Low-orbit satellite precise orbit determination method and device considering navigation signal distortion deviation

Abstract

The application discloses a low-orbit satellite precise orbit determination method and device considering navigation signal distortion deviation, and belongs to the technical fields of satellite navigation, satellite precise orbit determination and signal processing. The method is aimed at the high dynamicity of low-orbit satellite operation and complex space environment, function models and random models of a navigation signal distortion deviation estimation method suitable for the low-orbit satellite end are constructed, and high-precision extraction of the navigation signal distortion deviation of the low-orbit satellite end is realized; long-time sequence deviation values extracted are used for precision evaluation and characteristic analysis, and a low-orbit satellite navigation signal distortion deviation correction model is constructed; in the real-time orbit determination process, the correction value is added to the pseudo-range observation equation as a virtual observation value, and the low-orbit satellite precise orbit determination considering the navigation signal distortion deviation is realized. The application effectively eliminates systematic deviation caused by receiver hardware differences, firmware versions and navigation signal characteristics.

Description

Technical Field

[0001] This invention belongs to the fields of satellite navigation, precise satellite orbit determination, and signal processing technology. Specifically, it relates to a method and apparatus for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion and deviation. It can be applied to the precise orbit determination of low-Earth orbit satellites and to the systematic construction and maintenance of low-Earth orbit communication / remote sensing constellations. Background Technology

[0002] Precise orbit determination technology based on the Global Navigation Satellite System (GNSS) has become the primary method for precise orbit determination of Low Earth Orbit (LEO) satellites due to its advantages such as continuous observation, high measurement accuracy, and low cost. Currently, using post-hoc precise ephemeris products released by IGS, the accuracy of LEO satellite precise orbit determination has been gradually improved from the meter level to the centimeter level. Existing research on LEO satellite precise orbit determination mainly focuses on dynamic model refinement, ambiguity fixation, and antenna phase center deviation (PCO / PCV) calibration.

[0003] However, the impact of navigation signal distortion bias (SDB)—that is, downlink signal distortion caused by the non-ideal characteristics of navigation satellite payloads and transmitting devices, resulting in constant term biases of different magnitudes and signs in receivers with different technical parameters—on precise positioning is becoming increasingly apparent. Existing research shows that SDB affects wide-lane ambiguity resolution, standard point positioning (SPP) accuracy, and precise point positioning (PPP) convergence time, and is closely related to receiver type, code correlator spacing settings, and front-end filter bandwidth.

[0004] Current research on SDB (Short-Range Depth) primarily focuses on the ground-based user end. With the rapid development of low-Earth orbit (LEO) communication constellations, inherent differences exist between batches of LEO satellites in terms of receiver hardware models, firmware versions, and manufacturers. This leads to varying degrees of signal distortion even when receiving the same navigation signals at the same frequency. Such distortions not only cause systematic inconsistencies in inter-satellite observations but also significantly impact the accuracy of network-wide joint orbit determination and real-time orbit determination. Furthermore, existing SDB estimation methods designed for ground receivers are difficult to directly apply to LEO satellites, primarily due to the high dynamics of LEO satellite operation, the complex space environment, and the technical challenges of effectively eliminating ionospheric errors, dynamic attitude correction, and accurate subtraction of inter-satellite geometric distances.

[0005] Therefore, it is urgent to develop a navigation signal distortion deviation estimation algorithm and correction model suitable for onboard receivers, taking into account the operational characteristics of low-Earth orbit satellites, and to effectively integrate it into the real-time orbit determination algorithm, so as to further improve the accuracy and reliability of precise orbit determination of low-Earth orbit satellites. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and apparatus for precise orbit determination of low-Earth orbit (LEO) satellites that takes into account navigation signal distortion bias. By constructing a functional model and a stochastic model for estimating the navigation signal distortion bias (SDB) of an LEO satellite onboard receiver, the SDB value is accurately extracted and a correction model is established. Then, in real-time orbit determination, the corrected SDB value is added as a virtual observation value to the pseudorange observation equation, thereby improving the accuracy of precise orbit determination of LEO satellites that takes into account navigation signal distortion bias.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviations, the method comprising:

[0009] Step 1: Collect raw GNSS observation data from low-Earth orbit (LEO) satellites, construct a functional model and a stochastic model for estimating navigation signal distortion bias, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion bias value of the LEO satellite onboard receiver relative to the virtual reference receiver (i.e., absorbing the average influence of hybrid receivers in the network) corresponding to the precision clock bias product and differential code bias product. The functional model and stochastic model for constructing the navigation signal distortion bias correction model include: subtracting satellite clock bias and satellite-end hardware delay from the observation values ​​using the precision clock bias product and the differential code bias product; subtracting the geometric distance between the navigation satellite and the LEO satellite using the LEO satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data; subtracting ionospheric delay error using a three-dimensional ionospheric model; and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy.

[0010] Step 2: Based on the navigation signal distortion deviation value, a correction model is constructed. The on-board receiver of the low-Earth orbit satellite reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account the navigation signal distortion deviation.

[0011] Furthermore, in step 1, after verification, pseudorange observations with abnormal ionospheric residuals are eliminated by using a preset error threshold through residual verification, so as to further eliminate the adverse effects of the ionosphere.

[0012] Furthermore, in step 1, the original observation data includes carrier phase observation data, pseudorange observation data, and navigation satellite ephemeris; in the function model, the pseudorange observation value is represented as a combination of the corrected geometric distance between the receiver and the satellite, the speed of light in vacuum, the receiver clock error, the satellite clock error, the receiver-end hardware delay, the satellite-end hardware delay, the ionospheric delay, the observation noise, and the navigation signal distortion deviation.

[0013] Furthermore, after step 1, the method further includes: constructing a navigation signal distortion deviation sequence based on the extracted multiple navigation signal distortion deviation values; calculating the standard deviation and mean of the navigation signal distortion deviation sequence to evaluate accuracy and stability; selecting the navigation signal distortion deviation sequence values ​​of each satellite at at least two frequencies; comparing and analyzing the magnitude of signal distortion at different frequencies by statistically analyzing the average value of the navigation signal distortion deviation at each frequency; and comparing and analyzing the changing trend of navigation signal distortion deviation between different frequencies by using the time series of the navigation signal distortion deviation at each frequency; selecting the low-orbit satellite navigation signal distortion deviation sequence values ​​of the same frequency; and analyzing the signal distortion degree and volatility of different types of navigation satellites by statistically analyzing the average value and standard deviation of each satellite.

[0014] Furthermore, by utilizing the navigation signal distortion deviation sequence values ​​of different low-Earth orbit satellites, and selecting the navigation signal distortion deviation sequence values ​​of the same type of spaceborne receivers, the average value and corresponding time series of the navigation signal distortion deviation of some satellites are statistically analyzed to understand the differences and trends in signal distortion degree among similar spaceborne receivers. Additionally, by selecting the navigation signal distortion deviation sequence values ​​of different types of spaceborne receivers, the average value and time series of the navigation signal distortion deviation of some satellites are statistically analyzed to understand the response of different types of spaceborne receivers to changes in the same signal.

[0015] Furthermore, in step 2, the low-Earth orbit satellite uses a kinematic method based on pseudorange data to determine its real-time orbit. After adding the navigation signal distortion deviation correction value as a virtual observation value to the pseudorange observation equation, the low-Earth orbit satellite's real-time precise orbit is calculated using sequential least squares or Kalman filtering methods after deducting various error effects with precision products.

[0016] Furthermore, step 2 is followed by orbit determination performance analysis: the real-time precise orbits of the low-Earth orbit satellites without navigation signal distortion correction and with navigation signal distortion correction are compared with the reference orbits, and after conversion to the orbit coordinate system, the root mean square errors in the radial, tangential, and normal directions are calculated to evaluate the real-time precise orbit determination performance of the low-Earth orbit satellites after navigation signal distortion correction; the reference orbits include the post-hoc precise scientific orbits of the low-Earth orbit satellites and the precise orbits calculated by the satellite laser ranging observation system.

[0017] On the other hand, the present invention provides a low-Earth orbit satellite precision orbit determination device that takes into account navigation signal distortion deviation, comprising:

[0018] The calculation module is used to collect raw GNSS observation data from low-Earth orbit (LEO) satellites, construct a functional model and a stochastic model for estimating navigation signal distortion bias, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion bias value of the LEO satellite's onboard receiver relative to the virtual reference receiver (i.e., absorbing the average influence of hybrid receivers in the network) corresponding to the precision clock bias product and differential code bias product. The construction of the functional model and stochastic model for estimating navigation signal distortion bias includes: subtracting satellite clock bias and satellite-end hardware delay from the observation values ​​using the precision clock bias product and the differential code bias product; subtracting the geometric distance between the navigation satellite and the LEO satellite using the LEO satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data; subtracting ionospheric delay error using a three-dimensional ionospheric model; and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy.

[0019] The correction module is used to construct a correction model based on the navigation signal distortion deviation value. The on-board receiver of the low-Earth orbit satellite reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account the navigation signal distortion deviation.

[0020] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviations.

[0021] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviations.

[0022] The beneficial effects of this invention are as follows:

[0023] This invention fully considers the high dynamic operation characteristics of low-Earth orbit satellites and the influence of complex space environments, and constructs a functional model and a stochastic model for the estimation method of navigation signal distortion deviation on low-Earth orbit satellites. For the first time, it achieves high-precision extraction of navigation signal distortion deviation from low-Earth orbit satellite onboard receivers, solving the long-standing technical problem of extraction in this field.

[0024] Using the estimation algorithm proposed in this invention, the long-time navigation signal distortion deviation sequence of low-Earth orbit satellite onboard receivers was extracted and analyzed for the first time. The results revealed the differences and variation patterns of signal distortion between different frequencies, different satellites, and different types of receivers, providing a data foundation for subsequent deviation correction.

[0025] This invention innovatively introduces navigation signal distortion deviation correction values ​​into the real-time precise orbit determination process of low-Earth orbit satellites. The correction values ​​are added as virtual observation values ​​to the pseudorange observation equation, effectively eliminating systematic errors caused by differences in receiver hardware, firmware versions, and navigation signal characteristics. This fills the gap in existing low-Earth orbit satellite orbit determination methods that do not consider navigation signal distortion deviations.

[0026] This invention establishes a navigation signal distortion deviation correction model applicable to low-Earth orbit satellites, significantly improving the real-time orbit determination accuracy of low-Earth orbit satellites that takes into account navigation signal distortion deviation. Attached Figure Description

[0027] Figure 1 The flowchart of the low-Earth orbit satellite precise orbit determination method that takes into account navigation signal distortion deviation is shown in the present invention.

[0028] Figure 2 A schematic diagram of the SDB correction model for low-Earth orbit satellites;

[0029] Figure 3 This is a time-series diagram of the real-time precise orbit determination results before and after correcting the SDB values ​​of each satellite in this embodiment of the invention;

[0030] Figure 4 This is a time-series diagram showing the improvement of real-time precise orbit determination results after 31 days of SDB value correction for each satellite in this embodiment of the invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0032] This invention addresses the high dynamics of low-Earth orbit (LEO) satellite operation and its space environment, fully considering the impact of various errors. It constructs a functional model and a stochastic model for estimating navigation signal distortion bias in LEO satellites, achieving high-precision extraction of LEO satellite navigation signal distortion bias. Furthermore, this algorithm is used to extract and analyze the long-term time-series navigation signal distortion bias characteristics of LEO satellites, and based on this, a navigation signal distortion bias correction model suitable for LEO satellites is constructed. By correcting the navigation signal distortion bias during real-time orbit determination of LEO satellites, the real-time orbit determination accuracy of LEO satellites that takes into account navigation signal distortion bias is improved by at least 5% compared to that that does not. Figure 1 As shown, the precise orbit determination method for low-Earth orbit satellites that takes into account navigation signal distortion deviations provided by the present invention specifically includes:

[0033] Step 1, Precise Extraction of SDB from Low-Earth Orbit Satellite Receiver: Collect raw GNSS observation data from low-Earth orbit satellites, construct a functional model and a stochastic model for the navigation signal distortion deviation estimation method, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion deviation value of the low-Earth orbit satellite receiver relative to the virtual reference receiver (i.e., absorbing the average influence of hybrid type receivers in the station network) corresponding to the precise clock error product and differential code deviation product; wherein, the construction of the functional model and the stochastic model for the navigation signal distortion deviation estimation method includes: using the precise clock error product and the differential code deviation product to deduct the satellite clock error and satellite-end hardware delay in the observation values, using the low-Earth orbit satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data to deduct the geometric distance between the navigation satellite and the low-Earth orbit satellite, and using a three-dimensional ionospheric model to deduct the ionospheric delay error, and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy.

[0034] To evaluate the effectiveness of the correction model, this invention also conducted an accuracy assessment and characteristic analysis of the low-Earth orbit satellite navigation signal distortion deviation sequence: the standard deviation and mean of the navigation signal distortion deviation sequence composed of the navigation signal distortion deviation values ​​were calculated to assess the accuracy and stability, and the differences and trends of navigation signal distortion deviations among different frequencies, different satellites and different receiver types were analyzed.

[0035] Step 2, correction of low-Earth orbit satellite navigation signal distortion deviation: Based on the navigation signal distortion deviation value, a correction model is constructed. The low-Earth orbit satellite onboard receiver reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviation.

[0036] To evaluate the effectiveness of the correction model, this invention also conducted a performance analysis of precise orbit determination for low-Earth orbit satellites that takes into account navigation signal distortion deviations: the real-time precise orbit of the corrected low-Earth orbit satellite was compared with the reference orbit to evaluate the orbit determination performance.

[0037] Furthermore, in step 1:

[0038] Raw GNSS observation data from low-Earth orbit satellites are collected, including carrier phase observation data, pseudorange observation data, and navigation satellite ephemeris. Taking frequency i as an example, the above carrier phase and pseudorange observations are shown in equation (1):

[0039] (1)

[0040] In formula (1) and These represent the pseudorange and phase observations of the spaceborne receiver r at satellite s and frequency i, respectively. The distance between the low-Earth orbit satellite and the navigation satellite is represented by c; c represents the speed of light in a vacuum. and Indicates the onboard receiver and satellite clock bias; and These represent the hardware delay biases associated with the receiver and the satellite, respectively. and These represent the phase delay deviations at the receiver and satellite ends, respectively. This is expressed as ionospheric delay; and These represent the carrier wavelength and ambiguity at frequency i, respectively. and These represent the noise in the pseudorange and phase observations, respectively.

[0041] Considering the existence of navigation signal distortion deviation, the pseudorange observation value shown in equation (1) can be expressed as shown in equation (2).

[0042] (2)

[0043] in: This represents the navigation signal distortion deviation, which is related to receiver type, satellite, and frequency, and is expressed in meters (m).

[0044] Regarding the function model for estimating navigation signal distortion bias, for the original pseudorange observations of the spaceborne GNSS receiver, the satellite clock bias and satellite-end hardware delay included in the observations are deducted using precise clock bias products and DCB products; considering the high dynamic characteristics of low-Earth orbit satellites and their time characteristics, this invention uses post-hoc precise orbit determination data of low-Earth orbit satellites and post-hoc precise orbit data of navigation satellites to deduct the distance between navigation satellites and low-Earth orbit satellites.

[0045] Given the high dynamism of low-Earth orbit (LEO) satellites and their orbits located near the peak ionospheric altitude, traditional two-dimensional thin-layer ionospheric models are difficult to apply directly. To accurately subtract ionospheric delay errors from pseudorange observations, this invention employs the NeQuick-G three-dimensional ionospheric model used in the Galileo system for correction. This model calculates ionospheric delay by numerically integrating electron density along the signal propagation path, theoretically applicable to users at any altitude, and has been verified to have good correction performance in LEO satellite missions such as Swarm. According to the research results of Montenbruck et al., during periods of high solar activity, the NeQuick-G model's ability to correct the tilt total electron content of low-Earth orbit satellites is better than 70% in 87% of cases. This indicates that the model can significantly eliminate most of the ionospheric delay error and keep its residuals at a low level. Furthermore, the study also shows that the NeQuick-G model exhibits stronger applicability during periods of ionospheric calm. Analysis of Swarm-C satellite data indicates that during the period of low solar activity in 2017, the single-frequency positioning accuracy corrected by the NeQuick-G model was even better than the solution results of a dual-frequency ionospheric-free combination. This conclusion further confirms the reliability and advantages of the model selected in this invention in low-Earth orbit satellite scenarios.

[0046] After various error corrections, the pseudorange residual at this point only includes navigation signal distortion bias related to receiver type and receiver clock bias and its hardware delay bias:

[0047] (3)

[0048] In equation (3), Indicates the satellite receiver Compared to precision clock error products and DCB products, the navigation signal distortion deviation is relatively large; Indicates the clock bias of the onboard receiver; This indicates the hardware delay at the receiver end; This represents the distance to stars calculated using precise orbits; Indicates satellite clock bias provided by precision clock bias products; This indicates satellite-side hardware delay correction provided by DCB products; This represents the ionospheric delay calculated by the NEQUICK-G model.

[0049] It should be noted that, in order to ensure the accuracy of the ionospheric delay correction, this invention uses the variance of the ionospheric delay error calculated according to the following formula (4), and selects an empirical value of 0.5. This serves as an outlier removal threshold; if the value exceeds this threshold, the satellite residual value for the current epoch will be removed.

[0050] (4)

[0051] In formula (4) The ionospheric delay calculated by the model, As a scaling factor, This is the calculated ionospheric delay variance.

[0052] Three unknown parameters remain on the left side of formula (3). Since the receiver clock bias and receiver hardware delay are independent of the satellite, they are treated as overall receiver clock bias parameters. Simultaneously, a zero-sum constraint is applied to the satellite-related navigation signal distortion deviation parameters to extract their satellite-end difference components:

[0053] (5)

[0054] n represents the total number of satellites. Regarding the stochastic model for navigation signal distortion correction, based on the aforementioned functional model, a stochastic model characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy is constructed:

[0055] (6)

[0056] In equation (6), The variance of the pseudorange observation residuals is represented. The variance of pseudorange noise is represented. Indicates pseudorange noise, Indicates the satellite elevation angle at the current moment; This represents the calculated ionospheric delay variance.

[0057] Based on the function model and the stochastic model, the pseudorange observation data of the long arc segment is finally used to obtain the receiver clock error parameters that absorb the hardware delay at the receiver end, as well as the navigation signal distortion deviation of the current low-orbit satellite on-board receiver relative to the virtual reference receiver (i.e., the average influence of the hybrid type receivers of the station network) corresponding to the precision clock error product and the differential code deviation product.

[0058] To verify the reliability and stability of the SDB values ​​extracted in step 1, this invention conducted an accuracy assessment and characteristic analysis of the low-Earth orbit satellite SDB sequences:

[0059] Regarding the accuracy assessment of SDB sequences for low-Earth orbit satellites, the SDB values ​​for at least 31 days at each frequency of the onboard receiver of the low-Earth orbit satellite are extracted according to the method in step 1. For the SDB sequence values ​​of each frequency, the following formula (7) is used to assess their accuracy and stability.

[0060] (7)

[0061] In the formula, Let N be the standard deviation of the SDB sequence, and N represent the number of days in the SDB sequence. This represents the SDB value on day j. This represents the mean of the SDB sequence.

[0062] Regarding the feature extraction of SDB sequences from low-Earth orbit (LEO) satellites, the LEO satellite SDB sequences obtained in the previous step are used to select the SDB sequence values ​​of each satellite at at least two frequencies. By statistically analyzing the average value of the SDB of each satellite at each frequency, the degree of signal distortion at the two frequencies is compared and analyzed. Secondly, the time series of SDBs of each satellite at each frequency are used to compare and analyze the trend of SDB changes between different frequencies.

[0063] By selecting SDB sequence values ​​of low-Earth orbit satellites at the same frequency, and statistically analyzing the average value and standard deviation of each satellite in the sequence values, the signal distortion and volatility of different types of navigation satellites are analyzed. At the same time, the changing trends between different satellite SDB time series are compared and analyzed.

[0064] Using the method in step 1, SDB sequence values ​​of different low-Earth orbit satellites are extracted. SDB sequence values ​​of the same type of onboard receiver are selected, and a portion of the satellite SDB values ​​in the sequence are calculated. The average value of these satellite SDB values ​​and the corresponding time series are then analyzed to examine the differences and trends in signal distortion among receivers of the same type. Similarly, SDB sequence values ​​of different types of receivers are selected, and a portion of the satellite SDB values ​​are calculated. The corresponding average value and time series are then analyzed to examine the response of different types of receivers to changes in the same signal.

[0065] Furthermore, in step 2:

[0066] When low-Earth orbit satellites use kinematic methods based on pseudorange data for real-time orbit determination, this invention first uses raw observation data for real-time orbit determination. This method uses pseudorange observations for positioning.

[0067] (8)

[0068] In the formula, c represents the speed of light in a vacuum; and Indicates the onboard receiver and satellite clock bias; and These represent pseudorange hardware delay biases related to the onboard receiver and the satellite, respectively. This is expressed as ionospheric delay; This indicates the phase center deviation of a low-orbit satellite antenna; Due to relativistic effects, all other parameters are the same as in formula (1). After various error corrections, only the clock bias of the onboard receiver and the coordinates of the low-Earth orbit satellite remain to be estimated. With data from at least four navigation satellites, the real-time precise orbit of the low-Earth orbit satellite can be calculated using sequential least squares or Kalman filtering.

[0069] The distortion deviation value of the navigation signal of the low-Earth orbit satellite's onboard receiver was accurately extracted using the method in step 1, and an SDB correction model suitable for low-Earth orbit satellites was designed, such as... Figure 2 As shown, the onboard receiver of the low-Earth orbit satellite reads and identifies the corresponding navigation signal distortion deviation value based on information such as frequency and satellite PRN number, and uses it as the SDB correction value.

[0070] When performing real-time orbit determination, low-Earth orbit satellites incorporate the received SDB correction values ​​as virtual observation values ​​into the pseudorange observation equations, resulting in the equations shown below:

[0071] (9)

[0072] Ultimately, based on the above methods, it is possible to achieve real-time correction of navigation signal distortion deviation values ​​at the low-Earth orbit satellite end.

[0073] The real-time precise orbits of the low-Earth orbit satellites without and after SDB correction are compared with the subsequent precise scientific orbit data of the same low-Earth orbit satellites. At the same time, the positioning errors in the X, Y, and Z directions are transformed into the orbit coordinate system, and the root mean square errors in the R, T, and N directions are calculated to evaluate the real-time precise orbit determination performance of the low-Earth orbit satellites after SDB correction.

[0074] Since the orbit determination accuracy of low-Earth orbit satellites using the SLR observation system is much higher than that of GNSS observation data from onboard receivers, this invention compares the real-time precise orbits of low-Earth orbit satellites without SDB correction and with SDB-corrected precise orbits calculated by the SLR observation system. At the same time, the root mean square errors in the R, T, and N directions of both are statistically analyzed to evaluate the real-time precise orbit determination performance of low-Earth orbit satellites after SDB correction.

[0075] This invention uses measured data from five low-Earth orbit (LEO) satellites, GRACE-FO and SWARM-series, launched on January 1, 2024, as examples. Real-time precise orbit determination experiments were conducted on five LEO satellites (GRACE-C, GRACE-D, SWARM-A, SWARM-B, and SWARM-C) after incorporating SDB values. The obtained orbit determination results are as follows: Figure 3 As shown in Table 1 below (Relative improvement in real-time precision orbit determination RMS before and after SDB value correction), Figure 3 The blue dots represent real-time precise orbit determination results without SDB values, while the yellow squares represent real-time precise orbit determination results with SDB values. The values ​​in the legend represent the root mean square error (RMS). All orbit determination results are compared with the official scientific orbit.

[0076] The results show that after correcting the SDB value, the orbit determination accuracy of the five low-Earth orbit satellites improved by an average of 3.96%, 8.31%, and 10.73% in the radial (R), tangential (T), and normal (N) directions, respectively. This indicates that correcting the SDB value can effectively improve the real-time precision orbit determination accuracy of low-Earth orbit satellites, especially in the N direction where the improvement is the greatest.

[0077] Table 1

[0078]

[0079] To fully illustrate the impact of navigation signal distortion deviations on real-time precise orbit determination services for low-Earth orbit (LEO) satellites, this invention uses calibrated 31-day LEO satellite SDB values ​​to statistically analyze the improvement in real-time precise orbit determination results for five LEO satellites after correcting their SDB values ​​from January 1st to January 31st, 2024. The results are as follows: Figure 4 As shown in the figure. The blue line represents the boost value in the N direction, the green line represents the boost value in the T direction, and the red line represents the boost value in the R direction.

[0080] from Figure 4It can be seen that: 1) For the GRACE-C satellite, the 31-day average improvement values ​​in the R, T, and N directions are 3.94%, 8.30%, and 12.95%, respectively; for the GRACE-D satellite, the 31-day average improvement values ​​in the R, T, and N directions are 5.82%, 10.48%, and 12.04%, respectively; for the SWARM-A satellite, the 31-day average improvement values ​​in the R, T, and N directions are 5.22%, 6.71%, and 6.01%, respectively; for the SWARM-B satellite, the 31-day average improvement values ​​in the R, T, and N directions are 3.21%, 8.05%, and 8.16%, respectively; and for the SWARM-C satellite, the 31-day average improvement values ​​in the R, T, and N directions are 5.10%, 6.30%, and 5.83%, respectively; 2) For the GRACE-C satellite, the 31-day average improvement values ​​in the R, T, and N directions are 3.94%, 8.30%, and 12.95%, respectively; for the GRACE-D satellite, the 31-day average improvement values ​​in the R, T, and N directions are 5.10%, 6.30%, and 5.83%, respectively; The maximum daily improvement values ​​were 13.19%, 16.43%, and 20.43%, respectively. For the GRACE-D satellite, the maximum daily improvement values ​​in the R, T, and N directions were 8.76%, 13.76%, and 29.93%, respectively. For the SWARM-A satellite, the maximum daily improvement values ​​in the R, T, and N directions were 10.83%, 10.11%, and 10.75%, respectively. For the SWARM-B satellite, the maximum daily improvement values ​​in the R, T, and N directions were 5.34%, 11.08%, and 11.69%, respectively. For the SWARM-C satellite, the maximum daily improvement values ​​in the R, T, and N directions were 8.50%, 9.69%, and 8.03%, respectively. 3) The results show that for real-time precise orbit determination of low-Earth orbit satellites, the N direction showed the largest improvement after correcting the SDB value, while the R direction showed a relatively smaller improvement.

[0081] On the other hand, the present invention provides a low-Earth orbit satellite precision orbit determination device that takes into account navigation signal distortion deviations. Its various modules are capable of implementing the various steps of the aforementioned method, specifically including:

[0082] The calculation module is used to collect raw GNSS observation data from low-Earth orbit (LEO) satellites, construct a functional model and a stochastic model for estimating navigation signal distortion bias, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion bias value of the LEO satellite's onboard receiver relative to the virtual reference receiver (i.e., absorbing the average influence of hybrid receivers in the network) corresponding to the precision clock bias product and differential code bias product. The construction of the functional model and stochastic model for estimating navigation signal distortion bias includes: subtracting satellite clock bias and satellite-end hardware delay from the observation values ​​using the precision clock bias product and the differential code bias product; subtracting the geometric distance between the navigation satellite and the LEO satellite using the LEO satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data; subtracting ionospheric delay error using a three-dimensional ionospheric model; and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy.

[0083] The correction module is used to construct a correction model based on the navigation signal distortion deviation value. The on-board receiver of the low-Earth orbit satellite reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account the navigation signal distortion deviation.

[0084] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviations.

[0085] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviations.

[0086] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for precise orbit determination of low-Earth orbit satellites that takes into account navigation signal distortion deviation, characterized in that, The method includes: Step 1: Collect raw GNSS observation data from low-Earth orbit (LEO) satellites, construct a functional model and a stochastic model for estimating navigation signal distortion bias, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion bias value of the LEO satellite's onboard receiver relative to the virtual reference receiver reference corresponding to the precision clock bias product and the differential code bias product. The construction of the functional model and stochastic model for estimating navigation signal distortion bias includes: subtracting satellite clock bias and satellite-end hardware delay from the observation values ​​using the precision clock bias product and the differential code bias product; subtracting the geometric distance between the navigation satellite and the LEO satellite using the LEO satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data; subtracting ionospheric delay error using a three-dimensional ionospheric model; and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy. Step 2: Based on the navigation signal distortion deviation value, a correction model is constructed. The on-board receiver of the low-Earth orbit satellite reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account the navigation signal distortion deviation.

2. The method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 1, characterized in that, In step 1, pseudorange observations with abnormal ionospheric residuals are eliminated by post-verification residual check using a preset error threshold, so as to further eliminate the adverse effects of the ionosphere.

3. The method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 1, characterized in that, In step 1, the original observation data includes carrier phase observation data, pseudorange observation data, and navigation satellite ephemeris; in the function model, the pseudorange observation value is represented as a combination of the corrected geometric distance between the receiver and the satellite, the speed of light in vacuum, the receiver clock error, the satellite clock error, the receiver hardware delay, the satellite hardware delay, the ionospheric delay, the observation noise, and the navigation signal distortion deviation.

4. The method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 1, characterized in that, Following step 1, the method further includes: constructing a navigation signal distortion deviation sequence based on the extracted multiple navigation signal distortion deviation values; calculating the standard deviation and mean of the navigation signal distortion deviation sequence to evaluate accuracy and stability; selecting the navigation signal distortion deviation sequence values ​​of each satellite at at least two frequencies; comparing and analyzing the magnitude of signal distortion at different frequencies by statistically analyzing the average value of the navigation signal distortion deviation at each frequency; and comparing and analyzing the changing trend of navigation signal distortion deviation between different frequencies by using the time series of the navigation signal distortion deviation at each frequency; selecting the low-orbit satellite navigation signal distortion deviation sequence values ​​at the same frequency; and analyzing the signal distortion degree and volatility of different types of navigation satellites by statistically analyzing the average value and standard deviation of each satellite.

5. A method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 4, characterized in that, By using navigation signal distortion deviation sequence values ​​from different low-Earth orbit satellites, and selecting navigation signal distortion deviation sequence values ​​from satellite-borne receivers of the same type, the average value and corresponding time series of some satellite navigation signal distortion deviations are statistically analyzed to understand the differences and trends in signal distortion levels among similar satellite-borne receivers. Furthermore, by selecting navigation signal distortion deviation sequence values ​​from satellite-borne receivers of different types, the average value and time series of some satellite navigation signal distortion deviations are statistically analyzed to understand the response of different types of satellite-borne receivers to changes in the same signal.

6. The method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 1, characterized in that, In step 2, the low-Earth orbit satellite uses a kinematic method based on pseudorange data to determine its real-time orbit. After adding the navigation signal distortion deviation correction value as a virtual observation value to the pseudorange observation equation, the low-Earth orbit satellite's real-time precise orbit is calculated using sequential least squares or Kalman filtering methods after deducting various error effects with precision products.

7. A method for precise orbit determination of low-Earth orbit satellites considering navigation signal distortion deviation according to claim 1, characterized in that, Step 2 is followed by orbit determination performance analysis: the real-time precise orbits of the low-Earth orbit satellites without navigation signal distortion correction and with navigation signal distortion correction are compared with the reference orbits, and after conversion to the orbit coordinate system, the root mean square errors in the radial, tangential, and normal directions are calculated to evaluate the real-time precise orbit determination performance of the low-Earth orbit satellites after navigation signal distortion correction; the reference orbits include the post-hoc precise scientific orbits of the low-Earth orbit satellites and the precise orbits calculated by the satellite laser ranging observation system.

8. A precision orbit determination device for low-Earth orbit satellites that takes into account navigation signal distortion deviation, characterized in that, include: The calculation module is used to collect raw GNSS observation data from low-Earth orbit (LEO) satellites, construct a functional model and a stochastic model for estimating navigation signal distortion bias, and perform parameter estimation based on the functional model and the stochastic model to obtain the navigation signal distortion bias value of the LEO satellite's onboard receiver relative to the virtual reference receiver reference corresponding to the precision clock bias product and the differential code bias product. The construction of the functional model and stochastic model for estimating navigation signal distortion bias includes: subtracting satellite clock bias and satellite-end hardware delay from the observations using the precision clock bias product and the differential code bias product; subtracting the geometric distance between the navigation satellite and the LEO satellite using the LEO satellite's post-hoc precise orbit determination data and the navigation satellite's post-hoc precise orbit data; subtracting ionospheric delay error using a three-dimensional ionospheric model; and constructing a stochastic model jointly characterized by pseudorange observation noise, satellite elevation angle, and ionospheric model accuracy. The correction module is used to construct a correction model based on the navigation signal distortion deviation value. The on-board receiver of the low-Earth orbit satellite reads the corresponding navigation signal distortion deviation value according to the frequency and satellite number as the correction value, and adds it as a virtual observation value to the pseudorange observation equation for real-time orbit determination, so as to realize precise orbit determination of low-Earth orbit satellites that takes into account the navigation signal distortion deviation.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the low-Earth orbit satellite precise orbit determination method that takes into account navigation signal distortion deviation as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the low-Earth orbit satellite precision orbit determination method that takes into account navigation signal distortion deviations, as described in any one of claims 1-7.

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