A method for recovering the earth's gravity field in an inter-satellite tracking mode based on an optical clock

Abstract

The application provides an earth gravity field inversion method in an inter-satellite tracking mode based on an optical clock, comprising: using a numerical simulation method, the accuracy of the inversion of the earth gravity field in the inter-satellite tracking mode of the satellite-borne optical clock satellite is systematically evaluated. The simulator generates simulated observation data as input in the orbit of the gravity satellite (such as the GOCE and GRACE orbits), and estimates the gravity field coefficients by using a strict least square method. The accuracy of the results is evaluated by comparing the coefficient difference between the inversion model and the reference model. The application evaluates the accuracy of the inversion of the earth gravity field in the inter-satellite tracking mode based on the optical clock through the numerical simulation method, and verifies the potential of the optical clock in the high-precision gravity field measurement. In the future research, the optical clock noise model and the multi-sensor fusion method will be further optimized to improve the inversion accuracy of the high-order gravity field, and more accurate data support will be provided for the earth science and global climate change research.

Description

Technical Field

[0001] This invention relates to the field of Earth gravity field technology, and in particular to a method for inverting Earth gravity field in an inter-satellite tracking mode based on an optical clock. Background Technology

[0002] Accurate measurement of the Earth's gravity field is of great significance in the field of Earth sciences, such as monitoring global sea-level rise, optimizing ocean circulation models, and conducting geodynamic research. In recent years, breakthroughs in satellite gravity missions have propelled the development of Earth's gravity field research. The successful implementation of GRACE (Gravity Recovery and Climate Experiment) and its successors, such as GRACE-FO and GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), has provided crucial data support for gravity field research. Currently, satellite gravity research mainly focuses on upgrading airborne sensor systems, laser interferometric ranging technology, multi-satellite observation systems such as the Bender satellite constellation, and optimizing background models to reduce interference from high-frequency atmospheric and ocean mass changes—all measures aimed at improving the performance of future gravity measurement satellites.

[0003] In recent years, breakthroughs in quantum optics technology have provided an opportunity for the development of novel gravity sensors and the realization of new measurement concepts. Because optical clocks can provide extremely high-precision frequency information, by deploying optical clocks at different locations, minute frequency changes caused by gravitational potential differences (the gravitational redshift effect) can be observed. This principle has already been applied to the measurement of Earth's gravitational potential difference. [6] The resulting gravity potential difference can be directly converted into elevation difference. In geodesy, gravity potential is the core parameter for determining physical height. For elevation measurement, the next stage goal is to achieve a unified standard with an accuracy of 1 centimeter. Currently, the most advanced optical clocks have reached 1.0 × 10⁻⁶. -18 Even higher frequency uncertainties, equivalent to 0.1 m 2 / s 2 The optical clock boasts a high potential energy accuracy and a 1.0 cm elevation resolution. This level of accuracy significantly exceeds the unified standard of 1 cm accuracy and is highly compatible with the 1 mm positional accuracy required by the Global Geodetic Observation System (GGOS). Therefore, the optical clock is considered a highly promising new geodetic tool with wide applicability in various measurement scenarios. The optical clock time-frequency measurement method can directly measure the gravitational redshift effect to obtain gravitational potential difference information. Compared to indirect measurements in traditional methods, this direct measurement approach not only improves measurement accuracy but also opens up new avenues for high-resolution unified modeling of the global gravity field. The optical clock, with its high potential energy accuracy and 1.0 cm elevation resolution, achieves a high potential energy accuracy. This level of accuracy is significantly higher than the unified standard of 1 cm accuracy and is highly compatible with the 1 mm positional accuracy required by the Global Geodetic Observation System (GGOS). Therefore, the optical clock is considered a highly promising new geodetic tool with wide applicability in various measurement scenarios. -18Even higher frequency stability allows for the capture of minute changes in gravitational potential, making it valuable for applications in monitoring crustal movement, studying polar glacier changes, and observing global sea-level rise. The potential of optical clock technology in improving the Earth's gravitational field has attracted widespread attention from the physics, geodesy, and earth science communities. Summary of the Invention

[0004] This invention provides a method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock, in order to overcome the deficiencies in the existing technology.

[0005] In a first aspect, the present invention provides a method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock, comprising:

[0006] Acquire noisy observation data from satellites;

[0007] A system of normal equations is constructed using the noisy observation data, and the least squares adjustment algorithm is used to estimate the spherical harmonic coefficients and order variance of the gravity field.

[0008] The Earth's gravity field inversion results are obtained by calculating the residuals between the restored model and the reference model, and the inversion accuracy of the Earth's gravity field inversion results is analyzed.

[0009] According to the present invention, a method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock is provided to acquire noisy observation data from satellites, including:

[0010] The noisy observation data includes signal components and noise components;

[0011] The signal components are obtained by spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, and the noise components are generated by modeling the quantum noise characteristics based on an optical atomic clock.

[0012] According to the present invention, an Earth gravity field inversion method based on an optical clock in an inter-satellite tracking mode is provided, wherein the signal components are obtained by spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, including:

[0013] Optical clocks were installed on satellites A and B respectively and connected by a dedicated link. The frequency difference ratio was used to determine the optical clocks. Obtain the gravitational potential difference between the two satellites :

[0014]

[0015] in , These are the frequencies of the optical clocks mounted on satellites A and B, respectively. Calculations are made based on time-frequency signals transmitted via the microwave link between the two satellites. cIt's the speed of light. It contains c -4 Higher-order terms of magnitude Omitted;

[0016] The Earth's gravitational field model uses a spherical harmonic function expansion, and the gravitational potential V at any point on the Earth's surface is described as follows:

[0017]

[0018] in It is the Earth's gravitational constant. It is the equatorial radius of the reference ellipsoid. These are spherical coordinates of a point. and These are the order and degree of the spherical harmonic function. It is a fully normalized associated Legendre function. and These are spherical harmonic coefficients, which are unknown parameters to be estimated in the recovery of the gravitational field.

[0019] According to the present invention, a method for inverting the Earth's gravity field under inter-satellite tracking mode based on optical clocks is provided. This method utilizes the noisy observation data to construct a system of normal equations, and employs a least-squares adjustment algorithm to estimate the spherical harmonic coefficients and order variance of the gravity field. The method includes:

[0020] The instantaneous positional difference between the two satellites is:

[0021]

[0022] Further adjusting the order of summation and assuming that the spherical harmonic coefficients can be expanded to a finite order n, we obtain the following equation:

[0023]

[0024] In the above equation, the coefficients of the unknowns on the right-hand side and The satellite position at time t Obtained precisely.

[0025] The method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock, provided by the present invention, further includes:

[0026] A power-law spectral model is used to describe the time-frequency randomness error of atomic clocks. :

[0027]

[0028] in, For Fourier frequency, It is a constant characterizing the strength of various noises, and takes different values ​​for different atomic clocks.

[0029] Secondly, the present invention also provides an Earth gravity field inversion system based on an optical clock in an inter-satellite tracking mode, comprising:

[0030] The acquisition module is used to acquire noisy observation data from the satellite;

[0031] The estimation module is used to construct a normal equation system using the noisy observation data and to estimate the spherical harmonic coefficients and order variance of the gravity field using the least squares adjustment algorithm.

[0032] The inversion module is used to obtain the Earth's gravity field inversion results by calculating the residuals between the recovery model and the reference model, and to perform inversion accuracy analysis on the Earth's gravity field inversion results.

[0033] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clocks as described above.

[0034] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clocks as described above.

[0035] The Earth gravity field inversion method based on optical clocks in inter-satellite tracking mode provided by this invention quantitatively evaluates the impact of optical clocks on the accuracy of Earth gravity field inversion under different orbital altitudes and noise levels through a closed-loop simulation method. This provides a theoretical basis for the application of optical clocks in high-precision gravity field measurement and suggests that future research should further optimize the clock noise model and explore multi-sensor fusion methods to improve the inversion accuracy of higher-order gravity fields. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0037] Figure 1 This is one of the flowcharts of the Earth's gravity field inversion method based on optical clocks in inter-satellite tracking mode provided by the present invention;

[0038] Figure 2 This is the second flowchart of the Earth's gravity field inversion method based on optical clocks in the inter-satellite tracking mode provided by the present invention.

[0039] Figure 3 This is a schematic diagram of the principle of satellite-to-satellite tracking mode inversion of the Earth's gravity field based on optical clock provided by the present invention;

[0040] Figure 4 This is a comparison chart of the variance of clock errors at different orbital altitudes of 229km provided by this invention;

[0041] Figure 5 This invention provides a comparison chart of geoid errors at different clock altitudes of 229km.

[0042] Figure 6 This is a comparison chart of the variance of clock errors at different orbital altitudes of 400km provided by the present invention;

[0043] Figure 7 This invention provides a comparison chart of geoid errors at different clock altitudes of 400km.

[0044] Figure 8 This is a schematic diagram of the Earth gravity field inversion system based on an optical clock in the inter-satellite tracking mode provided by the present invention;

[0045] Figure 9 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0047] This invention utilizes numerical simulation to systematically evaluate the accuracy of retrieving the Earth's gravity field at different orbital altitudes and with varying clock noise levels in a satellite-borne optical clock tracking satellite mode. The simulator takes simulated observation data generated from gravity-like satellite orbits (such as GOCE and GRACE orbits) as input and employs a rigorous least-squares method to estimate the gravity field coefficients. The accuracy of the results is evaluated by comparing the coefficient differences between the retrieved model and the reference model.

[0048] Figure 1 This is one of the flowcharts illustrating the Earth's gravity field inversion method based on optical clocks in inter-satellite tracking mode provided in this embodiment of the invention, such as... Figure 1 As shown, it includes:

[0049] Step 100: Acquire noisy observation data from the satellite;

[0050] Step 200: Construct a normal equation system using the noisy observation data, and use the least squares adjustment algorithm to estimate the spherical harmonic coefficients and order variance of the gravity field;

[0051] Step 300: By calculating the residuals between the restored model and the reference model, the Earth's gravity field inversion results are obtained, and the inversion accuracy of the Earth's gravity field inversion results is analyzed.

[0052] Specifically, in order to quantitatively evaluate the performance advantages of optical atomic clocks in measuring the Earth's gravity field in satellite tracking mode, this invention designs and implements a time-domain-based numerical simulation system.

[0053] like Figure 2 As shown, the main steps include the following: First, noisy observation data is used as the core input for gravity field inversion, which consists of signal and noise components. Second, the signal components are synthesized using spherical harmonic functions along a predetermined satellite orbit through a reference gravity field model, while the noise components are generated based on the quantum noise characteristics of an optical atomic clock. Subsequently, a system of normal equations is constructed using the noisy observation data, and a rigorous least squares adjustment algorithm is used to estimate the spherical harmonic coefficients and their order variances of the gravity field. Finally, the inversion accuracy is quantitatively evaluated and the performance is analyzed by calculating the residuals between the recovered model and the reference model.

[0054] As is understandable, an optical clock is a frequency standard device based on the frequency of electron transitions in atoms within the electromagnetic spectrum, enabling unprecedented precision in frequency and time measurement. Since its initial development in the 1990s, the performance of optical clocks has significantly improved. Currently, optical clocks operating in multiple laboratories worldwide have reached 10... -18 Even higher levels of uncertainty. For example, two independent ytterbium optical lattice clocks (multi-atom systems) achieved 1.4 × 10⁻⁶. -18 The uncertainty is 9.4 × 10⁻⁶, while another single-atom system optical clock reaches an even higher level of 9.4 × 10⁻⁶. -19 The uncertainty and 1.2 × 10 -15 The instability is defined as / τ, where τ is the average time in seconds. Furthermore, researchers are working to develop compact optical clocks suitable for mobile vehicles and field measurements. These clocks have been installed in car trailers and have achieved a speed of 7.4 × 10⁻⁶. -17 The uncertainty.

[0055] To achieve ultra-high precision clock comparison over long distances, frequency transmission technologies have been extensively researched and developed, including fiber optics, microwaves, free-space laser beams, and time synchronization methods based on navigation satellites. Among these, fiber optic frequency links have achieved 2.5 × 10⁻⁶ precision over a distance of 1400 kilometers. -19 The fractional uncertainty perfectly satisfies 10 -18Even higher precision clock comparisons are needed. The two-way optical laser link has also been experimentally verified, with its free-space frequency transmission uncertainty reaching 10-1. -18 Microwave links, as an efficient and cost-effective technology, are being used for comparisons between space-based and ground-based atomic clocks, and hold promise for achieving 10... -16 The uncertainty. Time synchronization technology based on navigation satellites can also be used for long-distance links, achieving 10 over an average period of several days. -16 The accuracy of these technologies will continue to improve to support long-distance clock links in various scenarios. Optical clocks are opening up new frontiers in geodesy, with performance comparable to classical geodetic methods in inferring long-distance altitude information, achieving accuracy at the centimeter to decimeter level. This makes optical clocks valuable for unifying local altitude systems or constructing globally consistent elevation systems.

[0056] High-performance optical clocks can be used to test fundamental laws of physics, redefine time scales, and are closely related to various geodesy and geophysical applications, such as the realization of spatiotemporal reference systems, monitoring of vertical surface motion, and determination of the Earth's gravitational field. Optical clocks introduce a completely new measurement concept to physical geodesy: clock-based relativistic geodesy (or chronogeodesy). The successful implementation of the CHAMP, GRACE, and GOCE satellite gravity programs has provided crucial technical support for exploring the fine structure of the Earth's gravitational field and its time-varying nature. Long-distance, ultra-high-precision clock frequency transmission technology offers new insights for the future development of this model.

[0057] like Figure 3 As shown, by placing optical clocks on two satellites and connecting them via a dedicated link, the frequency difference ratio can be used to determine the optical clock frequency. Obtain the gravitational potential difference between the two satellites The formula is as follows:

[0058] (1)

[0059] in , It refers to the optical clock frequencies carried by satellites A and B. Time-frequency signals can be transmitted via the microwave link between the two satellites for calculation. c It's the speed of light, a higher-order term. The value of gravitational potential difference can be directly obtained based on this formula.

[0060] The Earth's gravitational field model is usually represented by a spherical harmonic function expansion. The gravitational potential V at any point on the Earth's surface can be described as:

[0061] (2)

[0062] Where GM is the Earth's gravitational constant, and R is the equatorial radius of the reference ellipsoid. r , θ , λ These are spherical coordinates of a point. n , m These are the order and degree of the spherical harmonic function. P nm It is a fully normalized associated Legendre function. C mn, S mn These are spherical harmonic coefficients, which are unknown parameters to be estimated in gravity field recovery. The instantaneous positional difference between the two satellites can be obtained from equation (3):

[0063] (3)

[0064] To obtain a more intuitive expression, we adjust the order of summation in the above equation and assume that the spherical harmonic series expands to a finite order n, resulting in the following equation: (4)

[0065] In the above equation, the coefficients of the unknowns on the right-hand side and The satellite position at time t can be used as a reference. If the gravitational potential difference between the two stars along their orbits can be precisely obtained, then... This allows us to use the observed values ​​to find the best estimate of the unknown position coefficients.

[0066] Furthermore, this invention selected two orbital altitudes, 229 km and 400 km, for simulation to construct a low-low satellite tracking constellation. The 229 km orbital altitude is typical of the European Space Agency's (ESA) GOCE mission, known for its low altitude and high spatial resolution, effectively capturing high-frequency signals from Earth's gravitational field. The 400 km orbital altitude corresponds to the typical orbit of the GRACE mission, which measures mid-to-low frequency signals from Earth's gravitational field through a two-satellite formation, resulting in relatively lower spatial resolution. Simulations at these two orbital altitudes were conducted to evaluate the performance of the optical clock under different satellite tracking modes.

[0067] Table 1 Satellite parameters for low-low satellite tracking mode

[0068]

[0069] Table 1 presents the simulated orbital parameters, with the interstellar distance set at 220 km. Using a 30-day period and a 5-second sampling rate, a series of raw gravity potential observations were generated using GOCO03s as the static field. These observations were then solved according to equation (1). The atomic clock reference frequency fSetting it to 411042129776400.41Hz, the following can be calculated. f 0 is taken as the truth value.

[0070] While the performance of atomic clocks in time and frequency transmission is relatively stable, some random errors still exist. Practice has shown that the power-law spectral model can effectively describe this noise.

[0071] (5)

[0072] In the formula, For Fourier frequency, This is a constant characterizing the strength of various noise levels, taking different values ​​for different atomic clocks. In this study, clock noise generation is modeled based on the quantum noise characteristics of optical clocks. Optical clock noise mainly manifests as frequency uncertainty, which can typically be described using a white noise model. We assume the clock noise is white noise and simulate it at different noise levels. We set the clock noise intensities as follows: , , , Using the Stable32 software commonly used in time-frequency signal processing, different noise intensity coefficients were set. The simulation generates optical clock noise signals and instrument error noise for each mechanism, and then superimposes them onto the frequency difference. The system generates noisy observation data, then solves for the gravitational potential difference obtained from the simulated observation, and finally uses the least squares method to obtain the gravitational potential coefficient obtained from the final observation.

[0073] To quantitatively assess the impact of optical atomic clock errors on the accuracy of gravity field inversion, the differences between the inverted gravity field and the reference gravity field at different clock noise levels and flight altitudes were analyzed. First, a binary star formation orbit was simulated based on the orbital parameters in Table 1, with a star spacing of 220 km, an orbital period of 30 days, and a sampling interval of 5 seconds. A simplified dynamic model was used to ensure orbital accuracy. Using GOCO03s as the reference static gravity field model, a series of original gravity potential observations were generated along the simulated orbit, and the gravity potential difference was obtained through spherical harmonic function synthesis. The frequency difference was calculated according to equation (1). Among them, the atomic clock reference frequency f 0 is set to 4.11042 × 10¹⁴ Hz. (Frequency difference) The simulated clock noise sequence is superimposed on the noise level, with the noise intensity set to 10. -17 10 -18 10 -19 and 10 -20The noise model uses white noise and considers frequency stability and systematic errors. Based on the noisy frequency difference data, the gravity potential difference value obtained from the simulated observation is solved, and the least squares adjustment method is used to invert the gravity field model, restoring it to order 60. Simulation experiments were conducted at orbital altitudes of 229 km and 400 km, and the order variance, geoid error, and gravity anomaly maps of the inverted gravity field and the reference gravity field were plotted, as shown below. Figure 4 As shown.

[0074] At an orbital altitude of 229 km, the uncertainty of the optical clock error is 1.0 × 10⁻⁶. -18 At that time, the root mean square error of the spherical harmonic coefficients calculated by the inversion solution was less than 1.0 × 10⁻⁶. -17 The baseline value decreased by about an order of magnitude overall, but compared to 1.0 × 10 -19 Compared to the solution results under high-precision conditions, its root mean square error still increases significantly by an order of magnitude. In 10... -17 At noise levels, the order variance of the middle and high order components approximates the Koala curve, while at 10... -19 and 10 -20 At lower noise levels, the order variance decreases significantly, indicating that the inversion accuracy is further improved under low noise levels. Figure 5 As shown.

[0075] Table 2. Geoid Error Values ​​at Different Clock Altitudes (229km)

[0076]

[0077] As shown in Table 2, the inversion results under different optical clock errors exhibit latitudinal differences, with the most significant errors in the low latitudes and equatorial regions, accompanied by a noticeable striping effect. This may stem from systematic errors introduced by limitations in satellite orbit repetition periods or data processing algorithms. Numerical results show that the geoid error is closely related to the magnitude of the clock error. In e -17 At the level of clock error, the root mean square error (RMS) is 0.109 meters, close to the decimeter level, mainly affected by clock error and striping effect; while at e -18 At and below the centimeter level, RMS decreases to the centimeter or even sub-centimeter level, indicating that the reduction in clock error significantly improves accuracy. To further reduce error, clock error accuracy can be optimized (controlled within e...). -18 (and below), improving the order of the gravity field model, refining data processing methods, and further enhancing accuracy through multi-source data fusion. Through these measures, the geoid error can be stably reduced to the centimeter or even sub-centimeter level, meeting the requirements of high-precision measurements, such as... Figure 6 As shown.

[0078] At an orbital altitude of 400 km, the order variance of the inverted gravity field is generally higher than that at an orbital altitude of 229 km. Especially in the medium and high order part (20 < n < 60), the difference is more significant, but all order variances are still below the reference error curve. The geoid error shows that the inversion accuracy at an orbital altitude of 400 km is generally lower than that at an orbital altitude of 229 km, but at low noise levels (10 -19 and 10 -20 ), it can still better reflect the basic characteristics of the global gravity field. Generally speaking, the influence of orbital altitude on inversion accuracy is more obvious in the medium and high order part, while the accuracy of the low order part is mainly affected by the clock noise level, as Figure 7 shown.

[0079] Table 3 Geoid error values at different clock errors for an orbital altitude of 400 km

[0080]

[0081] As shown in Table 3, in the data at an orbital altitude of 400 km, although the order variance of the gravity field parameters is below the Kaula curve, indicating a relatively high accuracy of the gravity field model itself, the performance of the geoid error is generally larger compared to that at an orbital altitude of 229 km. At the e -17 clock error magnitude, the root mean square (RMS) of the error reaches 1.172 m, significantly higher than 0.109 m at 229 km; while at the e -18 and lower magnitudes, the error gradually decreases, being 0.044 m at e -18 , 0.0016 m at e -19 , and 0.0012 m at e -20 . This change shows that an increase in orbital altitude will amplify the influence of clock error on the error, especially at the e -17 magnitude, where the error increases significantly. However, as the clock error decreases to e -18 and lower, the error rapidly decreases to the centimeter or even sub - centimeter magnitude, indicating that high - precision time synchronization can effectively offset the negative impact brought by the increase in orbital altitude. Generally speaking, the error performance of the 400 - km orbit is similar to that of the 229 - km orbit, but affected by the orbital altitude, the error is larger at the e -17 magnitude, further highlighting the importance of clock error accuracy in high - orbit measurements.

[0082] At an orbital altitude of 229 km, the inversion accuracy is significantly better than that at 400 km, especially in the middle and high order parts (20 < n < 60). This result is consistent with the experience of the GOCE mission. A lower orbital altitude can get closer to the Earth's surface, thus capturing more high-frequency gravity signals. In addition, the measurements at a lower orbital altitude are less affected by atmospheric drag and non-gravitational perturbations, further improving the inversion accuracy. However, a lower orbital altitude also brings higher fuel consumption and a shorter satellite lifespan, which needs to be weighed in actual missions.

[0083] At an orbital altitude of 400 km, the inversion accuracy is generally lower than that at 229 km, especially in the middle and high order parts. This result is consistent with the experience of the GRACE mission. Although a higher orbital altitude can cover a wider area, it has a lower sensitivity to high-frequency gravity signals. In addition, the measurements at a higher orbital altitude are more easily affected by atmospheric drag and non-gravitational perturbations, which may lead to a decrease in the inversion accuracy. Nevertheless, at a low noise level (10 -19 and 10 -20 ), the optical clock can still well reflect the basic characteristics of the global gravity field, indicating its potential in wide-area measurements.

[0084] The errors of this invention mainly come from clock errors, orbital altitude, and noise models. At a low noise level, the influence of clock errors on the inversion accuracy is significantly reduced, indicating that the high-frequency stability of the optical clock is a key factor in improving the accuracy. However, in the high order part, the inversion accuracy is still affected by the noise model. Future research can further optimize the noise model, such as considering flicker noise and random walk noise, to improve the inversion accuracy in the high order part.

[0085] This invention quantitatively evaluates the influence of the errors of optical atomic clocks on the inversion accuracy of the gravity field through numerical simulations, and focuses on analyzing the differences between the inverted gravity field and the reference gravity field under different clock noise levels and orbital altitudes. The research results show that the optical atomic clock exhibits excellent sensitivity in the low order part (n < 20). Even at a high noise level (10 -17 ), the inversion accuracy is still significantly higher than that of traditional gravity measurement methods. In the middle and high order parts (20 < n < 60), the influence of clock noise on the inversion accuracy gradually increases, but the errors of all inversion results are generally lower than the reference error curve, indicating that the inversion accuracy meets the theoretical expectations. Especially at a low noise level (10 -19 and 10 -20The inversion results show high consistency with the reference model globally. The impact of orbital altitude on inversion accuracy is more pronounced in the mid-to-high order regions. At an orbital altitude of 229 km, the inverted gravity field maintains low error in the lower order regions, and the results at low noise levels effectively capture local gravity anomalies. At an orbital altitude of 400 km, the inversion accuracy is generally lower than at 229 km, but it still reflects the basic characteristics of the global gravity field well under low noise conditions. Overall, optical atomic clocks have significant advantages in low-order gravity field measurements, especially in terms of high inversion accuracy at low orbital altitudes and low noise levels.

[0086] The Earth gravity field inversion system based on optical clocks in the inter-satellite tracking mode provided by this invention is described below. The Earth gravity field inversion system based on optical clocks in the inter-satellite tracking mode described below can be referred to in correspondence with the Earth gravity field inversion method based on optical clocks in the inter-satellite tracking mode described above.

[0087] Figure 8 This is a schematic diagram of the Earth gravity field inversion system based on an optical clock in the inter-satellite tracking mode provided in this embodiment of the invention, as shown below. Figure 8 As shown, it includes: an acquisition module 81, an estimation module 82, and an inversion module 83, wherein:

[0088] The acquisition module 81 is used to acquire noisy observation data from the satellite; the estimation module 82 is used to construct a normal equation system using the noisy observation data and to estimate the spherical harmonic coefficients and order variance of the gravity field using the least squares adjustment algorithm; the inversion module 83 is used to obtain the inversion results of the Earth's gravity field by calculating the residuals between the recovery model and the reference model, and to analyze the inversion accuracy of the Earth's gravity field inversion results.

[0089] Figure 9 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 9 As shown, the electronic device may include a processor 910, a communication interface 920, a memory 930, and a communication bus 940. The processor 910, communication interface 920, and memory 930 communicate with each other via the communication bus 940. The processor 910 can call logical instructions in the memory 930 to execute an Earth gravity field inversion method based on an optical clock-based inter-satellite tracking mode. This method includes: acquiring noisy observation data from satellites; constructing a normal equation system using the noisy observation data; estimating the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; obtaining the Earth gravity field inversion result by calculating the residual between the restored model and the reference model; and analyzing the inversion accuracy of the Earth gravity field inversion result.

[0090] Furthermore, the logical instructions in the aforementioned memory 930 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0091] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the Earth gravity field inversion method based on the optical clock inter-satellite tracking mode provided by the above methods. The method includes: acquiring noisy observation data of the satellite; constructing a normal equation system using the noisy observation data; estimating the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; obtaining the Earth gravity field inversion result by calculating the residual between the restored model and the reference model; and performing an inversion accuracy analysis on the Earth gravity field inversion result.

[0092] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the Earth gravity field inversion method based on optical clocks in the inter-satellite tracking mode provided by the above methods. The method includes: acquiring noisy observation data from satellites; constructing a normal equation system using the noisy observation data; estimating the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; obtaining the Earth gravity field inversion result by calculating the residual between the restored model and the reference model; and performing an inversion accuracy analysis on the Earth gravity field inversion result.

[0093] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0094] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting the Earth's gravity field under inter-satellite tracking mode based on optical clocks, characterized in that, include: Acquire noisy observation data from satellites; A system of normal equations is constructed using the noisy observation data, and the least squares adjustment algorithm is used to estimate the spherical harmonic coefficients and order variance of the gravity field. The Earth's gravity field inversion results are obtained by calculating the residuals between the restored model and the reference model, and the inversion accuracy of the Earth's gravity field inversion results is analyzed. Acquire noisy observation data from satellites, including: The noisy observation data includes signal components and noise components; The signal components are obtained by spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, and the noise components are generated by modeling the quantum noise characteristics based on an optical atomic clock. The signal components are obtained by spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, including: Optical clocks were installed on satellites A and B respectively and connected by a dedicated link. The frequency difference ratio was used to determine the optical clocks. Obtain the gravitational potential difference between the two satellites : in , These are the frequencies of the optical clocks mounted on satellites A and B, respectively. Calculations are made based on time-frequency signals transmitted via the microwave link between the two satellites. c It's the speed of light. It contains c -4 Higher-order terms of magnitude Omitted; The Earth's gravitational field model uses a spherical harmonic function expansion, and the gravitational potential V at any point on the Earth's surface is described as follows: in It is the Earth's gravitational constant. It is the equatorial radius of the reference ellipsoid. These are spherical coordinates of a point. and These are the order and degree of the spherical harmonic function. It is a fully normalized associated Legendre function. and These are spherical harmonic coefficients, which are unknown parameters to be estimated in the recovery of the gravitational field; A system of normal equations is constructed using the noisy observation data, and the least squares adjustment algorithm is used to estimate the spherical harmonic coefficients and order variance of the gravity field, including: The instantaneous positional difference between the two satellites is: Further adjusting the order of summation and assuming that the spherical harmonic coefficients can be expanded to a finite order n, we obtain the following equation: In the above equation, the coefficients of the unknowns on the right-hand side and The satellite position at time t Obtained precisely.

2. The method for inverting the Earth's gravity field in inter-satellite tracking mode based on optical clocks according to claim 1, characterized in that, Also includes: A power-law spectral model is used to describe the time-frequency randomness error of atomic clocks. : in, For Fourier frequency, It is a constant characterizing the strength of various noises, and takes different values ​​for different atomic clocks.

3. A system for retrieving the Earth's gravity field in an inter-satellite tracking mode based on an optical clock, based on the method for retrieving the Earth's gravity field in an inter-satellite tracking mode based on an optical clock as described in claim 1 or 2, characterized in that, include: The acquisition module is used to acquire noisy observation data from the satellite; The estimation module is used to construct a normal equation system using the noisy observation data and to estimate the spherical harmonic coefficients and order variance of the gravity field using the least squares adjustment algorithm. The inversion module is used to obtain the Earth's gravity field inversion results by calculating the residuals between the recovery model and the reference model, and to perform inversion accuracy analysis on the Earth's gravity field inversion results.

4. The Earth gravity field inversion system based on optical clocks in inter-satellite tracking mode according to claim 3, characterized in that, The acquisition module is specifically used for: The noisy observation data includes signal components and noise components; The signal components are obtained by spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, and the noise components are generated by modeling the quantum noise characteristics based on an optical atomic clock.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clock as described in claim 1 or 2.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clocks as described in claim 1 or 2.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clocks as described in claim 1 or 2.

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