Ultra-short-term forecasting model adaptive constraint low earth orbit satellite clock error estimation method

Abstract

The invention relates to a low earth orbit satellite clock error estimation method based on adaptive constraint of an ultra-short-term forecasting model. The method comprises the following steps: acquiring a historical post-processing batch clock error sequence of a low earth orbit satellite, and preprocessing the post-processing batch clock error sequence to obtain a preprocessed clock error sequence; constructing clock error forecasting models under different forecasting durations according to the preprocessed clock error sequence; calculating an instantaneous true anomaly according to the historical precise ephemeris of the low earth orbit satellite, and dynamically constructing a true anomaly model according to the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; adding the clock error estimation value of the clock error forecasting model under the corresponding forecasting duration as a constraint value into the observation equation to obtain a constraint observation equation, and constructing a target function according to the constraint observation equation and a posterior residual equation of the observation equation; and solving the target function to obtain the real-time clock error of the low-orbit satellite. By adopting the method, the precision and short-term stability of real-time clock error estimation can be effectively improved.

Description

Technical Field

[0001] The present application relates to the field of satellite navigation technology, and in particular to a method for estimating low-orbit satellite clock errors with adaptive constraints of an ultra-short-term prediction model. Background Art

[0002] With the rapid development of low-Earth Orbit (LEO) satellite constellations, their applications are becoming increasingly widespread in global communications, remote sensing, scientific experiments, and other fields. Compared to medium- and high-orbit satellites, LEO satellites, due to their lower orbital altitude, are subject to stronger perturbations, and their orbits and clock errors have a stronger correlation. Furthermore, the long-term stability of LEO satellites' onboard clocks is poor, and their time synchronization accuracy has a significant impact on orbit determination accuracy and subsequent applications. Therefore, achieving high-precision time synchronization in complex environments has become a key research direction in the development of LEO satellite time standards.

[0003] When it comes to clock error calculations for low-orbit satellites, limited ground stations are unable to meet the large-scale satellite-to-ground measurement and control needs. Therefore, onboard clock error estimation is a more efficient method. Since the orbit and clock errors are calculated simultaneously, early researchers focused on improving the orbit determination accuracy of low-orbit satellites. By modeling the GPS receiver clock, they reduced the correlation between the orbit and clock, improved the orbit accuracy, and ignored the time accuracy of the low-orbit satellites themselves. In the past two years, the industry has gradually carried out relevant research on the onboard time base and time synchronization of low-orbit satellites, including GRACE-FO satellites, Sentinel series satellites, SWARM and other non-navigation low-orbit satellites used for gravity and meteorological monitoring. Research directions mainly include three categories: low-orbit satellite clock error characteristic analysis and clock modeling, low-orbit satellite clock error prediction, and low-orbit satellite clock estimation. However, the technology is not yet mature and is mainly based on the optimization of traditional GNSS clock estimation methods.

[0004] Because low-Earth orbit satellite clock errors are subject to complex environmental influences and variations in their own clock characteristics, they exhibit a complex mixture of short-term and medium- to long-term cycles. Clock error characteristics vary significantly between satellites, making empirical models with fixed parameters unsuitable. Furthermore, orbit and clock errors are highly correlated, and coupling these errors in real-time estimation can degrade clock estimation performance. Therefore, improving the accuracy and stability of real-time low-Earth orbit satellite clock error estimation, achieving sub-nanosecond onboard clock estimation, is crucial for establishing and maintaining a high-precision time base for future low-Earth orbit satellites. Summary of the Invention

[0005] Based on this, it is necessary to provide a low-orbit satellite clock error estimation method with adaptive constraints of an ultra-short-term prediction model to address the above technical problems.

[0006] A method for estimating low-orbit satellite clock errors with an ultra-short-term prediction model adaptively constrained, the method comprising:

[0007] Obtaining a post-batch clock error sequence of the low-orbit satellite history, preprocessing the post-batch clock error sequence to obtain a preprocessed clock error sequence;

[0008] Based on the preprocessed clock difference sequence, clock difference prediction models with different forecast durations are constructed;

[0009] Calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite, and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights;

[0010] Obtaining the observation equation of the current observation event and the clock error estimate of the clock error prediction model at the corresponding forecast duration, adding the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and constructing an objective function based on the constrained observation equation and the posterior residual equation of the observation equation;

[0011] The objective function is solved to obtain the real-time clock difference of the low-orbit satellite.

[0012] A low-orbit satellite clock error estimation device with adaptive constraints of an ultra-short-term prediction model, comprising:

[0013] A preprocessing module is used to obtain the post-batch clock error sequence of the low-orbit satellite history, preprocess the post-batch clock error sequence, and obtain the preprocessed clock error sequence;

[0014] The clock error prediction model construction module is used to construct clock error prediction models under different forecast time lengths based on the preprocessed clock error sequence;

[0015] a true anomaly model construction module, configured to calculate the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite and dynamically construct a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights;

[0016] An objective function construction module is used to obtain the observation equation of the current observation event and the clock error estimate of the clock error prediction model under the corresponding forecast period, add the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and construct the objective function based on the constrained observation equation and the posterior residual equation of the observation equation;

[0017] The result output module is used to solve the objective function and obtain the real-time clock difference of the low-orbit satellite.

[0018] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0019] Obtaining a post-batch clock error sequence of the low-orbit satellite history, preprocessing the post-batch clock error sequence to obtain a preprocessed clock error sequence;

[0020] Based on the preprocessed clock difference sequence, clock difference prediction models with different forecast durations are constructed;

[0021] Calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite, and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights;

[0022] Obtaining the observation equation of the current observation event and the clock error estimate of the clock error prediction model at the corresponding forecast duration, adding the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and constructing an objective function based on the constrained observation equation and the posterior residual equation of the observation equation;

[0023] The objective function is solved to obtain the real-time clock difference of the low-orbit satellite.

[0024] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps:

[0025] Obtaining a post-batch clock error sequence of the low-orbit satellite history, preprocessing the post-batch clock error sequence to obtain a preprocessed clock error sequence;

[0026] Based on the preprocessed clock difference sequence, clock difference prediction models with different forecast durations are constructed;

[0027] Calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite, and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights;

[0028] Obtaining the observation equation of the current observation event and the clock error estimate of the clock error prediction model at the corresponding forecast duration, adding the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and constructing an objective function based on the constrained observation equation and the posterior residual equation of the observation equation;

[0029] The objective function is solved to obtain the real-time clock difference of the low-orbit satellite.

[0030] The above-mentioned method for estimating the clock error of low-orbit satellites with adaptive constraints in the ultra-short-term prediction model can obtain a data basis that is more suitable for analysis by obtaining and preprocessing the historical batch clock error sequence of low-orbit satellites, providing a reliable basis for subsequent modeling. Then, a clock error prediction model under different forecast time lengths is constructed based on the preprocessed clock error sequence. It can effectively predict the future clock error based on the complex characteristics of the clock error of low-orbit satellites, calculate the instantaneous true anomaly based on the historical precise ephemeris, and dynamically construct a true anomaly of multiple orbital arc segments containing adaptive weights based on its correlation with the preprocessed clock error sequence. The true anomaly model of angular data can use the relationship between orbit and clock error to provide more practical constraints for clock error estimation. Then, the clock error estimation value of the observation equation of the current observation event and the clock error prediction model is obtained, and the constrained observation equation and objective function are constructed. The clock error prediction information can be integrated into the real-time estimation process, and finally the objective function is solved. In the whole process, the ultra-short-term prediction value is used to establish the constrained observation equation for adaptive constraint, thereby effectively improving the accuracy and short-term stability of the real-time clock error estimation, and realizing sub-nanosecond spaceborne clock estimation that is more in line with the physical characteristics of the spaceborne clock. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 1 is a flow chart of a method for estimating low-orbit satellite clock errors with adaptive constraints of an ultra-short-term prediction model in one embodiment;

[0032] Figure 2 A data processing flow chart of low-orbit satellite real-time clock difference estimation under a constrained state in one embodiment;

[0033] Figure 3 Schematic diagram of clock error estimation principle under constraints in one embodiment;

[0034] Figure 4 A schematic diagram of a process for estimating the real-time clock difference of a low-orbit satellite under a constrained state in one embodiment;

[0035] Figure 5 This is a comparison chart of the RMSE of real-time clock difference estimation under different constraint parameters and without constraint in one embodiment;

[0036] Figure 6 A comparison diagram of frequency stability of real-time clock difference estimation under different constraint parameters and without constraint in one embodiment;

[0037] Figure 7 1. A structural block diagram of a low-orbit satellite clock error estimation device with adaptive constraints of an ultra-short-term prediction model in one embodiment;

[0038] Figure 8 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0040] In one embodiment, Figure 1 As shown, a method for estimating the clock error of a low-orbit satellite with an ultra-short-term prediction model adaptively constrained is provided, comprising the following steps:

[0041] Step 102: Obtain a post-batch clock error sequence of the low-orbit satellite history, and pre-process the post-batch clock error sequence to obtain a pre-processed clock error sequence.

[0042] A historical post-batch clock error series refers to a series of clock error data collected from low-orbiting satellites over a period of time, obtained using a batch processing method. This step can use various methods to obtain the data products required for clock error estimation, and the estimator is not limited to sequential least squares or square root information filtering. For post-batch clock error estimates, this example uses Sentinel-3 satellite observations as the data and products for the solution. The estimator uses sequential least squares with a processing interval of 10 seconds.

[0043] Preprocessing refers to operations such as gross error detection and repair to make the clock error series more suitable for subsequent analysis and modeling.

[0044] It can be understood that obtaining and preprocessing the post-batch clock error series removes the gross errors in the clock error data, making the clock error series smoother, providing a reliable data basis for the subsequent construction of an accurate clock error prediction model, and avoiding the interference of gross errors on model construction and clock error estimation.

[0045] Step 104: construct clock error prediction models under different prediction durations based on the preprocessed clock error sequence.

[0046] The clock error prediction model constructed based on the preprocessed clock error sequence is used to predict the clock error of low-orbit satellites at different future time lengths. For example, a first-order linear model is used when the forecast arc length is 30s, and a second-order polynomial model is used when the forecast arc length is 60s.

[0047] It can be understood that constructing a clock error prediction model under different forecast time lengths can predict the clock error of different time lengths in the future based on the complex characteristics of the low-orbit satellite clock error, providing prior information for real-time clock error estimation, and overcoming the problem that the clock error characteristics between different satellites are greatly different and the fixed parameter empirical model is not applicable.

[0048] Step 106 , calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite, and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence.

[0049] Historical precise ephemeris refers to data that records the precise past orbital information of low-orbit satellites and can be used to calculate parameters such as the satellite's position and velocity at different times. The instantaneous true anomaly represents the instantaneous angular position of a satellite relative to its perigee, reflecting its current position. The true anomaly model includes true anomaly data corresponding to multiple orbital segments with adaptive weights. The adaptive weights are dynamically adjusted based on the importance and impact of different orbital segments on clock error estimation. For example, if the perturbation force near perigee is large, the weight of this segment may be lower.

[0050] It can be understood that the true anomaly model is dynamically constructed using the correlation between the orbit and clock error sequences, and the influence of different orbital arc segments on the clock error is taken into account through adaptive weights, making the model more in line with the actual operation of the satellite, providing more accurate constraints for subsequent clock error estimation, and reducing the correlation between orbit and clock error parameters.

[0051] Step 108: Obtain the observation equation of the current observation event and the clock error estimate of the clock error prediction model under the corresponding forecast period, add the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and construct the objective function based on the constrained observation equation and the posterior residual equation of the observation equation.

[0052] The observation equation is a mathematical equation that describes the relationship between satellite observations and parameters to be estimated (such as clock error, position, etc.). The a posteriori residual equation is the equation obtained by linearizing the observation equation and is used to measure the difference between the observed value and the model calculated value. Figure 2 The data processing flow chart for constrained low-orbit satellite real-time clock error estimation is shown. By combining the constrained observation equation and the a posteriori residual equation to construct an objective function, solving this function for its minimum value yields the optimal estimate of the parameter to be estimated. Integrating clock error prediction information into the real-time clock error estimation process and adaptively constraining the real-time estimate through the constrained observation equation can improve the accuracy and stability of clock error estimation.

[0053] Step 110: Solve the objective function to obtain the real-time clock difference of the low-orbit satellite.

[0054] The real-time clock difference is obtained by solving the objective function. The obtained real-time clock difference is more consistent with the physical characteristics of the satellite-borne clock, can achieve sub-nanosecond satellite-borne clock estimation, and can effectively improve the accuracy and short-term stability of the real-time clock difference estimation.

[0055] In the above-mentioned method for estimating the clock error of low-orbit satellites with adaptive constraints of the ultra-short-term prediction model, by obtaining the historical batch clock error sequence of low-orbit satellites and preprocessing it, a data basis that is more suitable for analysis can be obtained, providing a reliable basis for subsequent modeling. Then, according to the preprocessed clock error sequence, a clock error prediction model under different forecast time lengths is constructed, which can realize effective prediction of future clock errors based on the complex characteristics of the clock error of low-orbit satellites, calculate the instantaneous true anomaly angle based on the historical precise ephemeris, and dynamically construct a true anomaly of multiple orbital arc segments containing adaptive weights based on its correlation with the preprocessed clock error sequence. The true anomaly model of angular data can use the relationship between orbit and clock error to provide more practical constraints for clock error estimation. Then, the clock error estimation value of the observation equation of the current observation event and the clock error prediction model is obtained, and the constrained observation equation and objective function are constructed. The clock error prediction information can be integrated into the real-time estimation process, and finally the objective function is solved. In the whole process, the ultra-short-term prediction value is used to establish the constrained observation equation for adaptive constraint, thereby effectively improving the accuracy and short-term stability of the real-time clock error estimation, and realizing sub-nanosecond spaceborne clock estimation that is more in line with the physical characteristics of the spaceborne clock.

[0056] In one embodiment, preprocessing the post-batch clock error sequence to obtain the preprocessed clock error sequence includes: using the 3 sigma rule and the median method to eliminate and repair the gross errors of the post-batch clock error sequence to obtain the preprocessed clock error sequence.

[0057] In this example, the estimated clock error sequence is treated using 3-sigma and the median method to remove gross errors and repair them, resulting in a smoother preprocessed clock error sequence. Gross error detection and repair are performed using both the 3-sigma and median criteria. The 3-sigma criterion is used to remove larger gross errors in the clock error sequence, while the median criterion is used to remove smaller errors. A complete post-processed clock error sequence is then obtained through interpolation and repair.

[0058] In one embodiment, constructing clock difference prediction models under different forecast time lengths based on the preprocessed clock difference sequence includes: constructing a first-order linear model under a first forecast arc length and a second-order polynomial model under a second forecast arc length based on the preprocessed clock difference sequence; the first forecast arc length is a 30s forecast arc length; the second forecast arc length is a 60s forecast arc length.

[0059] In this embodiment, the clock error model is selected according to the forecast time. When the forecast arc length is 30s, a first-order linear model is used, and the arc length is fitted. When the forecast arc length is 60s, a second-order polynomial model is used, and the arc length is fitted. 400s. Specifically, based on the half-month data analysis and modeling of the Sentinel-3 satellite, the optimal model parameters under the forecast arc lengths of 30s and 60s are obtained. The 30s forecast adopts a first-order linear model with a fitting arc length of 90s, and the 60s forecast adopts a second-order polynomial model with a fitting arc length of 400s. The forecast accuracy is between 0.02 and 0.04ns. The present invention performs modeling and analysis of historical data on the clock error model to obtain the specific model parameters of the satellite clock. The actual parameters for other satellites may not be limited to this. At the same time, the satellite clock model of the low-orbit satellite can be dynamically determined to prevent the forecast accuracy from decreasing due to model anomalies.

[0060] In one embodiment, the calculation of the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite includes: extracting the instantaneous orbit and instantaneous velocity at each moment from the historical precise ephemeris of the low-orbit satellite, using a broadcast ephemeris fitting method to process the extracted instantaneous orbit and velocity data to obtain six instantaneous orbit numbers of the satellite; and processing the six instantaneous orbit numbers to obtain the instantaneous true anomaly.

[0061] In this embodiment, the instantaneous orbit and instantaneous velocity are extracted from the historical precise ephemeris of the low-orbit satellite, and the six instantaneous orbital parameters are calculated using the broadcast ephemeris fitting algorithm. The instantaneous mean anomaly and true anomaly are calculated using the Kepler equation. Specifically, the precise ephemeris of the Sentinel-3 satellite is obtained, which includes the instantaneous satellite orbit and velocity. The instantaneous position and velocity are extracted from the historical precise ephemeris product, and the six instantaneous orbital parameters are calculated using the low-orbit ephemeris fitting algorithm. The mean anomaly M is solved for the eccentric anomaly E using the Kepler equation, as shown in formula (1):

[0062] M=E-esinE(1)

[0063] Furthermore, the instantaneous true anomaly v of the low-orbit satellite is calculated as shown in formula (2):

[0064]

[0065] Where e represents the eccentricity of the elliptical orbit. For Sentinel-3 satellites, the orbit is approximately a circular orbit.

[0066] In one embodiment, the dynamic construction of the true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence includes: calculating the times corresponding to the peaks and troughs of the clock error sequence based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence, and dividing the individual orbit into multiple orbital arc segments based on the times corresponding to the peaks and troughs; assigning a corresponding weight to each orbital arc segment based on the influence of the orbital position on the clock error, and dynamically constructing the true anomaly model based on the true anomaly data corresponding to the multiple orbital arc segments.

[0067] In this embodiment, the correlation between the true anomaly angle and the jitter characteristics of the clock error sequence is analyzed, and the single orbit arc is divided into segments l1, l2, l3 and l4 to obtain a true anomaly angle model that changes with time. Specifically, since the jitter peaks and troughs of the clock error sequence are correlated with the degree of the true anomaly angle, the arc segment of the satellite operation is further divided into segments, specifically referring to Figure 3 Schematic diagram of clock error estimation under constraints. Let the angle from the satellite approaching perigee to the satellite departing from perigee be α, and the angle from the satellite approaching apogee to the satellite departing from apogee be β. The four arc segments are defined as follows:

[0068] l1: the arc segment of the satellite from the perigee to the perigee, corresponding to the angle α;

[0069] l3: the arc segment of the satellite from close to the apogee to far from the apogee, corresponding to angle β;

[0070] l2: the middle arc segment between l1 and l3 (from perigee to apogee);

[0071] L4: the middle arc segment between L1 and L3 (from apogee to perigee);

[0072] According to the angles of α and β, the four different arc segments are adaptively weighted. Especially for the perigee, which may be subject to a large perturbation force, it is necessary to reduce a certain constraint weight to obtain a true perigee angle model that changes with time. The model parameters are dynamically changed.

[0073] In one embodiment, the objective function is:

[0074]

[0075] Among them, P Δ represents the weight of the original observation equation; P x represents the weight of the constraint observation equation, represents the constraint value, B is the design matrix, which contains the partial derivatives of the parameters to be estimated, and X is the parameter to be estimated, which contains the changes in the position and clock error of the low-orbit satellite. is the estimated value of the parameter to be estimated, and L is the difference between the actual observation value and the value calculated by the model.

[0076] Specifically, the dynamic PPP method is used to perform kinematic orbit determination and real-time clock error estimation on the Sentinel-3 satellite, and the estimator uses sequential least squares. For the onboard receiver of the low-orbit satellite, the observation equations for the pseudorange and carrier phase are as follows:

[0077]

[0078] Where, s represents a low-orbit satellite; r represents a receiver; f represents a frequency; represents the geometric distance from the low-orbit satellite to the GNSS satellite; c represents the speed of light; and t s,g Respectively represent the clock differences of the low-orbit satellite clock and the GNSS clock compared to the reference time (usually the GNSS system time); and d s,g Represent the hardware code delay of low-orbit satellite and GNSS satellite receivers respectively, and b s,g The hardware phase delay of the LEO satellite and GNSS satellite receivers respectively; represents the ionospheric error; λ f Indicates wavelength; N f Indicates the carrier phase integer ambiguity; and They represent the observation noise, multipath and other errors of pseudorange and carrier phase respectively. Since the orbital altitude of low-orbit satellites is between 160 and 2000 kilometers, the onboard observation equations do not consider the influence of tropospheric errors.

[0079] The following observations were obtained using the dual-frequency ionospheric-free combination mode:

[0080]

[0081] in, and They are the low-orbit satellite clock error and GNSS satellite clock error with pseudo-range hardware delay introduced; The ambiguity of pseudorange hardware delay and carrier phase hardware delay is introduced, and the solution is a floating point solution at this time; λ IF is the wavelength after combination; ε r,IF and e r,IF are the observation noise, multipath and other errors of pseudorange and carrier phase under the combined value.

[0082] The clock error of a low-orbit satellite is calculated together with its orbital position. Therefore, for real-time clock error estimation of a low-orbit satellite, based on this example, the above-mentioned onboard observation equation is linearized using Taylor expansion under the sequential least squares estimator to obtain the following a posteriori residual equation:

[0083] V=BX-L(7)

[0084] Among them, B is the design matrix, which contains the partial derivatives of the parameters to be estimated, X is the parameters to be estimated, which contains the changes in the position x, y, z and clock error dt of the low-orbit satellite, and L is the OMC, which represents the actual observation value minus the model calculation value. Specifically, it is expressed as:

[0085]

[0086] By combining the constraint equation and the posterior residual equation, we can get the following formula:

[0087]

[0088] Among them, P Δ represents the weight of the original observation equation; P x Represents the weight of the constraint observation equation, and the weight adopts adaptive weight for the arc segment l1~l4 according to the true anomaly model; represents the constraint value, i.e., the change in the LEO satellite clock error predicted based on the model value. The parameters are estimated using the sequential least squares estimation method, and the objective function is obtained based on the principle of minimizing the sum of squares of the least squares residuals.

[0089] In one embodiment, solving the objective function to obtain the real-time clock difference of the low-orbit satellite includes: using a sequential least squares estimation method to gradually update the parameter estimation value to obtain the optimal estimation value that minimizes the sum of squares of the residuals between the actual observation value and the model calculation value; and obtaining the real-time clock difference of the low-orbit satellite based on the clock difference parameter in the optimal estimation value.

[0090] In this embodiment, a sequential least squares estimator is used to solve the equation to achieve real-time estimation of the low-orbit satellite clock error. This example is not limited to this estimator, and square root information filtering can also be used to achieve real-time estimation of the clock error.

[0091] In a specific embodiment, Figure 4 The following is a flow chart of the real-time clock error estimation process for low-orbit satellites under constraints. By adding adaptive constraints to the real-time clock error estimation problem of existing low-orbit satellite onboard clocks, the accuracy and stability of the clock error estimation of low-orbit satellites can be improved. The specific process is as follows:

[0092] After starting, the process first determines whether a forecast is required for the current moment. If so, the latest 24-hour batch-processed historical clock error series of low-orbit satellites is obtained. Gross errors are detected and corrected using the 3-sigma and median methods, completing data preprocessing. Subsequently, the preprocessed clock errors of the low-orbit satellites are analyzed and modeled to obtain the clock error prediction model parameters. Clock error fitting and prediction are then performed, and the prediction parameters are updated. Observation events are then processed to obtain the current moment. Next, a determination is made as to whether constraints should be applied. If so, the latest clock error prediction value is obtained and added as a constraint to the observation equation for real-time clock error estimation, establishing a virtual observation equation. Simultaneously, historical precise ephemeris of low-orbit satellites is obtained to determine the satellite's real-time orbit and velocity parameters. Using the broadcast ephemeris fitting algorithm, the satellite's instantaneous true anomaly is calculated. The peak and trough moments of the clock error series are determined, and a historical model of the true anomaly is generated. Constraint weights are then determined accordingly. Finally, the normal equation is solved, the clock error is estimated and stored, and the process concludes, completing the real-time clock error estimation for the satellite.

[0093] like Figure 5 The following figure shows the RMSE comparison of real-time clock error estimation under different constraint parameters and without constraint. S1-S3 correspond to the RMSE comparison of real-time clock error estimation under the scenario of no constraint and adaptive constraint model prediction arc of 30s and 60s respectively. The true value of this example adopts the clock error estimated by simplified dynamics. This example is not limited to this. If there is an official precise clock error file, it can be used as the true value. The estimation accuracy of this method reaches 0.178ns in the 30s arc segment, which is an improvement of about 34.8%. The estimation accuracy reaches 0.18ns in the 60s arc segment, which is an improvement of about 34%. Figure 6 The following graphs compare the frequency stability of the real-time clock error estimation under different constraint parameters with that of the unconstrained model. S1-S3 correspond to the frequency stability comparisons of the real-time clock error estimation under the unconstrained, adaptively constrained, and model prediction arcs of 30s and 60s, respectively. The ground truth in this example uses the clock error estimated using simplified dynamics, but this example is not limited to this. Officially released precision clock error data can be used as the ground truth. For the 30s arc, this method achieves a 10-second stability of 4.5e-12, an improvement of approximately 39.4%, and a 100-second stability of 5.37e-12, an improvement of approximately 14.5%. For the 60s arc, the 10-second stability reaches 5.16e-12, an improvement of approximately 30.6%, and the 100-second stability reaches 5.88e-12, an improvement of approximately 0.06%.

[0094] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0095] In one embodiment, Figure 7 As shown, a low-orbit satellite clock error estimation device with an ultra-short-term prediction model adaptive constraint is provided, comprising:

[0096] A preprocessing module 702 is used to obtain a post-batch clock error sequence of the low-orbit satellite history, and preprocess the post-batch clock error sequence to obtain a preprocessed clock error sequence;

[0097] A clock error prediction model construction module 704 is used to construct clock error prediction models under different prediction time lengths based on the preprocessed clock error sequence;

[0098] a true anomaly model construction module 706 for calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights;

[0099] An objective function construction module 708 is configured to obtain the observation equation for the current observation event and the clock error estimate of the clock error prediction model at the corresponding forecast duration, add the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and construct an objective function based on the constrained observation equation and the posterior residual equation of the observation equation;

[0100] The result output module 710 is used to solve the objective function and obtain the real-time clock difference of the low-orbit satellite.

[0101] In one embodiment, it is also used to extract the instantaneous orbit and instantaneous velocity at each moment from the historical precise ephemeris of the low-orbit satellite, and use the broadcast ephemeris fitting method to process the extracted instantaneous orbit and velocity data to obtain the six instantaneous orbit numbers of the satellite; the six instantaneous orbit numbers are processed to obtain the instantaneous true anomaly.

[0102] In one of the embodiments, it is also used to calculate the time corresponding to the peak and trough of the clock error sequence based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence, and divide the individual orbit into multiple orbital arc segments according to the time corresponding to the peak and trough; assign a corresponding weight to each orbital arc segment according to the influence of the orbital position on the clock error, and dynamically construct a true anomaly model based on the true anomaly data corresponding to the multiple orbital arc segments.

[0103] In one embodiment, the objective function is:

[0104]

[0105] Among them, P Δ represents the weight of the original observation equation; P x represents the weight of the constraint observation equation, represents the constraint value, B is the design matrix, which contains the partial derivatives of the parameters to be estimated, and X is the parameter to be estimated, which contains the changes in the position and clock error of the low-orbit satellite. is the estimated value of the parameter to be estimated, and L is the difference between the actual observation value and the value calculated by the model.

[0106] In one embodiment, it is also used to gradually update the parameter estimation value using the sequential least squares estimation method to obtain the optimal estimation value that minimizes the sum of squared residuals between the actual observation value and the model calculated value; and the real-time clock difference of the low-orbit satellite is obtained based on the clock error parameter in the optimal estimation value.

[0107] In one embodiment, the method is also used to remove and repair the gross errors of the post-batch clock error sequence using the 3 sigma rule and the median method to obtain a pre-processed clock error sequence.

[0108] In one embodiment, it is also used to construct a first-order linear model under a first forecast arc length and a second-order polynomial model under a second forecast arc length based on the preprocessed clock difference sequence; the first forecast arc length is a 30s forecast arc length; the second forecast arc length is a 60s forecast arc length.

[0109] Regarding the specific limitations of the low-orbit satellite clock error estimation device with adaptive constraints of the ultra-short-term prediction model, please refer to the limitations of the low-orbit satellite clock error estimation method with adaptive constraints of the ultra-short-term prediction model mentioned above, which will not be repeated here. The various modules in the above-mentioned low-orbit satellite clock error estimation device with adaptive constraints of the ultra-short-term prediction model can be fully or partially implemented by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0110] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 8As shown. The computer device includes a processor, memory, network interface, display screen and input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a low-orbit satellite clock error estimation method with adaptive constraints of an ultra-short-term prediction model is implemented. The display screen of the computer device can be a liquid crystal display or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a key, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0111] Those skilled in the art will understand that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0112] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of the method in the above embodiment when executing the computer program.

[0113] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method in the above embodiment are implemented.

[0114] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0115] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and such modifications and improvements are intended to fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for estimating low-orbit satellite clock errors with adaptive constraints of an ultra-short-term prediction model, characterized in that: The method comprises: Obtain the post-batch clock error sequence of the low-orbit satellite history, preprocess the post-batch clock error sequence, and obtain the preprocessed clock error sequence; Based on the preprocessed clock difference sequence, clock difference prediction models with different forecast durations are constructed; Calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite, and dynamically constructing a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights; Obtaining the observation equation of the current observation event and the clock error estimate of the clock error prediction model at the corresponding forecast duration, adding the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and constructing an objective function based on the constrained observation equation and the posterior residual equation of the observation equation; The objective function is solved to obtain the real-time clock difference of the low-orbit satellite.

2. The method according to claim 1, characterized in that Calculating the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite includes: The instantaneous orbit and velocity at each moment are extracted from the historical precise ephemeris of the low-orbit satellite. The broadcast ephemeris fitting method is used to process the extracted instantaneous orbit and velocity data to obtain the six instantaneous orbit numbers of the satellite. The instantaneous true anomaly is obtained by processing the six instantaneous orbit numbers.

3. The method according to claim 1, characterized in that The dynamically constructing the true anomaly model according to the correlation between the instantaneous true anomaly and the preprocessed clock error sequence comprises: The time corresponding to the peak and the trough of the clock error sequence is calculated based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence, and the single orbit is divided into multiple orbital arc segments based on the time corresponding to the peak and the trough; According to the influence of the orbital position on the clock error, each orbital arc segment is assigned a corresponding weight, and the true anomaly angle model is dynamically constructed based on the true anomaly angle data corresponding to multiple orbital arc segments.

4. The method according to claim 1, wherein The objective function is: Among them, P Δ represents the weight of the original observation equation; P x represents the weight of the constraint observation equation, represents the constraint value, B is the design matrix, which contains the partial derivatives of the parameters to be estimated, and X is the parameter to be estimated, which contains the changes in the position and clock error of the low-orbit satellite. is the estimated value of the parameter to be estimated, and L is the difference between the actual observation value and the value calculated by the model.

5. The method according to claim 1, wherein Solving the objective function to obtain the real-time clock difference of the low-orbit satellite includes: The sequential least squares estimation method is used to gradually update the parameter estimates to obtain the optimal estimate that minimizes the sum of squares of the residuals between the actual observations and the model calculations. According to the clock error parameters in the optimal estimate, the real-time clock error of the low-orbit satellite is obtained.

6. The method according to claim 1, wherein The post-batch clock difference sequence is preprocessed to obtain the following clock difference sequence: The 3 sigma rule and median method are used to eliminate and repair the gross errors of the post-batch clock error series to obtain the preprocessed clock error series.

7. The method according to claim 1, characterized in that The clock error prediction models under different forecast durations are constructed based on the preprocessed clock error sequence, including: According to the preprocessed clock difference sequence, a first-order linear model under the first forecast arc length and a second-order polynomial model under the second forecast arc length are constructed respectively; the first forecast arc length is a 30s forecast arc length; the second forecast arc length is a 60s forecast arc length.

8. A low-orbit satellite clock error estimation device with adaptive constraints of an ultra-short-term prediction model, characterized in that: The device comprises: A preprocessing module is used to obtain the post-batch clock error sequence of the low-orbit satellite history, preprocess the post-batch clock error sequence, and obtain the preprocessed clock error sequence; The clock error prediction model construction module is used to construct clock error prediction models under different forecast time lengths based on the preprocessed clock error sequence; a true anomaly model construction module, configured to calculate the instantaneous true anomaly based on the historical precise ephemeris of the low-orbit satellite and dynamically construct a true anomaly model based on the correlation between the instantaneous true anomaly and the preprocessed clock error sequence; the true anomaly model includes true anomaly data corresponding to multiple orbital arcs with adaptive weights; An objective function construction module is used to obtain the observation equation of the current observation event and the clock error estimate of the clock error prediction model under the corresponding forecast period, add the clock error estimate as a constraint value to the observation equation to obtain a constrained observation equation, and construct the objective function based on the constrained observation equation and the posterior residual equation of the observation equation; The result output module is used to solve the objective function and obtain the real-time clock difference of the low-orbit satellite.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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