Earth gravitational field inversion method in inter-satellite tracking mode based on light clock

Abstract

The invention provides an earth gravitational field inversion method in an inter-satellite tracking mode based on an optical clock, and the method comprises the steps: systematically evaluating the earth gravitational field inversion precision of different orbit heights and different optical clock noise levels in a satellite-borne optical clock satellite tracking satellite mode through a numerical simulation method. The simulator uses simulation observation data generated by similar gravity satellite orbits (such as GOCE and GRACE orbits) as input, adopts a strict least square method to estimate gravity field coefficients, and performs precision evaluation on results by comparing coefficient differences between an inversion model and a reference model. Through a numerical simulation method, the precision of inverting the earth gravitational field based on the satellite-satellite tracking mode of the light clock is systematically evaluated, and the potential of the light clock in high-precision gravitational field measurement is verified. The optical clock noise model and the multi-sensor fusion method are further optimized in future research, so that the inversion precision of the high-order gravitational field is improved, and more accurate data support is provided for earth science and global climate change research.

Description

Technical Field

[0001] The present invention relates to the technical field of the Earth's gravity field, and in particular to an Earth's gravity field inversion method in an inter-satellite tracking mode based on an optical clock. Background Art

[0002] Accurately measuring the Earth's gravity field is of great significance in the field of Earth science, for example, in monitoring global sea level rise, optimizing ocean circulation models, and studying geodynamics. In recent years, breakthroughs in satellite gravity missions have promoted the development of Earth's gravity field research. Among them, the successful implementation of satellite gravity programs such as GRACE (Gravity Recovery and Climate Experiment) and its subsequent GRACE-FO and GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) have provided important data support for gravity field research. Currently, satellite gravity research focuses on upgrading onboard sensor systems, laser interferometry ranging technology, multi-satellite observation systems such as the Bender satellite formation, and optimizing background models to reduce interference from high-frequency atmospheric and ocean mass changes, etc., to improve the performance of future gravity measurement satellites.

[0003] In recent years, breakthroughs in quantum optics have provided an opportunity for the development of new gravity sensors and the realization of new measurement concepts. Since optical clocks can provide extremely high-precision frequency information, by deploying optical clocks at different locations, it is possible to observe tiny frequency changes caused by gravitational potential differences (gravitational redshift effect). This principle has been applied to the measurement of gravitational potential differences on Earth. [6] The obtained gravity potential difference can be directly converted into elevation difference. In geodesy, gravity potential value is the core parameter of physical height measurement. For elevation measurement, the next stage goal is to achieve a unified standard of 1 cm accuracy. Currently, the most advanced optical clock has reached 1.0×10 -18 Even higher frequency uncertainty, equivalent to 0.1 m 2 / s 2 The potential accuracy and elevation resolution of 1.0 cm are significantly higher than the unified standard of 1 cm accuracy, and are highly consistent with the 1 mm position accuracy required by the Global Geodetic Observing System (GGOS). Therefore, optical clocks are regarded as a new geodetic tool with great potential and can be widely used 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 with the indirect measurement in traditional measurement methods, this direct measurement method not only improves the measurement accuracy, but also opens up a new way for high-resolution unified modeling of the global gravity field. With a resolution of up to 10 -18Even higher frequency stability can capture minute changes in the gravitational potential, offering important applications in areas such as crustal movement monitoring, polar glacier changes, and global sea level rise observations. The potential of optical clock technology to improve Earth's gravity field has attracted widespread attention in the physics, geodesy, and earth science communities. Summary of the Invention

[0004] The present invention provides an Earth gravity field inversion method in an inter-satellite tracking mode based on an optical clock, so as to solve the defects existing in the prior art.

[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: Obtaining noisy observation data from satellites; The normal equation system is constructed using the noisy observation data, and the parameters of the spherical harmonic coefficients and order variance of the gravity field are estimated using the least squares adjustment algorithm; By calculating the residual between the restored model and the reference model, the inversion result of the Earth's gravity field is obtained, and the inversion accuracy of the inversion result of the Earth's gravity field is analyzed.

[0006] 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 obtain noisy observation data of a satellite, comprising: The noisy observation data includes a signal component and a noise component; The signal component is obtained by performing spherical harmonic integration along a predetermined satellite orbit with reference to a gravity field model, and the noise component is generated by modeling the quantum noise characteristics based on an optical atomic clock.

[0007] 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. The signal components are obtained by performing spherical harmonic synthesis along a predetermined satellite orbit using a reference gravity field model, including: Optical clocks are placed on satellite A and satellite B respectively and connected by a dedicated link. Get the gravitational potential difference between the two satellites :

[0008] in 、 are the frequencies of the optical clocks carried by satellites A and B respectively, Calculated by the time-frequency signal transmitted by the microwave link between the two satellites, c is the speed of light, Is included c -4 Higher-order terms of magnitude, higher-order terms is omitted; The Earth's gravity field model is expressed using spherical harmonic function expansion. The gravitational potential V at any point on the Earth's surface is described as:

[0009] in is the Earth's gravitational constant, is the equatorial radius of the reference ellipsoid, are the spherical coordinates of the point, and is the order and degree of the spherical harmonics, is the fully normalized associated Legendre function, and are the spherical harmonic coefficients, which are unknown parameters to be estimated in gravity field recovery.

[0010] 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. The method uses the noisy observation data to construct a normal equation system and adopts a least squares adjustment algorithm to perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field, including: The instantaneous phase difference between the two satellites is:

[0011] Further adjusting the order of summation and assuming that the spherical harmonic coefficients are expanded to a finite order n, we obtain the following equation:

[0012] In the above formula, the unknown coefficient on the right side of the equation is and The satellite position at the corresponding time t Accurately obtained.

[0013] 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 further includes: Using the power-law spectrum model to describe the random time and frequency errors of atomic clocks :

[0014] in, is the Fourier frequency, It is a constant that characterizes the strength of various noises and has different values ​​for different atomic clocks.

[0015] In a second aspect, the present invention further provides an Earth gravity field inversion system in an inter-satellite tracking mode based on an optical clock, comprising: An acquisition module is used to obtain satellite observation data containing noise; An estimation module is used to construct a normal equation system using the noisy observation data and perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; The inversion module is used to obtain the inversion results of the Earth's gravity field by calculating the residual between the restored model and the reference model, and to perform inversion accuracy analysis on the inversion results of the Earth's gravity field.

[0016] In a third aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements any of the above-described methods for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock.

[0017] In a fourth aspect, 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 an optical clock as described in any of the above.

[0018] The present invention provides an optical clock-based method for inverting the Earth's gravity field in the inter-satellite tracking mode. Based on a closed-loop simulation method, the method quantitatively evaluates the impact of optical clocks on the accuracy of Earth's gravity field inversion at different orbital altitudes and noise levels. This provides a theoretical basis for the application of optical clocks in high-precision gravity field measurements, and recommends that future research further optimize the clock noise model and explore multi-sensor fusion methods to improve the inversion accuracy of high-order gravity fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0020] Figure 1 This is one of the flow charts of the method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock provided by the present invention; Figure 2 This is the second flow chart of the method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock provided by the present invention; Figure 3 This is a schematic diagram of the principle of inverting the Earth's gravity field using the satellite-satellite tracking mode based on an optical clock provided by the present invention; Figure 4 This is a comparison chart of the variance of clock errors at different orbital altitudes of 229 km provided by the present invention; Figure 5 This is a comparison chart of geoid errors at different clock errors at 229km track altitudes provided by the present invention; Figure 6 This is a comparison chart of the variance of clock errors at different orbital altitudes of 400 km provided by the present invention; Figure 7 This is a comparison chart of geoid errors at different clock errors at 400km orbital altitudes provided by the present invention; Figure 8 Schematic diagram of the structure of the Earth gravity field inversion system in the inter-satellite tracking mode based on the optical clock provided by the present invention; Figure 9 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0021] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0022] This paper systematically evaluates the accuracy of Earth's gravity field inversion using numerical simulations for different orbital altitudes and different optical clock noise levels in a spaceborne optical clock satellite tracking satellite mode. The simulator uses simulated observational data generated by gravity-like satellite orbits (such as the GOCE and GRACE orbits) as input and employs a rigorous least-squares approach to estimate gravity field coefficients. The accuracy of the results is assessed by comparing the coefficient differences between the inversion model and a reference model.

[0023] Figure 1 FIG. 1 is a flow chart of a method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock according to an embodiment of the present invention. Figure 1 Shown, including: Step 100: Obtaining satellite observation data containing noise; Step 200: constructing a normal equation system using the noisy observation data, and performing parameter estimation on the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; Step 300: Obtain the inversion result of the Earth's gravity field by calculating the residual between the restored model and the reference model, and perform inversion accuracy analysis on the inversion result of the Earth's gravity field.

[0024] Specifically, in order to quantitatively evaluate the performance advantages of optical atomic clocks in measuring the Earth's gravity field in satellite tracking mode, the present invention designs and implements a time-domain based numerical simulation system.

[0025] like Figure 2As shown in the figure, the main key steps are as follows: first, the noisy observation data are used as the core input for gravity field inversion, and these data consist of signal components and noise components; secondly, the signal component is synthesized as a spherical harmonic function along the predetermined satellite orbit through the reference gravity field model, while the noise component is generated based on the quantum noise characteristics of the optical atomic clock; then, the noisy observation data are used to construct the normal equation system, and a rigorous least squares adjustment algorithm is used to estimate the parameters of the gravity field spherical harmonic coefficients and their order variances; finally, the inversion accuracy is quantitatively evaluated and the performance is analyzed by calculating the residual between the restored model and the reference model.

[0026] It is understood that optical clocks are frequency standard devices based on the frequency of electron transitions in atoms in the optical range of the electromagnetic spectrum, which can measure frequency and time with unprecedented accuracy. Since their initial development in the 1990s, the performance of optical clocks has improved significantly. Currently, there are more than 10 optical clocks operating in many laboratories around the world. -18 Even higher uncertainty levels can be achieved. For example, two independent ytterbium optical lattice clocks (multi-atom systems) have achieved an uncertainty of 1.4×10 -18 The uncertainty of another single-atom system optical clock reached 9.4×10 -19 The uncertainty is 1.2×10 -15 / τ instability, where τ is the averaging time in seconds. In addition, researchers are also working on developing compact optical clocks suitable for mobile vehicles and field measurements. Such optical clocks have been installed in car trailers and have achieved 7.4×10 -17 uncertainty.

[0027] To achieve long-distance ultra-high-precision clock comparison, frequency transmission technologies have been extensively researched and developed, including optical fiber, microwave, free-space laser beam, and navigation satellite-based time synchronization methods. Among them, optical fiber frequency links have achieved a 2.5×10 -19 The fractional uncertainty of -18 Even higher precision clock comparison is needed. Bidirectional optical laser links have also been experimentally verified, and the uncertainty of their free space frequency transmission can reach 10 -18 Microwave links are an efficient and economical technology used to compare atomic clocks in space with those on the ground, and are expected to achieve 10 -16 Time synchronization technology based on navigation satellites can also be used for long-distance links, achieving an average time of 10 over several days. -16These technologies will continue to improve to support long-distance clock links in a variety of scenarios. Optical clocks are opening up new areas of geodesy. Their performance in inferring long-distance altitude information is comparable to that of classical geodetic methods, with accuracy reaching centimeters to decimeters. This makes optical clocks valuable for unifying local altitude systems or building a globally consistent elevation system.

[0028] High-performance optical clocks can be used to test fundamental laws of physics and redefine the time scale. They are also closely related to a variety of geodetic and geophysical applications, such as the implementation of space-time reference systems, monitoring vertical surface motion, and determining the Earth's gravitational field. Optical clocks introduce a new measurement concept to physical geodesy: clock-based relativistic geodesy (or timing geodesy). The successful implementation of the CHAMP, GRACE, and GOCE satellite gravity missions has provided important technical support for exploring the fine structure of the Earth's gravitational field and its time-varying properties. Long-distance, ultra-high-precision clock frequency transmission technology offers new insights for the future development of this model.

[0029] like Figure 3 As shown in the figure, by placing optical clocks on two satellites and connecting them through a dedicated link, the frequency difference ratio can be obtained. Get the gravitational potential difference between the two satellites , the formula is as follows: (1) in 、 is the frequency of the optical clocks carried by satellites A and B, It can be calculated by transmitting time-frequency signals through the microwave link between the two satellites. c is the speed of light, a higher-order term is omitted, and the gravitational potential difference value can be directly obtained based on this formula.

[0030] The Earth's gravity field model is usually expressed using spherical harmonic expansion. The gravitational potential V at any point on the Earth's surface can be described as: (2) where GM is the Earth's gravitational constant, R is the equatorial radius of the reference ellipsoid, r , θ , λ are the spherical coordinates of the point, n , m is the order and degree of the spherical harmonics, P nm is the fully normalized associated Legendre function, C mn, S mnare the spherical harmonic coefficients, which are the unknown parameters to be estimated in gravity field recovery. The instantaneous position difference between the two satellites can be obtained by equation (3): (3) In order to obtain a more intuitive expression, the order of summing the terms in the above equation is adjusted, and assuming that the spherical harmonic series is expanded to a finite order n, the following equation can be obtained: (4) In the above formula, the unknown coefficient on the right side of the equation is and The satellite position at the corresponding time t can be If the gravitational potential difference of the binary star along the satellite orbit can be accurately obtained , the best estimate of the unknown coefficients can be obtained by using the observed values.

[0031] Furthermore, the present 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 (ESA) GOCE mission, known for its low altitude and high spatial resolution, effectively capturing high-frequency signals from Earth's gravity field. The 400 km orbital altitude corresponds to the typical orbit of the GRACE mission, which uses a dual-satellite formation to measure medium- and low-frequency signals from Earth's gravity field, with relatively low spatial resolution. Simulations at these two orbital altitudes evaluated the performance of the optical clock in different satellite-tracking modes.

[0032] Table 1 Satellite parameters for low-low satellite tracking mode

[0033] Table 1 gives the simulated orbit parameters, and the satellite spacing is set to 220 km. After generating a series of raw gravity potential observations using GOCO03s as the static field with a 30-day period and a 5-s interval as the sampling rate, we can solve the equation (1) to obtain , the atomic clock reference frequency f Set to 411042129776400.41Hz, you can calculate f 0 and take it as the true value.

[0034] The performance of atomic clock time and frequency transmission is now relatively stable, but some random errors still exist. Practice has shown that the power law spectrum model can better describe this part of the noise: (5) Where, is the Fourier frequency, is a constant that characterizes the strength of various noises and has different values ​​for different atomic clocks. In this study, the generation of clock noise is modeled based on the quantum noise characteristics of optical clocks. The noise of optical clocks is mainly manifested as frequency uncertainty, which can usually be described by a white noise model. Assuming the clock noise is white noise, simulations are performed at different noise levels. The clock noise intensity is set to , , , , using the Stable32 software commonly used in time-frequency signal processing, by setting different noise intensity coefficients , simulate and generate the optical clock noise signal of each institution and the instrument error noise, and superimpose them on the frequency difference The observation data with noise is generated, and then the gravitational potential difference value obtained by the simulated observation is solved, and finally the gravitational potential coefficient obtained by the final observation is obtained by the least square method.

[0035] In order to quantitatively evaluate the impact of optical atomic clock errors on the accuracy of gravity field inversion, the difference between the inverted gravity field and the reference gravity field at different clock noise levels and different flight altitudes was analyzed. First, the binary star formation orbit was simulated based on the orbital parameters in Table 1, with the inter-satellite distance set to 220 km, the orbital period to 30 days, the sampling interval to 5 seconds, and a simplified dynamic model 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 values ​​were obtained through spherical harmonics synthesis. The frequency difference was calculated according to formula (1): , where the atomic clock reference frequency f 0 is set to 4.11042×1014Hz. The simulated clock noise sequence is superimposed on the -17 , 10 -18 , 10 -19 and 10 -20 , the noise model uses white noise and takes frequency stability and systematic error into consideration. Based on the frequency difference data containing noise, the gravity potential difference value obtained by simulated observation is solved, and the gravity field model is inverted using the least squares adjustment method to restore it to the 60th order. The present invention conducted simulation experiments at orbital altitudes of 229km and 400km, and plotted the order variance, geoid error, and gravity anomaly map of the inverted gravity field and the reference gravity field, as shown in Figure 2. Figure 4 shown.

[0036] At an orbital altitude of 229 km, the uncertainty of the optical clock error is 1.0×10 -18 When the inversion solution is 1.0×10 -17 The overall benchmark value is reduced by about one order of magnitude, but it is still the same as 1.0×10 -19Compared with the solution results under high-precision conditions, its root mean square error still increases significantly by one order of magnitude. At 10 -17 noise level, the order variance of the middle and high orders is close to the Kaula curve, while at 10 -19 and 10 -20 noise levels, the order variance decreases significantly, indicating that the inversion accuracy is further improved under low noise levels, as Figure 5 shown.

[0037] Table 2 Geoid error values with different clock errors at an orbital altitude of 229 km

[0038] As shown in Table 2, the inversion results show latitude differences under different optical clock errors. The errors in the low-latitude and equatorial regions are the most significant, and there is an obvious strip effect, which may be due to systematic errors introduced by the satellite orbit repeat period or the limitations of the data processing algorithm. From the numerical results, the performance of the geoid error is closely related to the clock error magnitude. At the e -17 clock error magnitude, the root mean square (RMS) error is 0.109 m, close to the decimeter level, mainly affected by the clock error and the strip effect; while at the e -18 and lower levels, the RMS decreases to the centimeter or even sub-centimeter level, indicating that the reduction of the clock error significantly improves the accuracy. To reduce the error, the clock error accuracy can be optimized (controlled at e -18 and below), the order of the gravity field model can be increased, the data processing method can be improved, and the accuracy can be further enhanced by combining multi-source data fusion. Through these measures, the geoid error can be stably achieved at the centimeter or even sub-centimeter level, meeting the requirements of high-precision measurement, as Figure 6 shown.

[0039] At an orbital altitude of 400 km, the overall order variance of the inverted gravity field is higher than that at an orbital altitude of 229 km, especially in the middle and high orders (20 < n < 60), and the difference is more significant. However, 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 the orbital altitude on the inversion accuracy is more obvious in the middle and high orders, while the accuracy of the low orders is mainly affected by the clock noise level, as Figure 7 shown.

[0040] Table 3 Geoid error values with different clock errors at an orbital altitude of 400 km

[0041] 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 geoid error generally shows a larger value compared to that at an orbital altitude of 229 km. At the e -17 clock error magnitude level, the root mean square (RMS) error reaches 1.172 meters, significantly higher than 0.109 meters at an orbital altitude of 229 km; while at the e -18 and lower magnitude levels, the error gradually decreases, reaching 0.044 meters at e -18 , 0.0016 meters at e -19 , and 0.0012 meters at e -20 . This change indicates that an increase in orbital altitude will amplify the impact of clock error on the error, especially at the e -17 magnitude level, 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 level, 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 level, further highlighting the importance of clock error precision in high - orbit measurements.

[0042] At an orbital altitude of 229 km, the inversion accuracy is significantly better than that at an orbital altitude of 400 km, especially in the middle - and high - order part (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.

[0043] At an orbital altitude of 400 km, the inversion accuracy is generally lower than that at an orbital altitude of 229 km, especially in the middle - and high - order part. 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 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.

[0044] The errors of the present invention mainly come from clock errors, orbital altitudes, and noise models. At low noise levels, the influence of clock errors on the inversion accuracy is significantly reduced, indicating that the high-frequency stability of optical clocks is a key factor in improving accuracy. However, in the higher-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 higher-order part.

[0045] The present 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 optical atomic clocks exhibit excellent sensitivity in the lower-order part (n < 20). Even at high noise levels (10 -17 ), the inversion accuracy is still significantly higher than that of traditional gravity measurement methods. In the middle and higher-order part (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 low noise levels (10 -19 and 10 -20 ), the inversion results are highly consistent with the reference model globally. The influence of orbital altitude on the inversion accuracy is more obvious in the middle and higher-order part. At an orbital altitude of 229 km, the lower-order part of the inverted gravity field maintains a low error, and the inversion results at low noise levels can better capture the characteristics of local gravity anomalies; while at an orbital altitude of 400 km, the inversion accuracy is generally lower than that at 229 km, but it can still better reflect the basic characteristics of the global gravity field at low noise levels. Generally speaking, optical atomic clocks have significant advantages in the determination of the lower-order gravity field, especially with high inversion accuracy at low orbital altitudes and low noise levels.

[0046] The following describes the earth gravity field inversion system in the inter-satellite tracking mode based on an optical clock provided by the present invention. The earth gravity field inversion system in the inter-satellite tracking mode based on an optical clock described below can be mutually referred to and corresponding to the earth gravity field inversion method in the inter-satellite tracking mode based on an optical clock described above.

[0047] Figure 8 is a schematic structural diagram of the earth gravity field inversion system in the inter-satellite tracking mode based on an optical clock provided by an embodiment of the present invention. As shown in Figure 8 it includes: an acquisition module 81, an estimation module 82, and an inversion module 83, where: The acquisition module 81 is used to obtain noisy observation data from the satellite; the estimation module 82 is used to construct a normal equation system using the noisy observation data, and use the least squares adjustment algorithm to perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field; the inversion module 83 is used to obtain the inversion result of the earth's gravity field by calculating the residual between the restored model and the reference model, and perform inversion accuracy analysis on the inversion result of the earth's gravity field.

[0048] Figure 9 An example of a physical structure diagram of an electronic device is shown below. Figure 9 As shown, the electronic device may include: a processor 910, a communication interface 920, a memory 930, and a communication bus 940, wherein the processor 910, the communication interface 920, and the memory 930 communicate with each other via the communication bus 940. The processor 910 may call the logic instructions in the memory 930 to execute an Earth gravity field inversion method in an inter-satellite tracking mode based on an optical clock, the method comprising: acquiring noisy observation data from a satellite; constructing a normal equation system using the noisy observation data, and performing parameter estimation on the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; obtaining an 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.

[0049] Furthermore, the logic 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 portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product, stored in a storage medium, includes instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0050] On the other hand, the present invention also provides a computer program product, which includes a computer program, and the computer program 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 in the inter-satellite tracking mode provided by the above methods. The method includes: obtaining noisy observation data of the satellite; using the noisy observation data to construct a normal equation system, and using the least squares adjustment algorithm to perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field; obtaining the Earth gravity field inversion result by calculating the residual between the restored model and the reference model, and performing inversion accuracy analysis on the Earth gravity field inversion result.

[0051] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it is implemented to execute the Earth gravity field inversion method in the inter-satellite tracking mode based on optical clocks provided by the above-mentioned methods. The method includes: obtaining noisy observation data of the satellite; using the noisy observation data to construct a normal equation system, and using the least squares adjustment algorithm to perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field; obtaining the Earth gravity field inversion result by calculating the residual between the restored model and the reference model, and performing inversion accuracy analysis on the Earth gravity field inversion result.

[0052] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0053] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion 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, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock, characterized in that: include: Obtaining noisy observation data from satellites; The normal equation system is constructed using the noisy observation data, and the parameters of the spherical harmonic coefficients and order variance of the gravity field are estimated using the least squares adjustment algorithm; By calculating the residual between the restored model and the reference model, the inversion result of the Earth's gravity field is obtained, and the inversion accuracy of the inversion result of the Earth's gravity field is analyzed.

2. The method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock according to claim 1, characterized in that: Obtain satellite noise observation data, including: The noisy observation data includes a signal component and a noise component; The signal component is obtained by performing spherical harmonic integration along a predetermined satellite orbit with reference to a gravity field model, and the noise component is generated by modeling the quantum noise characteristics based on an optical atomic clock.

3. The method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock according to claim 2, characterized in that: The signal components are obtained by performing spherical harmonic integration along a predetermined satellite orbit with reference to a gravity field model, including: Optical clocks are placed on satellite A and satellite B respectively and connected by a dedicated link. Get the gravitational potential difference between the two satellites : in 、 are the frequencies of the optical clocks carried by satellites A and B respectively, Calculated by the time-frequency signal transmitted by the microwave link between the two satellites, c is the speed of light, Is included c -4 Higher-order terms of magnitude, higher-order terms is omitted; The Earth's gravity field model is expressed using spherical harmonic function expansion. The gravitational potential V at any point on the Earth's surface is described as: in is the Earth's gravitational constant, is the equatorial radius of the reference ellipsoid, are the spherical coordinates of the point, and is the order and degree of the spherical harmonics, is the fully normalized associated Legendre function, and are the spherical harmonic coefficients, which are unknown parameters to be estimated in gravity field recovery.

4. The method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock according to claim 3, characterized in that: The normal equation system is constructed using the noisy observation data, and the least squares adjustment algorithm is used to estimate the parameters of the spherical harmonic coefficients and order variance of the gravity field, including: The instantaneous phase difference between the two satellites is: Further adjusting the order of summation and assuming that the spherical harmonic coefficients are expanded to a finite order n, we obtain the following equation: In the above formula, the unknown coefficient on the right side of the equation is and The satellite position at the corresponding time t Accurately obtained.

5. The method for inverting the Earth's gravity field in the inter-satellite tracking mode based on an optical clock according to claim 1, characterized in that: Also includes: Using the power-law spectrum model to describe the random time and frequency errors of atomic clocks : in, is the Fourier frequency, It is a constant that characterizes the strength of various noises and has different values ​​for different atomic clocks.

6. An Earth gravity field inversion system in inter-satellite tracking mode based on an optical clock, characterized in that: include: An acquisition module is used to obtain satellite observation data containing noise; An estimation module is used to construct a normal equation system using the noisy observation data and perform parameter estimation on the spherical harmonic coefficients and order variance of the gravity field using a least squares adjustment algorithm; The inversion module is used to obtain the inversion results of the Earth's gravity field by calculating the residual between the restored model and the reference model, and to perform inversion accuracy analysis on the inversion results of the Earth's gravity field.

7. The Earth gravity field inversion system in inter-satellite tracking mode based on optical clocks according to claim 6, characterized in that: The acquisition module is specifically used for: The noisy observation data includes a signal component and a noise component; The signal component is obtained by performing spherical harmonic integration along a predetermined satellite orbit with reference to a gravity field model, and the noise component is generated by modeling the quantum noise characteristics based on an optical atomic clock.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for inverting the earth's gravity field in the inter-satellite tracking mode based on an optical clock is implemented as described in any one of claims 1 to 5.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock as described in any one of claims 1 to 5 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for inverting the Earth's gravity field in an inter-satellite tracking mode based on an optical clock as described in any one of claims 1 to 5 is implemented.

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