Low earth orbit satellite orbit determination accuracy improvement method and device under geomagnetic storm conditions

Abstract

The application discloses a low-orbit satellite orbit determination precision improvement method and device under geomagnetic storm conditions and belongs to the technical field of satellite navigation. The method proposes an adaptive orbit determination framework of dynamic model and stochastic model optimization. At the dynamic level, the segmented estimation length of empirical force and atmospheric resistance coefficient is dynamically adjusted according to the geomagnetic activity level, and the resolution capability for rapid changes of non-conservative force is improved. At the stochastic model level, an external physical driving weight function based on the SYM-H index and an internal data diagnosis weight function based on observation residuals are constructed, and real-time adaptive adjustment of observation value variance is realized. Through the "geomagnetic index-observation residual" double driving mechanism, the low-orbit satellite orbit determination error during the strong magnetic storm is reduced from the decimeter level to the centimeter level, and the precision and robustness of the low-orbit satellite orbit determination under the space weather event are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation technology, specifically relating to a method and apparatus for improving the orbit determination accuracy of low-orbit satellites under geomagnetic storm conditions. Background Technology

[0002] Low Earth Orbit (LEO) satellites, with their advantages of rapid geometrical configuration changes and high signal strength, are increasingly demonstrating their value in the field of positioning, navigation, and timing (PNT). Unlike MEO / GEO satellites in the current GNSS constellation, LEO satellites have an order of magnitude higher geometrical flip rate, amplifying the impact of ephemeris errors on convergence time and positioning accuracy by 3-5 times. Precise orbit determination of LEO satellites is crucial to the performance of navigation augmentation systems.

[0003] The impact of geomagnetic storms on satellite orbit determination is mainly reflected in two aspects: observational data and satellite dynamics models. During a geomagnetic storm, the impact of a large number of high-energy particles causes severe disturbances in the ionosphere, reducing the signal-to-noise ratio of GNSS signals and affecting the tracking frequency of onboard GNSS receivers. Although dual-frequency GNSS observations can be used to achieve an ionospheric-free combination to eliminate most of the ionospheric influence, studies show that higher-order terms of ionospheric delay (second- and third-order terms) can still lead to centimeter-level positioning errors during extreme space weather events such as geomagnetic storms. Simultaneously, geomagnetic storms significantly alter atmospheric density, reducing the accuracy of low-Earth orbit satellite dynamics models. Despite decades of continuous improvement in atmospheric models, due to the extreme complexity of upper atmospheric changes, statistics show that models still retain approximately 15% to 30% error. During geomagnetic storms, model errors increase dramatically, potentially exceeding 100% in severe cases.

[0004] Traditional orbit determination strategies establish satellite dynamic models incorporating perturbations such as Earth's gravity, lunar and solar gravity, tides, solar radiation pressure, and atmospheric drag. Empirical force models are introduced to compensate for errors in unmodeled non-conservative forces. Pseudorange and carrier phase observation data are acquired using onboard GNSS receivers, and parameter estimation is performed using methods such as least squares or Kalman filtering. Existing precise orbit determination methods for low-Earth orbit (LEO) satellites can achieve high accuracy during periods of geomagnetic storm calm. However, during geomagnetic storms, the accuracy degrades significantly due to the inability to adapt to rapid changes in the dynamic model and the sharp decline in observation data quality. LEO satellites are more significantly affected by geomagnetic storm disturbances, and their orbit determination accuracy is prone to a sharp degradation under storm conditions.

[0005] Current technologies primarily employ static segmentation strategies for dynamic parameters and fixed stochastic models. However, this approach fails to capture the rapid changes in perturbation forces during geomagnetic storms and cannot respond to the time-varying characteristics of observational noise caused by ionospheric disturbances. Current research mainly focuses on atmospheric density models during geomagnetic storms; however, due to the strong time-varying and uncertain nature of geomagnetic storms, non-conservative forces are constrained by numerous uncertainties, and existing models still suffer from approximation errors and unmodeled physical processes. Furthermore, the deterioration in observational data quality during geomagnetic storms places higher demands on stochastic models. Therefore, it is necessary to comprehensively optimize dynamic parameter calculation strategies and observational data stochastic models to further improve the orbit determination accuracy of low-Earth orbit satellites during space weather events. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and apparatus for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions. The method dynamically adjusts the segmented estimation duration of the dynamic model and the weight of the observation stochastic model in low-Earth orbit satellite orbit determination according to the intensity of the geomagnetic storm, thereby achieving adaptive and coordinated suppression of model error and observation noise.

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

[0008] A method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions, the method comprising:

[0009] Step 1, Dynamic Model Optimization: Optimize the segmented modeling time for empirical forces and atmospheric drag in the perturbation forces experienced by low-orbit satellites. This includes dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient.

[0010] Step 2, Stochastic Model Optimization: Construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time to achieve weight reduction processing of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process.

[0011] Both the dynamic model optimization and the stochastic model optimization are triggered based on the level of geomagnetic activity, and work together to improve the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0012] Furthermore, in step 1, the method for determining the segmented estimation duration of the empirical force is as follows: the total observation arc is divided by the number of time periods divided, the empirical force parameter vector is independently estimated within each segment, and the relationship between the observation residual vector and the design matrix is ​​solved by the least squares method.

[0013] Furthermore, in step 1, the method for determining the segmented estimation duration of the atmospheric drag coefficient is as follows: the total observation arc is divided by the number of time periods, the atmospheric drag parameter vector is independently estimated within each segment, and the relationship between the observation residual vector and the design matrix is ​​solved by the least squares method.

[0014] Furthermore, in step 2, the stochastic model based on the SYM-H index specifically involves: preprocessing the geomagnetic index sequence, aligning the preprocessed geomagnetic index sequence with the time system of the observations to obtain the geomagnetic index at each observation epoch, and constructing a weighting function based on the geomagnetic index. When the absolute value of the geomagnetic index exceeds a first set threshold, the observations for the corresponding time period are weighted down.

[0015] Furthermore, in step 2, the residual-based stochastic model specifically involves: for the current epoch to be solved, using the initial stochastic model or the previous iteration stochastic model to perform orbit determination, obtaining the residual of the corresponding observation epoch, and constructing a weight function based on the residual. When the residual exceeds a second set threshold, the observation values ​​of the corresponding time period are weighted down.

[0016] Furthermore, it also includes a determination mechanism for triggering optimization strategies: performing wavelet coherence analysis on the geomagnetic index and satellite orbit determination error, defining the period when the wavelet coherence coefficient is higher than the mean as the high coherence period, setting the geomagnetic index interval corresponding to the high coherence period as the determination threshold, and activating the dynamic model optimization and stochastic model optimization when the geomagnetic index is lower than the determination threshold, otherwise using the quiet period orbit determination strategy.

[0017] Furthermore, in step 2, the weight reduction processing of the observations of the disturbed epoch is achieved by updating the variance component of each epoch observation: the prior variance is divided by the weighting factor to obtain the variance component that changes over time, so as to assign a smaller weight to the observations of the disturbed epoch in the weighted least squares normal equation.

[0018] On the other hand, the present invention provides a device for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions, comprising:

[0019] The dynamic model optimization module is used to optimize the segmented modeling time of empirical forces and atmospheric drag in the perturbation forces of low-orbit satellites. This includes: dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient.

[0020] The stochastic model optimization module is used to construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time; and reducing the weight of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process.

[0021] Both the dynamic model optimization module and the stochastic model optimization module are triggered based on the level of geomagnetic activity, working together to improve the orbit determination accuracy of low-orbit satellites under geomagnetic storm conditions.

[0022] 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 improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0023] 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 improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0024] The beneficial effects of this invention are as follows:

[0025] Significantly improved accuracy: By adaptively adjusting the segmented duration of the dynamic model and combining it with the optimization of a dual-drive stochastic model based on the SYM-H index and observation residuals, the orbit determination error of low-orbit satellites during strong geomagnetic storms is reduced from the decimeter level to the centimeter level, approaching the accuracy level under undisturbed conditions.

[0026] Robustness and real-time performance are achieved simultaneously: the external SYM-H index (symmetric H index, minute resolution, a high time resolution version of the Dst index, used to accurately describe the axisymmetric perturbation component of the global geomagnetic field, the larger the negative value, the stronger the geomagnetic storm) and the internal residual data are dual-driven and complementary in weight, avoiding the failure of a single index and ensuring the robustness of the system during geomagnetic storms; at the same time, the dynamic adjustment strategy avoids over-computation and meets the real-time processing requirements of the satellite.

[0027] With strong systematicity and high engineering practical value, this invention constructs a complete optimization chain from "data input—model adjustment—solution output," coordinating the dynamic model and the stochastic model through the same geomagnetic activity index to achieve an overall optimization effect. As a pure algorithm upgrade, this method has low computational overhead, is easy to integrate into existing orbit determination systems, and has high practical value and promising prospects for widespread application. Attached Figure Description

[0028] Figure 1 This is a flowchart of the method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to the present invention.

[0029] Figure 2 This is a diagram illustrating the effect of implementing the method of the present invention. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] like Figure 1 As shown, this invention provides a method for improving the orbit determination accuracy of low-Earth orbit (LEO) satellites under geomagnetic storm conditions. First, at the dynamic model level, the perturbation forces acting on LEO satellites are analyzed, and an optimization method for the segmented modeling time of empirical forces and atmospheric drag is proposed based on the influence of geomagnetic storms. Then, in terms of observation data processing, a stochastic model optimization strategy based on geomagnetic parameters is constructed, achieving adaptive adjustment of the observation weight function, and an adaptive stochastic model based on residual changes is proposed, further improving the accuracy of orbit determination results during geomagnetic storms. Specifically, the method includes:

[0032] Step 1, Dynamic Model Optimization: Optimize the segmented modeling time for empirical forces and atmospheric drag in the perturbation forces experienced by low-orbit satellites. This includes dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient.

[0033] Step 2, Stochastic Model Optimization: Construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time to achieve weight reduction processing of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process.

[0034] Both the dynamic model optimization and the stochastic model optimization are triggered based on the level of geomagnetic activity, and work together to improve the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0035] Furthermore, in step 1:

[0036] The main perturbations included in the low-Earth orbit satellite dynamics model have:

[0037] (1)

[0038] The first term on the right side of the formula The gravitational pull at the Earth's center, of which The gravitational constant of Earth, For satellite quality, This is the distance between the satellite and the Earth's center. Perturbed by tides, The gravitational perturbation of N-body celestial bodies such as the Sun and Moon. Perturbations caused by relativistic effects Due to atmospheric drag perturbation, This is the solar radiation pressure. This invention introduces empirical force perturbations. Among them, atmospheric drag perturbations and empirical force perturbations are most affected under geomagnetic storm conditions. This invention mainly analyzes and discusses these two.

[0039] Since non-conservative forces acting on a satellite (such as atmospheric drag and solar radiation pressure) are difficult to accurately model in satellite orbital dynamics models, it is necessary to introduce empirical force models to estimate the errors of non-conservative force models and unmodeled errors. Empirical force segmentation refers to the time interval during satellite orbit determination where observation data is divided into multiple time periods, and empirical force model parameters are estimated for each time period.

[0040] The total observed arc segment is The total observation arc segment is divided into If there are several time periods, then the duration of each period is... :

[0041] (2)

[0042] Independently estimated empirical force parameter vectors within each segment Solve using the least squares method:

[0043] (3)

[0044] in, For the first The observed residual vector of the segment, To design the matrix.

[0045] During geomagnetic storms, drastic changes in factors such as atmospheric density significantly affect the orbit determination accuracy of low-Earth orbit (LEO) satellites, causing empirical forces, which absorb errors in non-conservative force models such as atmospheric drag, to change more frequently. To further improve the orbit determination accuracy of LEO satellites during geomagnetic storm events, this invention adaptively adjusts the estimation strategy of empirical forces during periods of high frequency of geomagnetic storms or when geomagnetic parameters affecting orbit determination are high. This increases the frequency of empirical force estimation based on geomagnetic parameters, thereby better ensuring the real-time performance and accuracy of empirical acceleration.

[0046] In low-Earth orbit satellite dynamics models, atmospheric drag perturbations are generally expressed as:

[0047] (4)

[0048] in, This is the atmospheric drag coefficient. Atmospheric density, For windward area, The magnitude of the satellite's velocity relative to the atmosphere. Its vector.

[0049] Atmospheric drag segment duration refers to dividing the observed data into multiple time segments during satellite orbit determination and estimating the atmospheric drag coefficient separately within each segment. The time interval.

[0050] The total observed arc segment is The total observation arc segment is divided into If there are several time periods, then the duration of each period is... :

[0051] (5)

[0052] The atmospheric drag parameter vector is estimated independently for each time period. Solve using the least squares method:

[0053] (6)

[0054] in, For the first The observed residual vector of the segment, To design the matrix.

[0055] This segmented processing aims to more accurately describe changes in atmospheric drag, as atmospheric drag is influenced by factors such as solar activity, geomagnetic activity, and satellite orbital altitude. During geomagnetic storms, atmospheric density... A violent disturbance will occur. At this time, shortening It can capture the atmospheric drag coefficient with greater precision. The instantaneous changes in atmospheric drag can be modeled more accurately. This reduces model error.

[0056] However, shorter segment durations require more parameters to be estimated, leading to increased computational complexity and data processing volume. Furthermore, shorter segment durations necessitate high-quality observational data to support frequent parameter estimations; otherwise, inaccurate estimations may occur. The segment duration should be dynamically adjusted based on the actual intensity of geomagnetic activity to achieve the optimal balance between accuracy and efficiency.

[0057] Furthermore, in step 2:

[0058] For observational data during the period of geomagnetic storms, the weights of the geomagnetic index in the variance-covariance matrix are adjusted according to the changes in the geomagnetic index during that period, i.e., the corresponding variance components are changed.

[0059] Based on geomagnetic storm conditions, this invention proposes two stochastic models: a stochastic model based on the SYM-H index and a stochastic model based on residuals. These two models, each with a different focus, quantify and incorporate the influence of the geomagnetic index on satellite orbit determination to refine the stochastic model.

[0060] The satellite orbit determination stochastic model describes the statistical characteristics of the observation data (such as variance and covariance), and is mainly used to deal with random errors in the observation data to improve the accuracy of satellite orbit determination.

[0061] For a sequence L of n satellite observations:

[0062] (7)

[0063] And m parameter sequences X to be determined:

[0064] (8)

[0065] There exists a linear function model:

[0066] (9)

[0067] or:

[0068] (10)

[0069] in, To design the matrix, This is a random error vector.

[0070] To minimize the weighted average of the residuals, i.e., to obtain the parameter estimates... , so that:

[0071] (11)

[0072] in, V is the weight matrix, and V is the residual vector;

[0073] Parameter estimates It can be solved using the weighted least squares average:

[0074] (12)

[0075] The residual vector expression is:

[0076] (13)

[0077] Observation residual vector during satellite orbit determination Generally, it follows a normal distribution with a mean of 0.

[0078] (14)

[0079] in, The variance matrix reflects the noise level and correlation of each observation, and is generally expressed as:

[0080] (15)

[0081] in, For the first The variance components of each observation can be expressed as:

[0082] (16)

[0083] in, The degrees of freedom corresponding to the observed values. For the corresponding i-th residual vector, Design a matrix for the corresponding i-th weight.

[0084] The covariance matrix of the parameter estimates can be written as:

[0085] (17)

[0086] In standard orbit determination, the stochastic model of observations is typically assumed to be static, meaning the variance-covariance matrix of the observation noise remains constant throughout the calculation period. However, during space weather events, factors such as ionospheric scintillation and intensified multipath effects cause observation noise to exhibit significant time-varying and non-stationary characteristics. Static models cannot accurately reflect these dynamically changing error characteristics, leading to biased parameter estimates and decreased orbit determination accuracy.

[0087] To address this issue, this invention introduces a dynamic weight adjustment strategy. The core idea is to adjust the variance components of the corresponding observations in the stochastic model in real time based on an indicator reflecting the intensity of space weather disturbances (i.e., the "weighting factor"). Specifically, the traditional constant variance components... Corrected to time-varying components :

[0088] (18)

[0089] in, is a time-related weighting factor, where t represents time. When When, it indicates that the observation quality is normal at that moment, and the prior variance is used; when When the time indicates that the observation is affected by space weather, the impact of unreliable observations in the adjustment is mitigated by increasing its variance (i.e., reducing its weight).

[0090] This invention constructs two types of weight functions from two complementary perspectives: external physical driving and internal data diagnostics. These functions form a stochastic model based on the SYM-H exponent and a stochastic model based on residuals, respectively. The specific implementation of these two strategies will be described in detail below.

[0091] Regarding the optimization strategy for stochastic models based on the SYM-H index: The SYM-H index characterizes the loop current flux affected by geomagnetic storms globally, and its drastic negative changes are a direct indicator of geomagnetic storm occurrence. During geomagnetic storms, injected high-energy particles heat and disturb the ionosphere and thermosphere, thereby causing phase scintillation and amplitude attenuation of GNSS signals, significantly increasing the noise level of carrier phase and pseudorange observations. Therefore, the SYM-H index can serve as an effective external physical proxy indicator for characterizing the degree of impact of global-scale space weather on GNSS observation signal links.

[0092] This strategy aims to establish a quantitative relationship between the SYM-H index and the weighting factors of observations. First, the SYM-H index sequence is preprocessed and aligned with the time system of GNSS observations to obtain the results for each observation epoch. SYM-H index under And based on this, a weighting function based on the SYM-H exponent is constructed. :

[0093] (19)

[0094] in, The first adjustment coefficient, The threshold is set, and when the SYM-H index exceeds the threshold, the observations for that period are downweighted.

[0095] Subsequently, dynamic weights are applied to the stochastic model to update the variance components of each type of observation at each epoch. :

[0096] (20)

[0097] in, Let be the prior variance of the observations. This correction is equivalent to assigning smaller weights to the observations at the perturbed epoch in the weighted least squares normal equation.

[0098] Regarding the residual-based stochastic model optimization strategy: The SYM-H-based strategy relies on the global geomagnetic index, but the impact of space weather on specific LEO satellite GNSS links is localized and asymmetric. Since satellites operate periodically, the SYM-H index, which characterizes the global impact of geomagnetic storms, cannot fully represent the satellite's influence from geomagnetic storms. Compared to the SYM-H index, residuals are closer to the satellite's own data. Based on this, to more directly respond to anomalies observed in actual observation data, this invention also uses residual data, which is more relevant to the satellite, as a weighting function factor, proposing a stochastic model optimization strategy based on residual changes. The core of this strategy is to use the observation residuals themselves as an endogenous indicator of the current observation quality. Large, unconventional residuals usually indicate errors caused by space weather at that epoch.

[0099] This strategy employs a post-hoc adaptive method. For the current epoch to be solved... First, the initial (or previous iteration) stochastic model is used to perform orbit determination, obtaining the corresponding observation epochs. residual And based on this, a weighting function based on residuals is constructed. :

[0100] (twenty one)

[0101] in, This is the second adjustment coefficient. The threshold is set, and when the residual exceeds the threshold, the observations for that period are weighted down.

[0102] Variance component estimation methods, based on a priori residual data, employ appropriate statistical methods and iterative approaches to estimate the variance, ultimately obtaining the unit-weighted variance of observations influenced by various factors. This belongs to the a priori stochastic model category. Commonly used methods include the Helmert variance component estimation weighting method and the least squares variance component estimation (LS-VCE) weighting method, which are widely applied in multi-mode GNSS joint precise positioning / orbit determination. In the initialization phase, we use the Helmert variance component estimation method to determine the prior variance components of various GNSS observations. In the dynamic orbit determination process, for the epoch... The Class of observations, whose dynamic variance is adjusted to :

[0103] (twenty two)

[0104] This invention calculates the correlation coefficient and performs wavelet coherence analysis on the relationship between the geomagnetic index and satellite orbit determination error, revealing a significant correlation between the two. This correlation is further enhanced during periods of severe geomagnetic storms. Therefore, this invention incorporates the geomagnetic index as a constraint into the orbit determination optimization framework and develops an adaptive optimization strategy for periods of strong geomagnetic storms. This invention defines periods with wavelet coherence coefficients above the mean as high-coherence periods, assuming that geomagnetic storms significantly impact orbit determination errors during these periods. The SYM-H index interval corresponding to high-coherence periods is set as a threshold. When the SYM-H index falls below this threshold, the optimization strategy is activated to suppress the degradation of orbit determination accuracy during geomagnetic storms; conversely, the orbit determination strategy used during calm periods is applied to reduce computational overhead. This mechanism enables the algorithm to adaptively adjust in complex space environments.

[0105] The final improved orbit determination accuracy of this invention is as follows: Figure 2 As shown in the figure, the three lines represent the original orbit determination result without processing, the orbit determination result after segmented duration adjustment, and the orbit determination result after incorporating a segmented weight function to optimize the stochastic model, respectively. It can be seen that compared to the unprocessed result, the orbit determination error 3D RMS after segmented optimization with a dynamic model decreased from 37.34 cm to 11.61 cm, and the orbit determination error after adaptive optimization of the stochastic model further decreased to 7.65 cm, a reduction of 79.51% compared to the original result, further reducing the impact of orbit determination errors caused by geomagnetic storms. Ultimately, this invention reduces the orbit determination error accuracy from the decimeter level to the centimeter level, approaching the level before geomagnetic storms.

[0106] On the other hand, the present invention provides a device for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions, which includes various modules capable of implementing the various steps of the aforementioned method. Specifically, it includes the following modules:

[0107] The dynamic model optimization module is used to optimize the segmented modeling time of empirical forces and atmospheric drag in the perturbation forces of low-orbit satellites. This includes: dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient.

[0108] The stochastic model optimization module is used to construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time; and reducing the weight of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process.

[0109] Both the dynamic model optimization module and the stochastic model optimization module are triggered based on the level of geomagnetic activity, working together to improve the orbit determination accuracy of low-orbit satellites under geomagnetic storm conditions.

[0110] 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 improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0111] 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 improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

[0112] 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 improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions, characterized in that, The method includes: Step 1, Dynamic Model Optimization: Optimize the segmented modeling time for empirical forces and atmospheric drag in the perturbation forces experienced by low-orbit satellites. This includes dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient. Step 2, Stochastic Model Optimization: Construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time to achieve weight reduction processing of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process. Both the dynamic model optimization and the stochastic model optimization are triggered based on the level of geomagnetic activity, and work together to improve the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions.

2. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, In step 1, the segmented estimation duration of the empirical force is determined by dividing the total observation arc by the number of time periods, independently estimating the empirical force parameter vector within each segment, and solving the relationship between the observation residual vector and the design matrix using the least squares method.

3. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, In step 1, the segmented estimation time of the atmospheric drag coefficient is determined by dividing the total observation arc by the number of time periods, independently estimating the atmospheric drag parameter vector within each segment, and solving the relationship between the observation residual vector and the design matrix using the least squares method.

4. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, In step 2, the stochastic model based on the SYM-H index specifically involves: preprocessing the geomagnetic index sequence, aligning the preprocessed geomagnetic index sequence with the time system of the observations to obtain the geomagnetic index at each observation epoch, and constructing a weighting function based on the geomagnetic index. When the absolute value of the geomagnetic index exceeds a first set threshold, the observations for the corresponding time period are weighted down.

5. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, In step 2, the residual-based stochastic model is specifically as follows: for the current epoch to be solved, the initial stochastic model or the previous iteration stochastic model is used to perform orbit determination and obtain the residual of the corresponding observation epoch, and a weight function based on the residual is constructed. When the residual exceeds the second set threshold, the observation values ​​of the corresponding time period are reduced in weight.

6. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, It also includes a determination mechanism for triggering optimization strategies: performing wavelet coherence analysis on the geomagnetic index and satellite orbit determination error, defining the period when the wavelet coherence coefficient is higher than the mean as the high coherence period, setting the geomagnetic index interval corresponding to the high coherence period as the determination threshold, and activating the dynamic model optimization and stochastic model optimization when the geomagnetic index is lower than the determination threshold, otherwise using the quiet period orbit determination strategy.

7. The method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions according to claim 1, characterized in that, In step 2, the weight reduction processing of the observations of the disturbed epoch is achieved by updating the variance component of each epoch observation: the prior variance is divided by the weight factor to obtain the variance component that changes over time, so that the observations of the disturbed epoch are assigned a smaller weight in the weighted least squares normal equation.

8. A device for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions, characterized in that, include: The dynamic model optimization module is used to optimize the segmented modeling time of empirical forces and atmospheric drag in the perturbation forces of low-orbit satellites. This includes: dividing the total observation arc into multiple time periods, independently estimating the empirical force parameter vector and atmospheric drag coefficient in each time period, solving them using the least squares method, and dynamically adjusting the segmented modeling time according to changes in geomagnetic parameters. During geomagnetic storms, the segmented time is shortened to increase the frequency of empirical force estimation and accurately capture the instantaneous changes in atmospheric drag coefficient. The stochastic model optimization module is used to construct a dynamic weight adjustment strategy based on the geomagnetic index to adjust the variance-covariance matrix of the stochastic model of the observation data. This includes: scaling the prior variance based on the weight factor to obtain the variance component that changes over time; constructing the variance-covariance matrix using the variance component that changes over time; and reducing the weight of the observations at the disturbed epoch. The weight factor is calculated using a stochastic model based on the SYM-H index or a stochastic model based on residuals. The stochastic model based on the SYM-H index maps the SYM-H index to the weight factor, while the stochastic model based on residuals calculates the weight factor using the residual information generated during the orbit determination process. Both the dynamic model optimization module and the stochastic model optimization module are triggered based on the level of geomagnetic activity, working together to improve the orbit determination accuracy of low-orbit satellites under geomagnetic storm conditions.

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 method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions 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 method for improving the orbit determination accuracy of low-Earth orbit satellites under geomagnetic storm conditions as described in any one of claims 1-7.

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