or hypotheses in experimental setups. system calibration, which may be user-initiated, to ensure the system's sensors and frequency counters are accurately measuring and responding to the quartz oscillator's behaviour. environmental compensation settings, in embodiments which account for environmental factors such as temperature, humidity, or pressure, may be adjustable by users. time zone and daylight saving adjustments: For embodiments that also serve practical timekeeping purposes, users may adjust settings to account for time zone changes or daylight saving time adjustments. alarm settings: In some applications, the user interface might allow setting alarms or notifications based on time or performance thresholds, alerting users to specific events or conditions. data logging preferences: Users could adjust settings related to data collection, such as the frequency of logging, specific data points to emphasize, or conditions under which to trigger more detailed logging. feedback loop parameters: Advanced users or system administrators might access settings related to the feedback loop's operation, such as gain levels, thresholds for making adjustments, or the sensitivity of the system to phase discrepancies. access control and security settings: In cases where the clock system is part of a larger, sensitive experimental setup, users may need to adjust access control settings, managing who can make adjustments or access the data. network and connectivity settings: For systems integrated into larger networks or requiring remote access, users may need to configure network settings, manage connections to other devices, or troubleshoot connectivity issues. software updates and system upgrades: The interface might provide options for initiating software updates or system upgrades, ensuring the clock system remains current with the latest features and improvements.

[0156] Access to the above-mentioned adjustments and settings allow users to fine-tune the clock system's operation, adapt it to a wide range of experimental conditions, and ensure it meets the specific needs of their research or application. However these are optional features and may be included as required for the particular implementation or application.

[0157] The user interface may also enable access to analysis performed on historical data, or for users to query historical data for analysis. As non-limiting examples, the historical data may include: records of past frequency adjustments made by the controller to align the system with desired setpoints, which may include both automatic adjustments and any manual corrections initiated by the user; setpoint variation data in relation to how the setpoints themselves have changed over time; system performance metrics such as metrics in relation to the accuracy of timekeeping, phase alignment discrepancies detected by the monitoring system, and any error signals generated by the PLL; historical environmental condition data, which may more specifically include data on environmental conditions that could affect the system's performance, such as temperature variations if the system uses temperature- compensated or oven-controlled oscillators; historical logs of user interactions with the system, such as manual adjustments or corrections made through the user interface, which can provide insights into how often and in what ways users need to intervene in the system's operation; error logs to record any errors or malfunctions detected within the system, providing critical information for troubleshooting, and improving system design.

[0158] Including such historical data in the user interface would allow users to not only monitor the system's current performance but also analyse trends, identify potential issues before they become problematic, and understand the long-term reliability and accuracy of the clock system. For example:

[0159] Verifying Relativistic Predictions: The historical data on frequency adjustments and setpoint variations could be used to verify predictions made by relativity about the effects of gravitational fields (General Relativity) or and relative motion (Special Relativity). By comparing the expected setpoints (which account for relativistic effects) with the actual adjustments made, researchers can test the accuracy of relativistic models in predicting the behaviour of timekeeping systems in different gravitational potentials or velocities.

[0160] Gravitational Effects Analysis: Data on how the setpoints change over time as the Earth moves in its orbit can provide insights into the gravitational effects on timekeeping. This is particularly relevant for General Relativity, which predicts that time passes at different rates in different gravitational potentials. Historical data showing the correlation between the Earth's position in its orbit (and hence its gravitational potential) and the required adjustments to maintain accurate timekeeping can serve as empirical evidence of these effects.

[0161] Environmental Conditions and Relativity: If the system collects data on environmental conditions, such as temperature, and correlates these with the performance of the clock, it could help isolate the relativistic effects from other variables. This is crucial for experiments aiming to measure the pure effects of relativity on timekeeping, free from environmental influences.

[0162] Long-term Trends and Anomalies: By analysing trends and anomalies in historical data, researchers can investigate if there are any long-term effects of relativity that were not previously accounted for, or if there are any deviations from expected relativistic behaviour. This could lead to refinements in the theoretical models of relativity or even to new discoveries about the nature of time and space.

[0163] Correlation with Other Relativistic Phenomena: Historical data from the clock system could be compared with data from other experiments or observations related to relativity, such as gravitational waves detection or the behaviour of clocks in satellites orbiting the Earth. This can help validate the universality of relativistic effects across different systems and scales.

[0164] It will be understood that the components, functionality, and performance criteria for a Control System Feedback Loop will be tailored to the specific requirements of the clock system depending on the application. The actual implementation details and hardware / software choices will depend on the application and system design preferences.

[0165] Clock systems with the feedback control design as shown in Figure 4 may be initialized with preset adjustment data. It is possible to further calibrate the system to achieve even better accuracy than conventional quartz oscillator clocks, possibly approaching the accuracy of some atomic clocks by effectively compensating for the gravitational effects resulting from Earth's orbit and the Moon's orbit around Earth, all without the significant expense associated with atomic clocks. This capability is particularly valuable in scientific experiments involving measurements of radioactive isotope decay rates or scenarios where Earth's gravitational effects are a critical consideration. It also offers advantages for Doppler tracking of space vehicles, such as NASA's Pioneer 10 and 11 spacecraft, by accommodating the unique relativistic and gravitational conditions encountered in space. While the onboard clocks of such spacecraft experience different relativistic and gravitational accelerations, the spirit of the invention remains the same: to provide precise timekeeping by dynamically adjusting to these unique conditions. The system is designed to be adaptable, allowing for modifications to setpoints and calculations that accurately account for the specific challenges of space navigation. Such flexibility ensures that the oscillator system can maintain accurate timekeeping, essential for the successful operation of space missions.

[0166] In the embodiments, the PLL in the feedback loop may be included as a part of the controller 104 as shown in Figure 5, or provided at an output side of the controller 104 where it is connected to the quartz oscillator 108.

[0167] For example, the embodiments may be modified to integrate additional frequency synchronisation. An optional synchronisation mechanism can be integrated into the system 100, without necessarily otherwise changing the current circuit design. In one implementation, the system 100 may be configured to have data communication capabilities, to download current frequencies from trusted time references (e.g., an official standard time source such as times provided by the National Institute of Standards and Technology “NIST”, or other atomic clocks) via internet time servers and compare them to the precalculated values to make adjustments for gravitational effects and other relevant factors.

[0168] A potential advantage of the aforementioned synchronisation is the potential to adjust the system to account for factors beyond gravitational effects that may cause an apparent variation in the crystal’s resonant frequency, such as crystal aging. While atomic signals from sources like GPS or NIST provide a precise reference for timekeeping, they do not directly measure the effects of crystal ageing or environmental factors on the quartz crystal. However, by continuously synchronizing the system with an atomic reference, any drift in the quartz oscillator's frequency due to crystal ageing or other factors can be detected and corrected for, provided the apparent resonant frequency of the quartz is measured. The system adjusts the setpoint frequency to compensate for these variations, improving the alignment between the oscillator and the atomic time standard.

[0169] It is however possible to compensating for crystal ageing without the GPS signal. In some embodiments, this may be done using algorithmic models for the crystal aging. In one example, the model may be a linear model, which models the crystal aging as a steady linear change over time. The model may assume the greatest change during crystal aging will occur in the first year. Specifically, the model assumes that the frequency change is largest in the first year and then decreases linearly each subsequent year. For example, if the crystal ages by 10 ppm (parts per million) in the first year, it may age by 6 ppm in the second year, 3 ppm in the third year, and 1 ppm in the fourth year, with the amount of aging decreasing each year. The adjustment may be performed as yearly calibrations of the clock. This may be implemented by the controller 104 and does not necessarily need to be a separate hardware module.

[0170] Figure 6 illustrates a synchronisation process 500 for adjusting the quartz frequency parameter on the basis of GPS or NIST data, in accordance with at least some of the embodiments. The synchronisation process may be implemented by a synchronisation module in the controller 104. This process may, for example, be invoked at step 206 in the processed depicted in Figure 7. At step 502, the system determines an external time information, from an external time source which utilises atomic frequency. In some embodiments this may involve reading or receiving an external time signal to determine a time information. As two examples, the external time signal may be a GPS satellite time signal, or it may be a time frequency from NIST. GPS signals are embedded with accurate time information from onboard atomic clocks. If required, the received time signal may be decoded to extract a time information, to determine the present time of the atomic clock onboard the satellite. NIST provides a time standard that is accessible through internet time servers. The NIST time signal may be obtained by syncing with the internet time server.

[0171] The system obtains at least two samples of external time as reported by the external time source, per above. The system also reads the internal time reported by the system’s internal clock, whenever the samples of the reported external time are obtained.

[0172] At step 504, external time information (tre / ) corresponding to the elapsed time between the samples reported by the external time source, is compared with the internal time information (tsys) corresponding to the elapsed time between the samples reported by the system 100, to determine the discrepancy At as follows:

[0173] At=tref - tsys

[0174] At step 506, the system calculates the frequency offset A / which is required to be made to the current frequency of the system fsys, on the basis of the time discrepancy At, in order to bring the internal time into alignment with the external time. A / may be calculated as follows: where tmeasurementis the time over which the measurement was taken, tmeasurement may be reported by the external clock (i.e. tref) or may be reported by the internal clock (i.e., tsys), depending on implementation (e.g., the time between synchronisation attempts).

[0175] At step 508, A / is used to adjust the current set point frequency for the system. For example, this may be as follows: In the above, represents the current setpoint frequency, which is the frequency our system is currently aiming to achieve, based on pre-stored adjustment data and the measured resonant frequency of the quartz crystal. The A represents the frequency adjustment needed based on the comparison with an external time reference like NIST or GPS, in order to obtain the new setpoint forthe system to align to.

[0176] The above equation applies a simplified model which assumes a linear behaviour of the crystal over the measurement interval. In practice, the system might implement more sophisticated algorithms to account for the non-linearities and potential noise in the measurements, especially if the measurements are being made over more extended periods or with varying environmental conditions.

[0177] At step 510, the system applies the adjustment by setting as current setpoint frequency i e

[0178] Once the setpoint frequency is updated, the controller 104 can use the updated setpoint to generate control signals needed to adjust the system's output frequency.

[0179] By adding this synchronisation module and associated features to the existing clock design, it can enhance the clock's accuracy and maintain synchronisation with highly precise time references without requiring significant changes to the core circuit design. This approach leverages the stable quartz crystal oscillator while benefiting from periodic adjustments based on external atomic clock references.

[0180] By combining the inherent stability of quartz crystal oscillators with the ability to periodically align the clock's frequency to atomic time references, a high level of accuracy can be achieved. This approach can be especially valuable in scenarios where atomic clocks are not practical or cost-effective but where precise timekeeping is still crucial.

[0181] The approach represents a practical and cost-effective solution for achieving atomic clocklike precision in various applications, from scientific experiments to telecommunications and navigation systems. Dynamic Adjustment

[0182] As outlined with reference to the system 100 of Figure 4, according to the present invention a quartz oscillating system may be equipped with the capability to dynamically calculate the adjustment data 102. The calculations may be performed in real time. This feature allows the system to adapt to current acceleration conditions, providing even more precise timekeeping by continuously updating its adjustment based on real-time data.

[0183] In one example, this real time data can be calculated within the system, as detailed with reference to the embodiment of Figure 8. The quartz oscillator system 800 of Figure 8 uses the same underlying concept as the embodiment of Figure 4, that is, correcting the oscillator / circuit frequency which has drifted due to acceleration.

[0184] Acceleration, as referred to in the embodiments of Figures 8-11, denotes any measurable net vector acceleration (expressed in m / s2) experienced by the quartz oscillator relative to a local inertial frame. Contributing aspects to the net acceleration may include, for example, one or more of the following:

[0185] • effective acceleration, e.g., gravitational acceleration due to planetary bodies (e.g., Earth’s, Moon’s, Sun’s gravity);

[0186] • Apparent accelerations arising in non-inertial frames, such as centrifugal and Coriolis effects resulting from planetary rotation. These effects may be modelled as effective accelerations when dealing with the local rotating frame (e.g., Earth’s surface), where the oscillator may be located;

[0187] • applied (mechanical) acceleration due to vehicle motion, thrust, vibration, manoeuvring, etc; and

[0188] • orbital or geodesic curvature-induced accelerations, such as those caused by the spacecraft’s motion in curved spacetime.

[0189] Quartz oscillators are typically manufactured to be relative to the local inertial frame of Earth, and as such are calibrated at static Earth gravity (denoted by standard gravity constant g = 9.81 m / s2), wherein the acceleration acts along the axis of highest acceleration sensitivity. This axis is defined by the crystal’s cut and mount, and is typically normal to the crystal cut and mounting plane. Therefore, their sensitivity to acceleration reflects changes from this baseline acceleration of 1g. That is, a stationary oscillator on Earth is already under constant 1g, and therefore the resonant frequency of the oscillator is defined under this condition, and the frequency shift is considered zeroed. Only deviations (positive or negative) from this baseline acceleration contribute to any frequency shifts experienced by the system. That is, when the system experiences 1g of acceleration (along the axis of highest sensitivity), it is defined as under conditions of zero acceleration.

[0190] Figure 8 illustrates an embodiment of a dual quartz oscillator system 800 according to the present disclosure. As quartz oscillators are often used in timekeeping (i.e., “clock”) systems where the oscillator’s output frequency is used to keep time, the dual quartz oscillator system 800 can also be considered a clock feedback system 800 designed to at least partially mitigate the issues experienced in conventional quartz oscillators clocks when undergoing changes in acceleration.

[0191] The system 800 comprises a first oscillator 808 and a second oscillator 809. The first and second oscillators 808, 809 are configured to have different sensitivities to accelerations, expressed using known sensitivity factors T i, H, respectively. In this example, the second quartz crystal oscillator 809 has a lower sensitivity to acceleration and is more stable than the first quartz crystal oscillator 808.

[0192] The system 800 comprises a mixer 802 configured to receive signals from the oscillator circuits 808, 809, and generate an output at the beat frequency fbeat, being the difference between the oscillator frequencies fl, fl, of the oscillators 808, 809. The monitoring system 806 is configured to monitor the output from the mixer 802 and measure the beat frequency, which will be used as the “ticking rate” for the overall clock system. The signals from the oscillators 808, 809 may pass via another signal processing component before reaching the mixer. Preferably, the beat frequency is continuously measured by the monitoring of the generated signal as the system is subjugated to acceleration.

[0193] The system 800 further comprises a controller 804 configured to compare the current measured beat frequency to a calibrated baseline beat frequency, defined under conditions of zero acceleration. An estimate of the effects of acceleration is determined based on this comparison, using the sensitivity factors (T i, lA) and oscillator frequencies (fi, fl), for the oscillators 808, 809. The information is fed-back to the monitoring system 806. The feedback is conceptually depicted by box 810 represented in dashed lines in Figure 8. The feedback may be used to help correct frequency shifts of the beat frequency (Afteai) that occur as a result of acceleration or other factors. The parameters, g, T 1, H, fi, f> , and Afz>ea / can be used to calculate the acceleration a, as

[0194] The controller 804 may determine the required correction to maintain timing stability using the beat frequency shift. To apply this correction, the controller dynamically adjusts the timing reference of a frequency counter within the monitoring system 806 such that the measured beat frequency no longer appears shifted from the baseline frequency. This process forms a closed feedback loop 810 between the controller 804 and monitoring system 806, which dynamically maintains synchronisation and long-term frequency stability. This feedback loop mitigates environmental influences, such as Earth’s orbital dynamics, ensuring long-term precision and stability. The feedback preferably occurs continuously, for the system 800 to automatically adjust its ticking rate in real-time or close to real-time, to optimise accuracy.

[0195] The controller is configured to implement a control algorithm to analyse the beat frequency and determine any deviation from the baseline beat frequency, i.e., the beat frequency shift Afieat The control algorithm may be configured to analyse Af / ,ra / to obtain one or more different characteristics of Af / )ra / , including but not limited to the magnitude and the sign. The control algorithm may also be configured to obtain further characteristics such as rate of change in the output frequency, or a rate of change in Afz>ea / relative to the set points.

[0196] The adjustment made to the ticking rate for the frequency counter (or “counter frequency”, for brevity) used in the monitoring system could involve decreasing the counter frequency of the monitoring system if it is found that the current beat frequency is lower than the baseline bead frequency, increasing it if it is higher, or making more complex adjustments based on the nature of the discrepancy represented by Afteat For example, the analysis implemented by the control algorithm may take into account environmental conditions, or historical data to predict and pre-emptively correct future discrepancies. For example, if temperature fluctuations are causing periodic variations in frequency, the algorithm might adjust the temperature compensation settings. Additionally, if long-term aging effects are identified, the algorithm could implement gradual compensations to counteract these changes.

[0197] Furthermore, the algorithm employed by controller 804 may be adaptive. It may be configured to learn from past adjustments and improve its accuracy over time, ensuring that the system becomes more efficient and precise in maintaining the oscillator's frequency at the desired setpoint.

[0198] Referring again to Figure 8, the oscillator circuit 808, being more sensitive to acceleration, serves to produce the acceleration-sensitive signal in the system. It is configured to exhibit a measurable frequency shift in response to acceleration in order for the system to function. This may be a standard uncompensated quartz oscillator circuit. It may be optionally enhanced with passive temperature compensation (e.g., using specific crystal cuts or analogue shaping circuits) or environmental shielding (e.g., mechanical or thermal insulation) to supress non-acceleration effects such as thermal drift. However, the quartz oscillator circuit 808 utilises no active compensation methods, such as an active temperature compensated quartz oscillators (TCXO) circuit or an oven-controlled quartz oscillator (OCXO) circuit. These active compensation methods are excluded to prevent suppression of frequency shifts within the system, and ensures the oscillator circuit exhibits a measurable frequency shift in response to acceleration, thereby preserving the frequency shift the system is designed to measure. The first, more sensitive oscillator 808 may be designed to exhibit the dominant frequency shift due to its higher acceleration sensitivity factor (T), e.g., T i ~ 10'9. The acceleration-induced frequency shifts in the second, less sensitive oscillator 809 may be an order of magnitude smaller (e.g., H ~ 1 O'10) than that of the first, more sensitive oscillator 808. This stability allows the second oscillator 809 to serve as a reliable reference signal for mixing with the frequency of the first oscillator 808, allowing controller 804 to detect micro-scale accelerations via measured changes to the beat frequency (i.e. beat frequency shift, Aftea / ). Although this shift is an order of magnitude smaller, it is still included in the calculation of net acceleration, as the difference in sensitivity between the two oscillators forms the basis for the beat frequency shift used in the feedback loop. This ensures accurate measurement of both positive and negative accelerations, while minimising signal bias.

[0199] The less sensitive oscillator 809 may be implemented as a temperature-compensated crystal oscillator (TCXO) circuit or oven-controlled crystal oscillator (OCXO) circuit, so that the circuit is minimally affected by environmental changes like temperature and humidity, and mechanical stress. These configurations supress frequency drift through thermal regulation and mechanical isolation, thereby reducing the oscillator circuit’s sensitivity to acceleration.

[0200] The difference in acceleration sensitivity between the oscillators 808, 809 may result from other features related to the mechanical and physical configuration of the quartz crystals, such as crystal cut, mounting design, and any enclosure and environmental compensation. Different cuts (e.g., AT-cut, SC-cut, BT-cut) have varying sensitivities to acceleration, temperature, and stress. The first oscillator 808 may use a quartz cut (e.g., AT or custom high-sensitivity configuration) that is deliberately more responsive to acceleration, for example, yielding a sensitivity factor on the order of 10'9. The second oscillator 809, on the other hand, may use a more stable cut (such as SC-cut or BVA) which has lower sensitivity, for example, yielding a sensitivity on the order of 10'10or less. The first oscillator 808 may use a less mechanically isolated or more acceleration-coupled mount, intentionally exposing it to acceleration-induced stress. The second oscillator 809 may use more robust mechanical isolation, such as vacuum packaging, shock-absorbing materials, or symmetric mounting structures to minimize such coupling. The second oscillator 809 may also utilize an OCXO or TCXO configuration, incorporating temperature control and environmental shielding to maintain long-term frequency stability. The first oscillator 808 typically prioritizes acceleration response over such stabilisation.

[0201] Therefore, while both oscillators 808, 809 may operate at nearly the same base frequency (e.g., 50 MHz), their behaviour under acceleration may differ due to one or more of the above distinctions. This contrast, which may result from the inclusion of thermal or mechanical compensation (or lack of), or a difference in one or more of the above mentioned physical distinctions, allows the system to detect differential shifts and isolate the effects of acceleration.

[0202] In some embodiments, the crystals have difference resonant frequencies, for example, the resonant frequency for each circuit may be carefully tailored during the quartz crystal’s design and cutting phase. For example, if fi is selected to be 50 MHz, and fi is selected as 50.1 MHz, then f2 is 100 kHz higher than fi and a pre-selected beat frequency of 100 kHz is established.

[0203] A non-zero pre-selected or predetermined beat frequency can be considered as the baseline beat frequency. I.e.,

[0204] This baseline beat frequency is defined as the difference in resonant frequencies between the first and second quartz oscillators under zero acceleration. The baseline beat frequency allows the system to track dynamic changes in beat frequency resulting from acceleration- induced frequency shifts in the oscillators. The advantage of a non-zero baseline is that it facilitates signal detection and phase-locking, while allowing both positive and negative shifts to be distinguished relative to the baseline value.

[0205] Shift in Beat Frequency

[0206] As the first and second quartz oscillators 808, 809 experience acceleration, their frequencies shift, with the more sensitive oscillator 808 exhibiting a greater frequency shift than the less sensitive oscillator 809. That is, the amount of change in the frequency of output from the first oscillator 808, Afi, will be greater than the amount of change in the frequency of output from the second oscillator 809, Afi. This alters the difference between the two frequencies resulting in a dynamic beat frequency shift away from the baseline value.

[0207] The frequency shift for each oscillator when experiencing acceleration is according to:

[0208] Wherein the base frequency refers to the resonant frequency of the quartz crystal used in the oscillator. As the baseline beat frequency is attributed to the difference in the oscillator crystals’ cut and structure, it does not change with downstream adjustment to the system’s internal clock, i.e. the ticking rate of the monitoring system 806 as driven by controller 804. In this case, the magnitude of the acceleration-induced frequency shift is directly proportional to this baseline resonant frequency. This shift in beat frequency is measured by the monitoring system 806 and used by the controller 804 to calculate the acceleration and apply corrective feedback. The frequency shifts can be expressed as:

[0209] And since the beat frequency is:

[0210] The current beat frequency becomes:

[0211] The shift in beat frequency (presumed to be due to acceleration), Af / ,ra / can be expressed as:

[0212] AAA-^s ~ (AA -- AA.) Where Af / ,ra / is the net frequency shift in the beat frequency due to acceleration. The system specifically interprets the shift in the beat frequency (Afteaz) as the net result of the frequency changes in both oscillators:

[0213] Afw«f~ Ws - AA) ivnert- aW Because both oscillators respond to the same external acceleration, but with different sensitivities (P) > r2), their differential shift encodes the acceleration directly. Hence, the control system includes both terms when calculating the applied acceleration:

[0214] Therefore, by anti-intuitively accounting for the response to acceleration of the quartz oscillator circuit (Circuit 2) having the less sensitive quartz crystal, the applied acceleration can be calculated with more accuracy, which is important, particularly in high-precision applications such as inertial navigation.

[0215] Notably, the sign of the beat frequency is crucial such that when there is a frequency shift within the system due to external acceleration, the system is able to determine whether the acceleration is in the positive or negative direction, and therefore whether the clock rate of the internal system needs to increase or decrease.

[0216] While there may be other external factors that also cause a frequency shift of the oscillator, e.g. temperature, the calculated acceleration (a) provides a useful proxy for how much the frequency has shifted. The system doesn’t need to distinguish the source of the frequency shift — rather, it uses the observed beat frequency deviation to apply the appropriate correction.

[0217] Signal Amplification

[0218] Before the signals of the oscillators 808, 809 are passed to the mixer 802, they may each optionally pass through a separate signal amplifier in order to improve readability of the amplified signals. In particular, the amplification may be chosen to power match the respective signals of the oscillators 808, 809 when entering the mixer 802. Individual dedicated signal amplifiers may be arranged within each the oscillators 808, 809 respectively, or the oscillators 808, 809 may be arranged to provide their signal into separate channels of a single, dual-channel, independently buffered signal amplifier. There is no strict requirement for both oscillators 808, 809 to have the same amplification factor. However, both outputs should ideally have matched or similar power levels when entering the mixer 802. Imbalance in power levels could cause mixer saturation (if one signal is too strong) and may result in poor conversion efficiency or increased phase noise (if one signal is too weak). In practice, the gain may be tuned individually for each circuit to achieve equal amplitude at the mixer’s 802 inputs.

[0219] Impedance matching ensures maximum signal transfer, prevents signal reflections, and reduces standing wave effects, especially in high-frequency systems. As outlined above, impedance matching can be handled in this circuit via the amplifiers. Alternatively, impedance matching can be handled via external matching networks (if needed). The amplifier may be an RF amplifier, e.g., designed with matching input and output impedance, e.g., 50 ohms which matches the impendence commonly used in standard RF systems. In some cases, a passive matching network, such as an LC (inductor-capacitor) filter or a resistive divider, may be added to fine-tune the match. For example, this may be appropriate if an oscillator or the mixer used in the system has a non-standard impedance, or if the signal levels need additional conditioning before mixing.

[0220] Frequency Step-Up

[0221] In some situations, the oscillators 808, 809 may be configured to implement higher overtone modes of the respective quartz crystals of the oscillators 808 and 809, to amplify the base frequency of the circuit to an overtone frequency. The magnitude of a frequency shift due to external (applied) acceleration is proportional to the oscillator’s baseline frequency for a given acceleration sensitivity factor (T). Therefore, a higher base frequency results in a proportionally larger absolute frequency shift.

[0222] Stepping up the frequency by using an overtone frequency as the baseline — for example, from 50 MHz to 500 MHz — increases the absolute frequency shift resulting from a given acceleration. Since the shift is proportional to the baseline frequency, this effectively amplifies the resultant beat frequency shift. This allows the system to detect small changes over shorter integration periods, which is advantageous for dynamic applications like inertial navigation, where the system tracks rapidly varying accelerations in real time. Furthermore, in applications with high-speed or high-temporal resolution (such as tracking fast-moving objects or compensating for rapidly varying accelerations), stepping up the frequency enables the system to detect and correct frequency drift with greater responsiveness without compromising accuracy and precision.

[0223] In contrast, where accurate clocks are stationary or on Earth’s surface, and not involved with inertial navigation, much longer integration times of hours or days are acceptable and may be beneficial for averaging out noise. Thus, the use of overtone frequencies in such cases may not be necessarily required or desired.

[0224] Alternatively, the frequency of the signal of from the oscillators 808, 809 can be stepped up after being generated, and before entering the mixer 802, without the use of overtone frequencies. This may be through the use of a PLL based frequency synthesizer. The signal output from oscillator 808 and / or oscillator 809, which will be at the base frequency, is stepped up by a PLL circuit before being passed to the mixer 802. This approach avoids relying on overtone modes within the quartz crystal itself, and allows greater flexibility in selecting output frequencies as they do not need to be overtone frequencies.

[0225] The use of a PLL to step up the frequency of the signals output from the oscillators may be adopted, for example, when operating in the GHz frequency range. The PLL locks onto the beat frequency, stabilises it, and filters out noise before it is passed to the mixer 802. The PLL enables precise frequency multiplication, stable and controlled frequency scaling, and flexibility in tuning or locking to a reference signal, while still maintaining a lock to the original quartz resonant frequency. Once stepped up and stabilized, this multiplied frequency can be passed to the mixer 802.

[0226] Using overtone modes to step up the frequency may be used when operating in the MHz range, as the system may achieve sufficient stability without requiring further frequency filtering within the feedback loop 810 before passing to the monitoring system 806. Using overtone modes enables a simpler, analogue hardware path without active frequency synthesis, and is advantageous when phase noise is less critical and the quartz crystal oscillators are designed to operate in 3rd, 5th, or 7thovertone modes, thereby naturally producing higher output frequencies while retaining the underlying resonator’s stability characteristics. A PLL can introduce phase noise through its loop dynamics and VCO characteristics. The overtone modes often have less phase stability than quartz oscillators operating at fundamental, i.e. resonant frequency. Therefore, in embodiments utilizing either overtones or a PLL to step up the base frequency, preferably, the system is further configured to handle phase noise. This refers to small, rapid fluctuations in the phase of a signal, typically resulting in spectral spreading of a sine wave.

[0227] In high-precision frequency measurement systems, phase noise can have undesirable consequences such as: mask small shifts in frequency caused by acceleration; reduce the resolution and stability of beat frequency measurements; and add jitter that can degrade the system's effective sensitivity.

[0228] The phase noise may be minimized through component selection, shielding, or circuit design to preserve the system’s ability to detect micro-Hz shifts reliably. Examples of how phasenoise is handled are described below.

[0229] For example, separate to the use of a PLL to step up the frequencies of the oscillators 808, 809 as mentioned above, output from the mixer 802 may pass through another PLL, which may be considered a stabilization PLL as it serves to stabilize and filter the beat signal before it reaches the monitoring system 806. As will be described with reference to Figure 9, this stabilisation PLL may be implemented as a part of the controller 804 of the feedback loop 810. The use of this stabilization PLL depends on the system’s beat frequency range; it is typically required in GHz or high-MHz applications, but may be bypassed for lower- frequency configurations where noise is minimal. The signal from the stabilisation PLL, being at a stabilised and filtered beat frequency, is provided to the monitoring system 806.

[0230] Notably, even if the beat frequency signal is not first passed to the PLL of the controller for filtering before being measured by the monitoring system (i.e. it is sent directly to the mixer in the first instance), it will still pass through the PLL of the controller when the feedback loop 810 is in operation, as will be further detailed with reference to Figure 9.

[0231] Figure 9 depicts an embodiment of the controller 804. Algorithmic or processing modules provided by controller 804 may be implemented by a microcontroller or a digital controller with processing capabilities. The controller 804 is adapted to generate control signals, such as voltage control signals, or precursors thereof, to implement control logic and adjustments to the timing of the monitoring module. The controller 804 may provide control signals to external circuitries for generating the required voltages, or the microcontroller may be provided in the same module as the required circuitries.

[0232] In Figure 9, the mixer 802 is shown feeding a signal to the feedback loop 810 (i.e. passing the calculated beat frequency). As noted above, the beat frequency signal can be passed directly to the monitoring system 806 of the system 800 if stabilisation is not required (depending on the frequency range of the beat frequency). For example, if the beat frequency signal is in the kHz -MHz range, and is inherently stable, then the beat frequency signal could be passed directly to the monitoring system 806. However, this configuration foregoes noise filtering, stability and dynamic correction. Alternatively, and more preferably, the beat frequency signal passes through the PLL 814 within the controller 804 before being passed to the monitoring system 806.

[0233] In the embodiment, the controller 804 includes a Phase-Locked Loop (PLL) 814, arranged to receive and lock onto the beat frequency of the signal supplied by the mixer 802, filtering out noise and jitter, before being passing the stabilized output 816 at the beat frequency to the monitoring system 806. Here, the PLL 814 is provided within the controller to clean up the signal overall (if required) such that the monitoring system 806 can perform precise frequency counting on a stable signal. A Voltage-Controlled Oscillator (VCO) 812 in the PLL 814 is configured to provide the required voltage adjustment output 813, for the controller 804 to adjust the timing of the frequency counter within the monitoring system 806. The VCO may be a tuneable analogue oscillator, typically implemented using voltagedependent components, for example, varactors. The VCO 812 does not utilise a quartz oscillator such as oscillators 808, 809, and may instead be completely electronic. This allows the VCO to drive the frequency counter of the monitoring system 806 and not exhibit its own acceleration-induced drift in the same way that oscillators 808, 809 do.

[0234] The controller 804 in the embodiment of Figure 9 comprises an adjustment module 818 configured to calculate the adjustment required. The adjustment module 818 is configured to receive input relating to the beat frequency as measured by the monitoring system 806 and compare it with the baseline beat frequency in order to calculate the required adjustment.

[0235] For example, if the beat frequency becomes “out of phase” with the baseline frequency, this is measured by the monitoring system 806 and detected by the adjustment module 818 which then modulates the VCO output so as to maintain frequency alignment between the beat frequency as measured by the frequency counter of the monitoring system 806, and the beat frequency baseline. This fine-tunes the system’s output frequency, i.e. the ticking rate (clock) output of the monitoring system 806, ensuring the measured beat frequency stays aligned with the baseline beat frequency and maintains the desired ticking rate accounting for external acceleration with precision akin to atomic time standards.

[0236] To do this, the adjustment module 818 determines the voltage adjustment required to correct the output of the VCO 812. The correction signal is sent to the input of the VCO 812 within the PLL 814, such that the correct output voltage of the VCO is used to adjust the ticking rate of the frequency counter within the monitoring system 806, thereby closing the feedback loop 810.

[0237] Exemplary Control Process

[0238] An example control process 1000 implemented by a controller 804 incorporating a phase- locked loop (PLL) and adjustment module is described with reference to Figure 10. If the current beat frequency is lower than the baseline beat frequency, then the PLL (as instructed by the adjustment module) will work to maintain the system’s output frequency (i.e. the clock frequency of the monitoring system) at a lower frequency until the monitoring system measures the current beat frequency to match the baseline beat frequency (as determined by the adjustment module). In this circumstance, it works in the following manner:

[0239] - Create Circuit 1 and Circuit 2 frequencies: At steps 1010 and 1011, the oscillator 1 and the oscillator 2 are arranged to create respective signals at frequency fi and f2. This may be the resonant frequency of quartz crystals used in the oscillators. To ensure high resolution and sensitivity required for detecting subtle variations due to external acceleration on the system 800, the system may employ an overtone frequency, e.g., a third overtone frequency of each respective resonant, or higher, in order to enhance the measurement precision of the resultant beat frequency. This overtone frequency is a higher harmonic of the fundamental frequency (e.g., 3x). The frequencies may alternatively be stepped up through a step-up PLL.

[0240] - Optional signal amplification: At step 1020, the respective oscillator signals may be amplified, e.g., through separate signal amplifiers, or through separate channels of a joint signal amplifier, for example a dual-channel low-noise amplifier (LNA) or a differential amplifier with isolated paths. Such implementation of a single amplifier as opposed to separate amplifiers may be advantageous when space or component count needs to be reduced, or if phase consistency across both signals must be maintained through a symmetric path. Preferably, the input impedance matching and gain are independently configurable per amplification path (or channel). In practice, as long as the amplifier architecture preserves channel isolation and maintains low phase noise and consistent gain, this setup is suitable and helps ensure both signals arrive at the mixer with matched power levels and clean waveforms.

[0241] The signal amplifications step 1020 may be carried out to either or both the respective oscillator signals to ensure compatibility with the input requirements of the mixer 802. Amplifying the signals may prevent signal degradation and maintain stability in the overall system performance. This may help to ensure that the respective power levels and impedances of the oscillator signals are not mismatched, resulting in potential signal loss. Amplification may further minimize phase noise and prevent distortion, crucial for high- precision frequency measurement.

[0242] There is no strict requirement for the same amplification factor to be applied for both oscillator signals. However, both oscillator signals should ideally have matched or similar power levels when entering the mixer. Imbalance could cause mixer saturation (e.g. if one signal is too strong), and poor conversion efficiency or increased phase noise (e.g. if one signal is too weak). In practice, the gain may be tuned individually for each circuit to achieve equal amplitude at the mixer’s inputs.

[0243] The power amplification, i.e. gain, may be adjustable, for example, up to 20 dB to provide sufficient amplification without distortion. The gain may be further optimised to ensure amplitude stability of the signal or signals, particularly if they are to be stepped up to higher frequencies by the PLL 814 at step 1050.

[0244] When the amplifier is performing impedance matching, a 50-ohm impedance may be employed to ensure minimal reflection and signal lose. This is critical for maintaining high- fidelity signal transfer to the mixer 802.

[0245] The at least one signal amplifier of the system 800 may be implemented using an off-the- shelf RF amplifier module (e.g., Mini-Circuits ZX60-33LN-S+), combined with power supply filtering and impedance matching circuitry. Custom design options to carry out any amplification that may be required within the system may also be implemented, for example a discrete single-transistor amplifier may be implemented in low-cost applications. Alternatively, a custom high-gain, low noise RF amplifier integrated circuit could be implemented to provide a more compact design.

[0246] By amplifying one or both of the oscillator signals, the mixer receives a robust, stable input signal, ensuring reliable beat frequency generation and accurate external acceleration measurement by the system.

[0247] - At step 1030, the oscillator signals, which may be amplified as discussed above, are provided to the mixer 802.

[0248] - Calculate beat frequency: At step 1040, the mixer 802 then calculates the beat frequency.

[0249] To isolate the beat frequency, a low-pass filter may be implemented. The low-pass filter may be applied to the mixer’s output to remove the high-frequency sum component (f™m= fi + f ) while preserving the lower frequency beat component, i.e. the beat frequency ( beat). The cutoff frequency of the low-pass filter is appropriately selected based on the expected beat frequency range, such as to accurately pass the beat frequency while blocking unwanted high frequencies. For example, for a beat frequency of fbeat = 100 kHz, a suitable cutoff frequency may be several hundred kHz, such as 300-500 kHz, to ensure minimal attenuation of the desired signal while effectively supressing the higher frequency components. At step 1040, the isolated signal is output from the mixer 802, considered to be at the beat frequency. The mixer may be arranged so that the beat frequency is in the range of, for example, 1 kHz to 1 GHz (in some embodiments, 10 kHz to 1 MHz).

[0250] The mixer of the system 800 may be implemented using an off-the-shelf mixer (e.g., MiniCircuits Double-Balanced Mixer: ZFM-2H-S+), combined with a standard low-pass filter. Alternatively, a custom design option could be implemented to carry out the required task, for example a diode-based passive mixer with low-pass filter. A custom design option requires careful tuning for stability and proper signal attenuation.

[0251] The routing of the beat frequency signal may depend on the frequency range of the output, e.g. whether frequency step-up via overtones or the step-up PLL.

[0252] If the beat frequency is in the low to mid MHz range, the system may achieve sufficient stability without requiring stabilization via a PLL (e.g., the PLL 814 mentioned in relation to Figure 9). The beat frequency signal may be passed directly to the monitoring system 806. This path is suitable where the beat frequency signal is already stable and does not require additional filtering or stabilisation.

[0253] If the beat frequency is in the high MHz to GHz range (e.g., due to stepped-up oscillator signals), the mixer 802 routes the beat frequency signal first to a stabilization PLL (e.g. the PLL 814 of the controller 804). In this case, at step 1050, the PLL 814 then locks onto and stabilises the beat frequency to filter out phase noise and high frequency artifacts.

[0254] This flexibility allows the system to support multiple operating ranges and precision requirements by adapting the signal path based on the characteristic of the beat frequency and overall system configuration.

[0255] -Initial beat frequency conditioning via stabilisation PLL: At step 1050, the beat frequency may be initially passed through the stabilisation PLL 814 in order to lock onto and stabilise the beat frequency to filter out phase noise and high frequency artifacts before it is first passed to the monitoring system 806. Optionally, the PLL 814 may also step up, or condition, the beat frequency signal for use by the monitoring system 806, allowing the system to produce a clean, high resolution signal, which is useful for digital counters or control loops.

[0256] A PLL alone not does inherently multiply frequency. To step up the frequency, the PLL may be configured with additional components — such as frequency dividers or multipliers — that modify the relationship between the reference signal (the beat frequency) and the output frequency of the Voltage-Controlled Oscillator (VCO).

[0257] In practice, the beat frequency is passed into the input of the PLL as the reference signal. To step up this signal, the PLL uses a divider in the feedback path of the feedback loop. This forces the VCO to run at a higher frequency so that when divided down, its output matches the input beat frequency signal. For example, if the beat frequency is 100 kHz and the divider is set to N = 100, the VCO will lock at 10 MHz.

[0258] The output of the VCO then becomes a stable, higher-frequency signal that can be used as the timing reference for the frequency counter or further digital processing, ensuring both frequency multiplication and phase coherence with the original beat frequency.

[0259] - Frequency counter measures beat frequency: At step 1060, the frequency counter within the monitoring system monitors the beat frequency.

[0260] The frequency counter within the monitoring system 806 may utilise a high-resolution counter, which may measure the beat frequency with precision greater than 0.0003 Hz.

[0261] The frequency counter may be implemented as a microcontroller or FPGA, including one input for the beat frequency (either directly from the mixer 802 or the PLL 814 output), another input as the clock reference (from the VCO 812 output), and logic to count how many beat cycles occur per unit of time or, alternatively, how many time-base cycles occur per beat frequency cycle.

[0262] The VCO output may also be used to clock the microcontroller directly or drive a timing interrupt, allowing the counter to operate in real time and continuously track acceleration- induced shifts.

[0263] - Controller analyses beat frequency: At step 1070, the measured beat frequency is passed to the controller 804 from the monitoring system 806 to be analysed. If the beat frequency has shifted from the baseline value (“yes” 1071), at step 1080 the adjustment module calculates the required voltage adjustment signal, and at step 1090 the VCO applies the required voltage adjustment and the ticking rate for the frequency counter is updated. The process returns to step 1060, whereby the frequency counter, now with an updated ticking rate (serving as the clock reference to measure the beat frequency), measures the beat frequency based on the monitored signals.

[0264] When analysing the beat frequency to determine if there is a detectable shift from the baseline value, a tolerance threshold may be utilised to filter out noise and minor frequency fluctuations. For example, a small value 10'6. If the deviation is within the tolerance, no adjustment is made, and the control process goes back to step 1040. If the deviation exceeds the tolerance value, the control process progresses to step 1080.

[0265] The adjustment module 818 uses the shift in beat frequency from the baseline beat frequency to calculate the external acceleration according to:

[0266] Since the beat frequency shift arises from the difference in response between the two quartz oscillators, each with potentially different base frequencies and acceleration sensitivities, the shift Afteai alone indicates that a shift has occurred but does not reveal how much the frequency of the first oscillator (i.e. the more sensitive oscillator) has shifted.

[0267] As such, to generate the required correction signal to the VCO for the oscillator that the VCO is correcting, (e.g., first oscillator 808) from the above derived acceleration, we can use the equation:

[0268] A Uo ~ * «

[0269] The required correction to the VCO’s frequency can then be calculated based on a known mapping between VCO control voltage and output frequency (this is the VCO’s tuning slope Kv, typically expressed in Hz / V):

[0270] Hence, Af / ,ra / reflects a differential quantity. To determine how much the VCO must adjust the more sensitive oscillator, we must first extract the actual acceleration, then compute the corresponding frequency shift for that oscillator. This ensures the adjustment signal accurately matches the physical effect being corrected.

[0271] Whilst the beat frequency reflects the differential shift between the two oscillator frequencies, the correction target is that of the more sensitive oscillator, treating the second oscillator as a stable reference.

[0272] The calculated correction voltage signal may be delivered to the VCO via a digital-to- analogue converter (DAC) for precise, real-time control. In alternative embodiments, an analogue control loop may be used with filters and op-amps to generate the correction voltage directly from signal comparisons. In such an embodiment, utilising an analogue control loop, the system may not perform discrete digital steps such as 1070 (beat frequency analysis), 1080 (acceleration calculation), or 1090 (voltage determination). Instead, the analogue control loop may detect beat frequency shifts through continuous signal comparisons, and only generate the appropriate correction voltage, in real time, if a beat frequency shift is detected. This eliminates the need for separate computational steps, allowing voltage corrections to emerge naturally from analogue signal processing.

[0273] In an example implementation, the monitoring system uses the output of the VCO to clock the beat frequency. In this implementation, when the measured beat frequency is below the baseline beat frequency, the adjustment module determines that the VCO output frequency is too high, and generates an adjustment signal indicating that a corrective voltage needs to be delivered to the VCO input to reduce its voltage, thereby lowing the VCO’s output frequency. Since the frequency counter uses the VCO output as its time base, this correction slows the ticking rate (clock) of the frequency counter driven by the timing reference of the VCO. The adjustments made to the VCO’s control voltage are made in real time, and bring the systems internal timekeeping back in sync with the baseline reference such that the system clock remains accurate despite environmental perturbations.

[0274] Therefore, as long as an amount of phase difference between the measured beat frequency and the baseline beat frequency exists (or is higher than a non-zero threshold amount), indicating that the ticking rate of the clock of the frequency counter within the measurement system needs correcting, the system will continue to adjust the VCO voltage to correct for the drift in the measured beat frequency. The feedback loop will run continuously until the measured beat frequency meets the baseline beat frequency (within a predetermined threshold limit), at which point the system will cycle back to step 1040 and proceed again from there.

[0275] Advantageous of Dual Oscillator System

[0276] By operating the feedback in this manner, it is possible to effectively offset the error resulting from the acceleration on the natural resonance frequencies of the quartz oscillators within the crystal, creating a stable output frequency that corrects for external effects.

[0277] Accordingly, by using two quartz oscillators to create beat frequency to measure such deviations, there is no set-point frequency, for example as disclosed in the embodiments of Figures 4 through 7. Rather, the system operates by continuously measuring the relative difference between two oscillator outputs, making it both self-referencing and adaptive.

[0278] Notably, the dual oscillator system utilises a frequency counter with a timing reference that is not derived from a fixed quartz oscillator, but is instead driven by the output of a VCO. This configuration allows the system to adapt its own timing base in real time, enabling high-precision, acceleration-aware measurement and correction. Furthermore, in embodiments wherein the beat frequency is routed from the mixer to the PLL before its first iteration being measured by the monitoring system, the VCO is phase-locked to the beat frequency via the phase-locked loop (PLL). In this configuration, a phase detector compares the VCO output to the beat signal from the mixer. The resulting voltage error is used to adjust the VCO in real time to stay in phase with the beat signal, ensuring tight, low-noise tracking of the beat frequency. For reference, a conventional frequency counter uses a fixed internal clock (usually quartzbased) to define its gate time — i.e., how many cycles of an input signal occur within a given time interval. This reference clock is independent of the input signal being measured and does not self-adjust to compensate for environmental effects such as acceleration.

[0279] In the dual oscillator system, the fixed internal clock of a conventional frequency counter is replaced with a tuneable clock input — the output of a Voltage-Controlled Oscillator (VCO) embedded in a Phase-Locked Loop (PLL). When the system utilising PLL filtering at first instance before the beat frequency is initially measured by the monitoring system, the PLL tracks the beat frequency, and the VCO output becomes the timing reference (i.e., the clock input) for the frequency counter. As the beat frequency shifts with acceleration, the counter’s timing base is updated in real time, forming a closed feedback loop.

[0280] This design makes the frequency counter dynamically responsive to changes in acceleration, since its clock source is derived from the VCO that is phase-locked to the beat frequency. That is, the phase detector within the PLL compares the VCO output to the beat signal from the mixer in the first iteration, and the resulting voltage error is used to adjust the VCO in real time to stay in phase with the beat signal, ensuring tight, low noise tracking of the beat frequency. Then, as the beat frequency changes due to acceleration, the monitoring system (driven by the VCO output) still observes deviations via its frequency counter. The control system uses the information from these detected deviations to calculate acceleration and compute an additional correction voltage to apply to the VCO. The corrected VCO output then redefines the timing of the counter, closing the loop. While the VCO is phase-locked, the beat frequency it tracks is dynamic, allowing the system to function as both a high- precision clock and an accelerometer.

[0281] Also notable for the dual oscillator system is that the frequency counter within the measurement system is a measurement tool, not a frequency-generating component (e.g. compared to the single quartz oscillator system, utilising a set point frequency, for example as disclosed in the embodiment s) of Figures 4 through 7). The frequency counter derives timing form the VCO, but performs standard counting logic based on that dynamic clock. This is fundamentally different from conventional quartz-locked frequency counters, which have fixed timing and cannot compensate for acceleration-induced drift. The use of a PLL- VCO pair to drive the frequency counter’s time base introduces new mechanisms for realtime adjustment, effectively embedding environmental awareness in the clocking system.

[0282] This architecture enables a self-correcting quartz-based timekeeping mechanism that uses measurable physical effects (acceleration) to maintain or improve long-term frequency accuracy. The frequency counter effectively becomes a high-stability, self-correcting clock, which outputs time intervals and frequency with precision comparable to or better than conventional quartz clocks, and in some regimes, rivalling low-level atomic clocks. The clock output of the frequency counter reflects a dynamically stabilised time base. This time base is continuously corrected by the control system to compensate for acceleration.

[0283] As a result, the frequency counter can be used not only for measurement, but also may be used to timestamp events, distribute precise timing, or serve as the system’s primary reference clock. Compared to conventional quartz-based clocks, this dual oscillator system may provide superior long-term stability, especially in dynamic or vibration prone environments, and may approach the performance of low-level atomic clocks in stationary applications.

[0284] Non- Acceleration Induced Frequency Shifts

[0285] Furthermore, although the dual oscillator system is designed to detect acceleration-induced frequency shifts, it may compensate for other environmental effects that influence quartz oscillator stability, including temperature, humidity, pressure, and aging. These effects cause frequency drifts in the quartz oscillators deployed in the system, just like external acceleration does.

[0286] To counteract such effects, the dual oscillator system continuously monitors the beat frequency, regardless of the cause of the frequency change. Any deviation from the precalibrated baseline beat frequency is interpreted as a shift to be corrected. The PLL tracks this change, the VCO adjusts accordingly, and the control system applies a correction — restoring the stability of the internal timing reference. In the embodiments, based on long term drifts resulting from other factors (e.g. crystal aging), pre calibrated corrections may be implemented to separately account for these known long term frequency drifts. This may be implemented in the form of pre-calibrated correction tables used to model slow, deterministic long-term drifts, providing additional stability for long-duration applications, or after power cycling.

[0287] Design Flexibility

[0288] As disclosed above, the actual frequencies of the quartz oscillators 808, 809 system can be adjusted based on specific design requirements. In a preferred embodiment, the objective is to achieve a beat frequency within an optimal range (e.g., 1 MHz to 100 MHz) to balance the following properties:

[0289] • Measurement precision: Ensuring frequency shifts due to acceleration remain detectable.

[0290] • Noise reduction: Avoiding excessive phase noise while maintaining signal integrity.

[0291] • Processing efficiency: Selecting frequencies compatible with the PLL and frequency counter for high-resolution measurement.

[0292] As previously disclosed with reference to exemplary embodiment of Figures 8 through 10, this circuit design, leveraging precision frequency-based acceleration measurement, has a broad range of applications across multiple industries. The dual oscillator system allows for adaptability and scalability, as both oscillators can be operated at their fundamental mode or stepped up using a PLL / VCO, depending on the target application. This flexibility, combined with the systems inherent sensitivity and stability, enables the design to be adapted for various use cases, including high-stability clocks, precision inertial navigation, telecommunications, scientific instrumentation, and aerospace systems all while maintaining its core functionality.

[0293] For example, the dual oscillating system may be particularly suited to:

[0294] - Inertial Navigation: The dual oscillator system’s ability to detect small acceleration- induced frequency shifts makes it highly suitable for aerospace, maritime, and land-based navigation, especially in GPS-denied environments (e.g., submarine navigation, spacecraft guidance). High-stability acceleration measurements may further enable long-duration dead reckoning with improved position accuracy over extended distances.

[0295] - Telecommunications applications, where the system can be integrated into high-stability frequency references to reduce drift in satellite and terrestrial communication networks. Also, by compensating for acceleration-induced variations, the system may help to ensure more stable transmission frequencies, particularly in mobile or spaceborne communication systems.

[0296] - Satellite Systems, in which the system may provide stable frequency references for onboard oscillators in satellites and space probes, mitigating the effects of acceleration and gravitational perturbations. It may improve precision timing in deep-space navigation and supports high-resolution Doppler tracking of spacecraft.

[0297] - Scientific Instrumentation: the system may support precision timing applications, such as atomic clocks, frequency standards, and high-resolution spectrometry in laboratories. It may also be used in gravitational physics experiments, where detecting minute acceleration changes is crucial for testing fundamental physics theories.

[0298] -Aerospace and Defence applications: the system may enable high-precision inertial measurement for missile guidance, flight stabilisation, and spacecraft manoeuvring. The system can further be integrated into next-generation accelerometers for detecting sub-pg acceleration forces in high-dynamic environments.

[0299] - Automotive Industry: the system may be incorporated into an automotive application to enhances advanced driver-assistance systems (ADAS) and autonomous vehicle navigation, improving lane-keeping, collision avoidance, and dead reckoning when GPS signals are lost. The use of the system may provide a stable frequency reference for automotive radar systems, improving distance estimation and object tracking in autonomous driving applications. Multi-Axis Implementation

[0300] As quartz oscillators are manufactured under 1g of acceleration, typically normal to the mounting plane, oscillators may be aligned each to a separate orthogonal axis (X, Y, Z) to improve accuracy for applications involving inertial navigation or multi-directional motion tracking.

[0301] In an embodiment, there may be provided three dual oscillator modules (e.g. of the embodiments of Figures 8-10), each aligned to a separate axis (e.g. three orthogonal axes). The three modules may operate independently of each other. This configuration allows an oscillator pair of each dual-oscillator module to independently measure beat frequency shifts resulting from acceleration along its corresponding axis.

[0302] In a multi-axis inertial navigation configuration, temperature-induced frequency shifts (or other shifts induced by the environment) affect all oscillator axes in a similar and predictable manner. In contrast, acceleration causes asymmetric frequency shifts depending on axis orientation. The system may be configured to distinguish between these effects by analysing the directional pattern of the frequency shifts across all three axes. For example, if all shifts are of similar magnitude and direction, they are interpreted as common-mode thermal effects. If they vary per axis in a directional pattern, they are attributed to acceleration. This differential analysis allows the system to separate environmental drift from true inertial input, even without a temperature sensor.

[0303] For example, referring to Figure 11, a frequency shift (expressed in parts per million, ppm, of the original frequency) of each axis is plotted against time. In the depicted example, the system experiences a temperature increase of +5°C over a period of ~3 hours, whilst also experiencing a 1g acceleration along the X-axis over a period of ~30 minutes. The frequency shift from the temperature increase can be seen affecting each axis slowly over time, and equally across all three-axes. The frequency shifts affecting the Y and Z axes follow the curve 1120. Comparatively, the frequency shift from the acceleration experienced along the X-axis can be seen as a sharp frequency shift affecting the X-axis only, as shown in the curve 1110. Determination of the acceleration along the axes (ax, ay, az) allows a vectorial calculation of the combined effect of the acceleration along the direction of travel. This provides a way of calculating a 3D acceleration vector. Such 3D vector calculation may be particularly suitable for accurate inertial measurement.

[0304] To calculate the 3D vector, first the system calculates the acceleration along each axis:

[0305] In such multi-axis embodiments, when exposed to temperature changes, the oscillator pair of each dual-oscillator module experience similar temperature change. As such, the temperature change experienced on all three axes does not produce a directional vector, rather a scalar frequency shift is experienced across all three axes. Hence, the oscillator pair of each dual-oscillator module experience similar scalar frequency shifts, which does not correspond to a directional acceleration.

[0306] In some embodiments, the system calculates the vector magnitude of the acceleration, to determine if the frequency shift is a result of temperature. If one or two axes dominate, the frequency shift is a result of acceleration.

[0307] As each oscillator pair of each dual-oscillator module is monitored independently, these common-mode frequency shifts can be detected and compensated through baseline correction (i.e. by adjusting the baseline beat frequency of each oscillator pair) or by comparison to a temperature-stable reference. This ensures that true vector acceleration components of the frequency shift in each dual-oscillator module remain distinguishable from scalar frequency shifts arising from temperature fluctuations. This enables applications utilising a multi-axis embodiment to maintain accurate internal navigation, even in environments with fluctuating temperature. Furthermore, when both acceleration and temperature changes occur simultaneously, the system remains functional and accurate. This is because the architecture responds to any frequency shift — regardless of cause — by continuously monitoring the beat frequency between a sensitive oscillator and a stable reference.

[0308] Temperature shifts produce similar drift across all axes, while acceleration affects each axis differently depending on orientation. By comparing the frequency shifts across the three axes, the system can mathematically distinguish between common-mode temperature drift and directional acceleration-induced shifts.

[0309] Thus, even under simultaneous thermal and mechanical stress, the system can isolate the acceleration vector while passively compensating for temperature.

[0310] PLL Bandwidth Selection

[0311] When looping the beat frequency using a PLL, greater flexibility can be afforded to the integration times required to calculate external acceleration induced frequency shifts. Depending on the desired application of the dual oscillator system, the frequency range of the beat frequency and the required bandwidth of the PLL need to be selected according to the target acceleration sensitivity, and the required integration time for the application.

[0312] For example, for smaller baseline beat frequencies, e.g. 100 kHz, a longer integration time (e.g. up to 18hrs) is required when looping the beat frequency via the PLL. This level of integration time is practical timeframe for clocks based on Earth, where the primary external acceleration is Earth’s orbital dynamics.

[0313] By selecting a higher beat frequency, for example 1 MHz = 1000, the system is able to detect small accelerations over shorter integration times, which is crucial for dynamic applications such as inertial navigation, where long integration times are not practical. That is, in applications where high temporal resolutions are required (such as tracking fastmoving objects or compensating for rapidly varying accelerations), stepping up the frequency enables the system to respond more quickly while still maintaining high accuracy.

[0314] Hence, the PLL bandwidth is selected to be narrow for applications with short integration times, and is selected to be wider for applications with longer integration times. For example, below are some exemplary applications, and potential PLL bandwidth ranges (i.e. accuracy required to registered shifts in beat frequency) corresponding to the target external acceleration being detected for said application. As such, when selecting the PLL bandwidth for the desired application, a narrower bandwidth results in a higher frequency resolution, but slower response (therefore ideal for clocks). Meanwhile, a wider bandwidth results in a faster response, which is suitable for navigation or tracking dynamic events, but at the cost of micro-Hz sensitivity.

[0315] Variations and modifications may be made to the parts previously described without departing from the spirit or ambit of the disclosure.

[0316] The matter set forth in the foregoing description and accompanying drawings is offered by way of illustration only and not as a limitation. While particular embodiments have been shown and described, it will be apparent to those skilled in the art that changes and modifications may be made without departing from the broader aspects of the inventors’ contribution. The actual scope of the protection sought is intended to be defined in the following claims when viewed in their proper perspective based on the prior art

[0317] In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word “comprise” or variations such as “comprises” or “comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention.

Claims

CLAIMS1. A quartz oscillator system (100) comprising: a quartz oscillator (108, 808) comprising a quartz crystal and an oscillator circuit whose frequency is based on a resonant frequency of the quartz crystal; a monitoring module (106) for monitoring an output frequency of the quartz oscillator (108); a control system (104) external to the quartz oscillator, and configured to compare the output frequency with a setpoint frequency, and apply an adjustment signal to an electronic circuit of the quartz oscillator to adjust a frequency of the quartz oscillator based on the comparison with the reference frequency.

2. The system (100) of claim 1, wherein the controller (104) comprises a setpoint determination module configured to determine the setpoint frequency.

3. The system (100) of claim 1 or claim 2, wherein the setpoint frequency is determined based on at least the resonant frequency of the quartz crystal, and an adjustment data in relation to an orbital position of the earth around the sun.

4. The system (100) of claim 3, comprising data storage to store the adjustment data, the control system having access to the data storage.

5. The system (100) of claim 3, comprising a communication module (119) for querying the setpoint frequency from a data source.

6. The system (100, 800) of claim 1, comprising a second quartz oscillator (809) comprising a second quartz crystal having a resonant frequency and a second oscillator circuit whose frequency is based on the resonant frequency of the second quartz crystal, the second quartz oscillator having a different sensitivity to acceleration than the first quartz oscillator.

7. The system (100, 800) of claim 6, wherein the set point frequency is a baseline beat frequency calculated based on output frequencies of the first quartz oscillator and the second quartz oscillator, when they are not subjected to acceleration.

8. The system (100, 800) of claim 6 or claim 7, wherein the monitoring module is configured to monitor a beat frequency calculated based on the output frequencies of the first and the second quartz oscillators.

9. The system (100, 800) of claim 8, comprising a mixer (802) configured to provide a mixer input to the monitoring module, wherein the monitoring module is configured to determine the beat frequency by monitoring the mixer input, wherein the mixer is configured to receive signals output from, or generated based on outputs of, the first and second quartz oscillators.

10. The system (100) of any preceding claim, wherein the control system (104) comprises a phase locked loop (PLL) (114), wherein a signal at the setpoint frequency is provided as a reference input for the PLL, and wherein a signal at the output frequency determined by the frequency monitor is at an output for the PLL.

11. The system (100) of any preceding claim, wherein the control system (104) is configured to generate control signals based on a comparison between the output frequency determined by the frequency monitor, and the setpoint frequency, wherein the control signals are provided as input to an adjustment module (118) configured to generate adjustment signals to adjust the output frequency of the quartz oscillator (108).

12. The system (100) of any one of claims 1 to 5, 10, or 11, wherein the control system (104) comprises a synchronisation module, configured to synchronise the setpoint frequency with frequency determined based on an external time source.

13. The system (100) of claim 12, wherein the external time source comprises an atomic clock or a time source in a global positioning system.

14. The system (100) of any preceding claim, wherein the monitoring module (106) is configured to use the output frequency of the system as a base frequency for monitoring a ticking rate of the quartz crystal.

15. The system (100) of any preceding claim, wherein the monitoring module (106) is configured to provide a data generated based on an output signal from the quartz oscillator, to the controller (104).

16. The system (100) of any preceding claim, wherein the quartz oscillator (108) is a temperature-compensated quartz crystal oscillator or oven-controlled crystal oscillator.

17. The system (100) of any preceding, wherein the controller (104) is configured to receive user input for system calibration and / or setting data.

18. The system of claim 17, wherein the controller is configured to provide a user interface displayable on a display screen, the user interface being configured to enable the user input to be provided.

19. An apparatus providing three quartz oscillator systems, each system being in accordance with any one of claims 1 to 18, wherein the quartz oscillators for the three systems are respectively mounted along three orthogonal axes.

20. A timing device comprising the apparatus of claim 19 or the quartz oscillator system of any one of claims 1 to 18.

21. A method for improving accuracy of a quartz oscillator clock, comprising: monitoring an output frequency of a quartz oscillator of the quartz oscillator clock; comparing the output frequency with a setpoint frequency to determine an error between the output frequency and the setpoint frequency; providing a voltage adjustment signal to the quartz oscillator, the voltage adjustment signal being determined on the basis of the error, to adjust the output frequency of the quartz oscillator.

Images