A High-Precision Modeling Method for Low-Earth Orbit Satellites Based on Measured Data Correction

Abstract

This application relates to a high-precision modeling method for low-Earth orbit (LEO) satellite orbits based on measured data correction. The method includes: first, acquiring measured orbital error data of in-orbit LEO satellites; setting the simulation scenario duration; periodically extending or pruning / segmenting the error data; generating a pseudo-random sequence using a 10-level feedback shift register; modulating and combining the pseudo-random sequence to obtain a first and a second sequence; filtering the valid second sequence through correlation calculation to obtain uncorrelated sequences for each segment; finally, combining and sampling according to the number of satellites, adding the orbital error to the error-free orbit to achieve high-precision modeling. This method can accurately reflect the characteristics of measured orbital errors, achieving high-precision modeling of LEO satellite orbits.

Description

Technical Field

[0001] This application relates to the field of satellite navigation simulation technology, particularly orbit modeling technology, and more specifically to a high-precision modeling method for low-Earth orbit satellites based on measured data correction. Background Technology

[0002] Currently, most low-Earth orbit (LEO) constellations are still in the demonstration and testing phase, lacking sufficient measured LEO constellation ephemeris products. Therefore, when simulating the orbits of LEO satellites, a zero-error orbit is typically first fitted using methods such as orbital elements and dual planetary ephemeris, and then errors generated by researchers are added to simulate the real orbit. Researchers generate orbital errors in various ways, ranging from simply adding zero-mean normal distribution random errors to more complex methods such as adding fitted periodic trigonometric function errors based on the quasi-periodic sine and cosine fluctuation characteristics of LEO satellite orbit determination errors. However, none of these error generation methods are based on measured data, and therefore cannot accurately reflect the characteristics of measured orbital errors. Furthermore, research has shown that when the LEO satellite orbital error exceeds 0.35m, the accuracy of precise point positioning based on LEO enhancement is significantly affected. Therefore, simulating more accurate LEO orbits is crucial for verifying LEO navigation and positioning. Summary of the Invention

[0003] Therefore, it is necessary to provide a method for high-precision modeling of low-Earth orbit satellites based on measured data, which can accurately reflect the characteristics of measured orbit errors and achieve high-precision modeling of low-Earth orbit satellite orbits, in order to address the above-mentioned technical problems.

[0004] A high-precision modeling method for low-Earth orbit satellites based on measured data correction, the method comprising:

[0005] Obtain n sets of measured orbital error data from some in-orbit low-Earth orbit satellites and set the simulation scenario duration;

[0006] Based on ensuring that the duration of the measured track error data is equal to the duration of the simulation scenario, the measured track error is periodically extended or trimmed to obtain the processed track error data, which is then divided into m segments.

[0007] Design a 10-stage feedback shift register to generate 1023 sets of pseudo-random sequences; An extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences to obtain the first sequence; using the segments of the processed orbital error data, one sequence is taken from each of the n sets of 1023 modulation sequences and combined to obtain multiple second sequences;

[0008] Calculate the correlation between each second sequence and the first sequence. If they are correlated, discard the second sequence; otherwise, the second sequence is valid, resulting in multiple uncorrelated sequences for each segment.

[0009] Based on the number of low-Earth orbit satellites in the simulation scenario, multiple sets of uncorrelated orbit error sequences are combined from multiple uncorrelated sequences. The resulting orbit errors are then sampled according to the sampling interval of the original sequences and added to the error-free orbit in the simulation to achieve high-precision modeling of low-Earth orbit satellite orbits.

[0010] The aforementioned method for high-precision modeling of low-Earth orbit (LEO) satellite orbits based on measured data obtains measured orbit error data from some in-orbit LEO satellites. By periodically extending or trimming the data to adapt to the simulation scenario duration, the true orbit error characteristics are preserved, addressing the problem of traditional methods lacking a measured foundation. A 10-level feedback shift register is introduced to generate a pseudo-random sequence. The measured error segments are modulated onto this sequence, and after correlation screening, uncorrelated sequences are obtained, ensuring the independence and accuracy of the error sequences and avoiding unreasonable synchronization of errors in multi-satellite simulations. Then, based on the number of simulated satellites and combining sequences, sampling is performed at the original sampling interval, and the errors are added to error-free orbits. Using measured data to generate orbit errors more realistically reflects the LEO satellite orbit characteristics. This allows for more accurate verification of the navigation enhancement effect of LEO satellites on GNSS, especially in precise point positioning, where higher-precision orbits significantly improve positioning accuracy. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating a high-precision modeling method for low-Earth orbit satellites based on measured data correction in one embodiment.

[0012] Figure 2 This is a schematic diagram illustrating the execution process of a high-precision modeling method for low-Earth orbit satellites based on measured data correction in one embodiment. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0014] In one embodiment, such as Figure 1 and Figure 2 As shown, a high-precision modeling method for low-Earth orbit satellites based on measured data correction is provided, including the following steps:

[0015] Step 102: Obtain n sets of measured orbit error data from some in-orbit low-Earth orbit satellites and set the simulation scenario duration; Based on making the duration of the measured orbit error data equal to the duration of the simulation scenario, perform periodic extension or trimming on the measured orbit error to obtain the processed orbit error data and divide the processed orbit error data into m segments.

[0016] Obtain the measured orbital error of a low-Earth orbit (LEO) satellite within a visible arc segment, along with the corresponding elevation angle variation trend and sampling interval. Determine the duration of the simulation scenario based on simulation requirements. If the simulation scenario duration is longer than the duration of the measured LEO satellite orbital error data, the measured data is periodically extended by concatenating the beginning and end. If the simulation scenario duration is shorter than the measured data duration, the corresponding measured data is trimmed based on the visible arc segment of the satellite during the simulation period. For example, if the satellite elevation angle increases from 10° to 90° during the simulation period, the portion of the measured data where the elevation angle increases from 10° to 90° is extracted. Divide the periodically extended or truncated data into segments equal to 1 / m of the total length. Each measured satellite data set consists of m segments, where m can be adjusted according to simulation requirements. The subsequences are denoted as follows:

[0017] …, …, ,…, …, .

[0018] Step 104: Design a 10-stage feedback shift register to generate 1023 sets of pseudo-random sequences; An extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences to obtain a first sequence; using the segments of the processed orbital error data, one sequence is taken from each of the n sets of 1023 modulation sequences and combined to obtain multiple second sequences.

[0019] The characteristic polynomial of a 10-stage feedback shift register is:

[0020] .

[0021] A total of 1023 pseudo-random sequences can be obtained, denoted as... …, .

[0022] Will Each subsequence is modulated onto the pseudo-random sequence generated in step 3:

[0023] .

[0024] Total The new sequences are denoted as follows: ,

[0025] …, ,…, …, , where k ranges from 1 to 1023.

[0026] From each of the corresponding segments, one sequence is taken from each of the n groups of 1023 modulation sequences and combined to obtain a new sequence D. Taking the first segment as an example:

[0027] .

[0028] in, a, b, c .

[0029] The first sequence is obtained by modulating n×m extended segmented sequences based on measured orbital error data onto 1023 sets of pseudo-random sequences. This step achieves the fusion of measured error characteristics and pseudo-random sequence properties. The modulation process can be understood as using the amplitude, trend, and other characteristics of the measured error to label the pseudo-random sequence, so that the generated first sequence contains both the real error information of the measured data and the mathematical regularity of the pseudo-random sequence. Then, by combining one sequence from each of the n sets of 1023 modulated sequences from the segmented orbital error data, multiple second sequences are obtained. This is based on the need for multiple satellites and multiple segments in the simulation scenario, allowing for flexible combination of the fused sequences and initially constructing an error sequence library adapted to different satellites and different orbital segments.

[0030] Step 106: Calculate the correlation between each second sequence and the first sequence. If they are correlated, discard the second sequence; if they are not correlated, the second sequence is valid, resulting in multiple uncorrelated sequences for each segment.

[0031] Calculate the generated separately The correlation between the sequence and the P sequence is assessed; if a correlation is found, the sequence is discarded. Sequences; if uncorrelated, the sequence is valid. In low-Earth orbit constellation simulations, the orbital errors of different satellites should be independent. If there is a strong correlation between sequences, it will lead to unreasonable synchronization of the orbital errors of multiple satellites in the simulation, deviating from the real scenario. By calculating the correlation, correlated sequences are eliminated, and independent valid sequences are retained, ensuring that the error sequence of each segment and each satellite can independently reflect the orbital error characteristics. This provides accurate and independent error components for high-precision multi-satellite orbit simulation, solving the problem of the lack of independence of error sequences and the tendency to cause distortion of simulation results in traditional methods.

[0032] Step 108: Based on the number of low-Earth orbit satellites in the simulation scenario, combine multiple sets of uncorrelated orbit error sequences from multiple uncorrelated sequences, and sample according to the sampling interval of the original sequence. The obtained orbit errors are added to the error-free orbit of the simulation to achieve high-precision modeling of low-Earth orbit satellite orbits.

[0033] Based on the number v of low-orbit satellites in the simulation scenario, from Combine v sets of uncorrelated orbital error sequences, and follow the original sequences. By sampling at specific intervals, the orbital errors obtained are added to the simulated error-free orbit, achieving high-precision modeling of the low-Earth orbit satellite orbit and completing the final connection from the error sequence to the simulated orbit. The sampling interval of the original sequence records the data acquisition pattern of the measured orbital errors. Sampling at this interval can accurately reproduce the distribution characteristics of the errors in the time dimension. Adding these errors to the fitted error-free orbit ensures that the simulated orbit retains the basic framework of the theoretical orbit while incorporating the real errors from the measured data. Compared with traditional error addition without measured basis, this significantly improves the fit between the simulated orbit and the real orbit, effectively solving the problem that insufficient accuracy of the simulated orbit affects the verification of low-Earth orbit navigation enhancement effects.

[0034] The aforementioned method for high-precision modeling of low-Earth orbit (LEO) satellite orbits based on measured data obtains measured orbit error data from some in-orbit LEO satellites. By periodically extending or trimming the data to adapt to the simulation scenario duration, the true orbit error characteristics are preserved, addressing the problem of traditional methods lacking a measured foundation. A 10-level feedback shift register is introduced to generate a pseudo-random sequence. The measured error segments are modulated onto this sequence, and after correlation screening, uncorrelated sequences are obtained, ensuring the independence and accuracy of the error sequences and avoiding unreasonable synchronization of errors in multi-satellite simulations. Then, based on the number of simulated satellites and combining sequences, sampling is performed at the original sampling interval, and the errors are added to error-free orbits. Using measured data to generate orbit errors more realistically reflects the LEO satellite orbit characteristics. This allows for more accurate verification of the navigation enhancement effect of LEO satellites on GNSS, especially in precise point positioning, where higher-precision orbits significantly improve positioning accuracy.

[0035] In one embodiment, the simulation scenario duration is set by obtaining the measured orbital errors of a portion of the low-Earth orbit satellites in orbit, including:

[0036] Obtain the measured orbital error of a low-orbit satellite within a visible arc segment, along with the corresponding elevation angle variation trend and sampling interval; determine the duration of the simulation scenario based on simulation requirements.

[0037] In one embodiment, the measured orbit error is periodically extended or trimmed based on making the duration of the measured orbit error data equal to the duration of the simulation scenario, resulting in processed orbit error data. The processed orbit error data is then divided into m segments, including:

[0038] If the duration of the simulation scenario is longer than the duration of the measured orbit error data, the measured data will be periodically extended by connecting the beginning and end of the simulation scenario; if the duration of the simulation scenario is shorter than the duration of the measured orbit error data, the corresponding measured data will be cropped according to the visible arc of the satellite during the simulation period.

[0039] The periodically extended or truncated data is divided into segments of 1 / m of the total length. Each measured satellite data consists of m segments, where the size of m is adjusted according to the needs of the simulation service.

[0040] In one embodiment, the 10-stage feedback shift register designed to generate pseudo-random sequences is as follows:

[0041] .

[0042] in, Represents formal variables.

[0043] In one embodiment, An extended segmented sequence based on measured data is modulated onto 1023 pseudo-random sequences to obtain the first sequence, which includes:

[0044] Will An extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences, resulting in the first sequence as follows:

[0045] .

[0046] in, This represents the measured track error data after segmentation. This represents a pseudo-random sequence.

[0047] The first sequence is The new sequences are denoted as follows: ,

[0048] …, ,…, …, , where k ranges from 1 to 1023.

[0049] In one embodiment, by segmenting the processed orbital error data, one sequence is taken from each of the n groups of 1023 modulation sequences and combined to obtain multiple second sequences, including:

[0050] From the corresponding segment, one sequence is taken from each of the n groups of 1023 modulation sequences and combined to obtain the second sequence D. Taking the first segment as an example:

[0051] .

[0052] in, a, b, c .

[0053] In one embodiment, calculating the correlation between each second sequence and the first sequence includes:

[0054] Calculate separately sequence and sequence , , ..., To determine the correlation between the two sequences, first calculate the mean of the two sequences, and then calculate the covariance and standard deviation based on the mean.

[0055] The Pearson correlation coefficient is calculated based on the covariance and standard deviation. This coefficient is then compared to a pre-set threshold. If the absolute value of the Pearson correlation coefficient is less than the pre-set threshold, the current value is retained. Sequence, otherwise discard.

[0056] In a specific embodiment, the irrelevant threshold adopted in this paper is: D sequences exceeding this threshold are retained; otherwise, they are discarded.

[0057] In one embodiment, the means of the two sequences are calculated as follows:

[0058] ;

[0059] ;

[0060] in, This represents the mean of the second sequence. This represents the total number of measured track error data. Indicates the first The second sequence corresponding to the set of measured track error data. This represents the mean of the first sequence. Indicates the first The first sequence corresponding to the measured track error data.

[0061] In one embodiment, the covariance and standard deviation are calculated based on the mean:

[0062] ;

[0063] ;

[0064] ;

[0065] in, Describing covariance, This represents the mean of the second sequence. This represents the total number of measured track error data. Indicates the first The second sequence corresponding to the set of measured track error data. This represents the mean of the first sequence. Indicates the first The first sequence corresponding to the set of measured orbital error data. This represents the standard deviation of the second sequence. This represents the standard deviation of the first sequence.

[0066] In one embodiment, the Pearson correlation coefficient is calculated based on the covariance and standard deviation as follows:

[0067] .

[0068] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed 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 some of the sub-steps or stages of other steps.

[0069] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0070] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A high-precision modeling method for low-Earth orbit satellites based on measured data correction, characterized in that, The method includes: Obtain n sets of measured orbital error data from some in-orbit low-Earth orbit satellites and set the simulation scenario duration; Based on making the duration of the measured track error data equal to the duration of the simulation scenario, the measured track error data is periodically extended or clipped to obtain processed track error data, which is then divided into m segments. Design a 10-stage feedback shift register to generate 1023 sets of pseudo-random sequences; An extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences to obtain the first sequence; using the segments of the processed orbital error data, one sequence is taken from each of the n sets of 1023 modulation sequences and combined to obtain multiple second sequences; Calculate the correlation between each second sequence and the first sequence. If they are correlated, discard the second sequence; otherwise, the second sequence is valid, resulting in multiple uncorrelated sequences for each segment. Based on the number of low-Earth orbit satellites in the simulation scenario, multiple sets of uncorrelated orbit error sequences are combined from multiple uncorrelated sequences. The resulting orbit errors are then sampled according to the sampling interval of the original sequences and added to the error-free orbit in the simulation to achieve high-precision modeling of low-Earth orbit satellite orbits.

2. The method according to claim 1, characterized in that, The simulation scenario duration was set by obtaining the measured orbital errors of some in-orbit and low-Earth orbit satellites, including: Obtain the measured orbital error of a low-orbit satellite within a visible arc segment, along with the corresponding elevation angle variation trend and sampling interval; determine the duration of the simulation scenario based on simulation requirements.

3. The method according to claim 1, characterized in that, Based on ensuring the duration of the measured orbit error data is equal to the duration of the simulation scenario, the measured orbit error is periodically extended or trimmed to obtain processed orbit error data. This processed orbit error data is then divided into m segments, including: If the duration of the simulation scenario is longer than the duration of the measured orbit error data, the measured data will be periodically extended by connecting the beginning and end of the simulation scenario; if the duration of the simulation scenario is shorter than the duration of the measured orbit error data, the corresponding measured data will be cropped according to the visible arc of the satellite during the simulation period. The periodically extended or truncated data is divided into segments of 1 / m of the total length, with each measured satellite data set consisting of m segments, where the size of m is adjusted according to the needs of the simulation service.

4. The method according to any one of claims 1 to 3, characterized in that, The 10-stage feedback shift register designed for generating pseudo-random sequences is as follows: in, Represents formal variables.

5. The method according to claim 1, characterized in that, Will An extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences to obtain the first sequence, which includes: Will Each extended segmented sequence based on measured orbital error data is modulated onto 1023 sets of pseudo-random sequences, resulting in the first sequence as follows: in, This represents the measured track error data after segmentation. Represents a pseudo-random sequence; The first sequence is The new sequences are denoted as follows: …, …, ,…, …, , where k ranges from 1 to 1023.

6. The method according to claim 5, characterized in that, By segmenting the processed orbital error data, one sequence is taken from each of the n groups of 1023 modulation sequences and combined to obtain multiple second sequences, including: From the corresponding segment, one sequence is taken from each of the n groups of 1023 modulation sequences and combined to obtain the second sequence D. Taking the first segment as an example: in, a, b, c .

7. The method according to claim 1, characterized in that, Calculate the correlation between each second sequence and the first sequence, including: Calculate separately sequence and sequence , , ..., To determine the correlation between the two sequences, first calculate the mean of the two sequences, and then calculate the covariance and standard deviation based on the mean. The Pearson correlation coefficient is calculated based on the covariance and standard deviation; the Pearson correlation coefficient is compared with a preset threshold; if the absolute value of the Pearson correlation coefficient is less than the preset threshold, the current value is retained. Sequence, otherwise discard.

8. The method according to claim 7, characterized in that, Calculate the means of the two sequences as follows: in, This represents the mean of the second sequence. This represents the total number of measured track error data. Indicates the first The second sequence corresponding to the set of measured track error data. This represents the mean of the first sequence. Indicates the first The first sequence corresponding to the measured track error data.

9. The method according to claim 7, characterized in that, The covariance and standard deviation are calculated based on the mean: in, Describing covariance, This represents the mean of the second sequence. This represents the total number of measured track error data. Indicates the first The second sequence corresponding to the set of measured track error data. This represents the mean of the first sequence. Indicates the first The first sequence corresponding to the set of measured orbital error data. This represents the standard deviation of the second sequence. This represents the standard deviation of the first sequence.

10. The method according to claim 9, characterized in that, The Pearson correlation coefficient is calculated based on the covariance and standard deviation: 。

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