Method for detecting orbital maneuvers based on kinematic inter-epoch differences

Abstract

The present application belongs to the technical field of satellite orbit maneuver detection, and specifically discloses an orbit maneuver detection method based on kinematic orbit epoch difference. The present application uses kinematic orbit data to obtain the orbit maneuver force through the non-difference method, thereby getting rid of the dependence on the prior dynamic model and directly using the high-precision satellite-borne GNSS kinematic orbit product. The kinematic orbit is a pure geometric solution obtained through precise point positioning (PPP), and it does not undergo any dynamic smoothing, so it truly records the position jump of the satellite during the maneuver. The present application is simple and reliable, the kinematic orbit data is easy to obtain, and it does not need to provide additional bias products externally. The algorithm is simple and easy to implement, and it is convenient for real-time application. In addition, the present application method also fills the data gap during the accelerometer shutdown period, and can provide more pure background field information for the earth gravity field inversion.

Description

Technical Field

[0001] This invention belongs to the field of satellite orbital maneuver detection technology, specifically relating to an orbital maneuver detection method based on the difference between kinematic orbital epochs. Background Technology

[0002] Throughout the lifecycle of a Low Earth Orbit Satellite (LEO) mission, precise orbit determination (POD) and orbit maintenance are the two cornerstones ensuring mission success. During its operation in orbit, a satellite inevitably performs various orbital maneuvers, including orbit maintenance maneuvers to counteract atmospheric drag, relative position adjustments to maintain formation configuration, and attitude maneuvers to avoid space debris or adjust data transmission attitude. These maneuvers manifest in orbital dynamics as instantaneous velocity pulses or constant acceleration within a rectangular window. For precise orbit determination based on dynamic models, these unmodeled changes in satellite state are a significant source of interference for real-time or post-hoc precise orbit determination, causing the dynamic model to fail to accurately reflect the satellite's trajectory, resulting in abnormally large observation residuals and compromising the continuity and reliability of orbit determination calculations. Traditional dynamic orbit determination methods rely on accurate modeling of satellite perturbations (including Earth's gravity, lunar and solar gravity, atmospheric drag, solar radiation pressure, etc.) and numerical integration of the equations of motion. In the event of an unknown thrust event, the dynamic model will be unable to fit the actual observation data, leading to divergence in parameter estimation solutions. Alternatively, the orbit determination software may spread the thrust error across the entire arc in an attempt to force a fit to the data, resulting in overall orbital deviation. Therefore, accurately determining satellite orbital maneuver events, including the start and end epochs, is a prerequisite for orbital maneuver perturbation modeling and precise orbit determination.

[0003] Current methods for detecting orbital maneuvers primarily rely on two types of data: telemetry data and orbit determination GNSS residuals. However, the telemetry data method is not only limited by performance discrepancies caused by thruster aging and calibration deviations, but also frequently fails due to accelerometer saturation or protective shutdown under high thrust conditions. Furthermore, it faces challenges such as non-public data and inconsistencies between satellite and ground commands. Meanwhile, the GNSS residual method based on dynamic models is constrained by the accuracy of the background force model, exhibiting low detection sensitivity and significant time delays. It also struggles to effectively decouple continuous low-thrust maneuvers from drastic atmospheric drag changes, often requiring complex statistical inference and filtering algorithms for effective discrimination. In summary, telemetry data is often difficult to obtain due to mission limitations, while the GNSS residual-based method relies on cumbersome dynamic modeling and integral iteration, resulting in high algorithmic complexity and susceptibility to errors in the dynamic model. Summary of the Invention

[0004] The purpose of this invention is to propose a method for detecting orbital maneuvers based on the difference between kinematic orbital epochs. The method uses kinematic orbital data to obtain the orbital dynamics through a non-difference method, thereby eliminating the dependence on prior dynamic models. The method is simple and reliable.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] The orbital maneuver detection method based on the difference between kinematic orbital epochs includes the following steps:

[0007] Step 1. Use the kinematic orbit data of the low-Earth orbit satellite, which is obtained through precise single-point positioning calculation, to record the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system;

[0008] Step 2. Perform SG filtering smoothing on the low-Earth orbit satellite position data;

[0009] Step 3. Based on the original orbit of the low-Earth orbit satellite and the orbit smoothed by SG filtering, the five-point center difference method is used to extract acceleration information from the discrete position sequence and calculate the original acceleration and the reference background acceleration.

[0010] The five-point central difference method utilizes the positional information of five points, including the current epoch and the two epochs before and after it;

[0011] Step 4. Transform the original acceleration and background reference acceleration to the satellite body coordinate system (SRF);

[0012] Using attitude quaternion data provided by low-orbit satellites, the coordinate transformation of the maneuvering force from the inertial coordinate system to the SRF coordinate system is realized, and the rotation matrix from the SRF coordinate system to the inertial coordinate system is constructed according to Euler's rotation theorem.

[0013] Since the rotation matrix is ​​an orthogonal matrix, its inverse matrix is ​​equal to its transpose matrix;

[0014] Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system;

[0015] Step 5. Extract high-frequency acceleration residuals and perform track motion detection;

[0016] A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration to eliminate the influence of the background field and extract the high-frequency residual containing information of both the orbital control maneuver signal and the residual high-frequency noise.

[0017] Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

[0018] Furthermore, based on the aforementioned orbital maneuver detection method based on the difference between kinematic orbital epochs, this invention also proposes a corresponding orbital maneuver detection system based on the difference between kinematic orbital epochs, which adopts the following technical solution:

[0019] The orbital maneuver detection system based on the difference between kinematic orbital epochs includes the following modules:

[0020] The kinematic orbit acquisition module is used to obtain the kinematic orbit data of the low-Earth orbit satellite through precise single-point positioning calculation, and records the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system.

[0021] The Savitzky-Golay filtering and smoothing module is used to filter and smooth the position data of low-Earth orbit satellites.

[0022] The numerical differential acceleration calculation module is used to extract acceleration information from the discrete position sequence based on the original trajectory and the trajectory smoothed by SG filtering, and to calculate the original acceleration and the reference background acceleration using the five-point center difference method.

[0023] The five-point central difference method utilizes the positional information of a total of five points, including the current epoch and the two epochs before and after it.

[0024] The coordinate transformation module is used to transform the original acceleration and background reference acceleration to the satellite body coordinate system (SRF).

[0025] Using attitude quaternion data provided by low-orbit satellites, the coordinate transformation of the maneuvering force from the inertial coordinate system to the SRF coordinate system is realized, and the rotation matrix from the SRF coordinate system to the inertial coordinate system is constructed according to Euler's rotation theorem.

[0026] Since the rotation matrix is ​​an orthogonal matrix, its inverse matrix is ​​equal to its transpose matrix;

[0027] Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system;

[0028] And a track motion detection module, used to extract high-frequency acceleration residuals and realize track motion detection;

[0029] A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration. The influence of the background field is eliminated, and the high-frequency residual containing information of both the orbit control maneuver signal and the residual high-frequency noise is extracted.

[0030] Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

[0031] Furthermore, based on the above-mentioned orbital maneuver detection method based on the difference between kinematic orbital epochs, this invention also proposes a computer device, which includes a memory and one or more processors.

[0032] Executable code is stored in memory. When the processor executes the executable code, it implements the steps of the above-described orbital maneuver detection method based on the difference between kinematic orbital epochs.

[0033] Furthermore, based on the above-mentioned orbital maneuver detection method based on the difference between kinematic orbital epochs, this invention also proposes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the above-mentioned orbital maneuver detection method based on the difference between kinematic orbital epochs.

[0034] The present invention has the following advantages:

[0035] This invention proposes a method for detecting orbital maneuvers based on inter-epoch difference in kinematic orbits. This method innovatively introduces Savitzky-Golay (SG) filtering to construct a smoothed non-conservative force background field for kinematic orbit data acquired by precise point positioning (PPP) of low-Earth orbit satellites, and combines this with a high-precision five-point center difference algorithm to obtain the acceleration. By performing inter-epoch difference between the original kinematic acceleration and the smoothed background acceleration, the influence of Earth's gravity and conventional non-conservative forces is eliminated, and the high-frequency thrust residual is directly extracted in the satellite body coordinate system (SRF). The high-precision kinematic orbit of the spaceborne GNSS kinematic orbit product is a pure geometric solution obtained through precise point positioning (PPP), which does not undergo any dynamic smoothing and truthfully records the position jumps of the satellite during maneuvers. This method eliminates the dependence on high-precision prior dynamic models and engineering telemetry data, and can independently and sensitively detect the occurrence time, duration, and thrust direction of satellite maneuvers. The method is simple, reliable, and easy to implement in engineering. The method of this invention is simple and reliable, the kinematic trajectory data is easy to acquire, and it does not require external bias products. The algorithm is simple and easy to implement, facilitating real-time applications. Furthermore, this invention fills the data gap during accelerometer shutdown and provides cleaner background field information for Earth's gravity field inversion. Attached Figure Description

[0036] Figure 1 This is a flowchart of the orbital maneuver detection method based on the difference between kinematic orbital epochs in an embodiment of the present invention. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0038] Example 1

[0039] To address the limitations of telemetry data acquisition in existing orbital maneuver detection technologies and the time lag and susceptibility to background force model errors in traditional dynamic orbit determination residual methods, this invention proposes an independent satellite orbital maneuver detection method based on high-precision kinematic orbit numerical differentiation. This method achieves independent thrust acceleration inversion without relying on prior dynamic models or engineering telemetry data. The advantage of the kinematic orbit determination method is that the orbit calculation process is independent of the satellite's dynamic characteristics, and the orbit determination accuracy is unaffected by the dynamic model and orbital maneuver control. Therefore, the kinematic orbits of low-Earth orbit satellites are often used for inversion studies of the Earth's gravity field.

[0040] like Figure 1 As shown, the orbital maneuver detection method based on the difference between kinematic orbital epochs includes the following steps:

[0041] Step 1. Obtain the kinematic trajectory.

[0042] Using kinematic orbit data from a low-Earth orbit satellite, which was obtained through precise point positioning (PPP) technology, the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system were recorded. .

[0043] Step 2. Smooth the surface using Savitzky-Golay filtering.

[0044] The obtained low-orbit satellite position data is smoothed using SG filtering.

[0045] In kinematic trajectory data processing, due to the presence of high-frequency observation noise (such as GPS receiver measurement errors), directly performing the second derivative will severely amplify the noise, making the acceleration calculation results unusable.

[0046] Therefore, it is crucial to introduce Savitzky-Golay (SG) filtering for preprocessing in this embodiment.

[0047] SG filtering is essentially a local polynomial least squares fitting method based on the time domain.

[0048] Compared to other smoothing methods (such as moving average and Gaussian filtering), the biggest advantage of SG filtering is:

[0049] While effectively filtering out high-frequency random noise, it can maintain the high-order moment characteristics of the signal (such as the width, height and shape of the peaks) very well, avoiding excessive smoothing or distortion of real non-gravitational disturbance signals (such as thruster pulses).

[0050] For high-frequency sampling data of low-Earth orbit satellites, it is assumed that the satellite's trajectory in a very short time conforms to smooth physical laws.

[0051] Therefore, in this embodiment, the current epoch is selected. The small orbital arc segment, including the arc segment before and after it, is fitted using a 6th-order polynomial to remove observation noise. The SG filtering smoothing process is as follows:

[0052] Set window length ,in Represents the half-length of the sliding window and the order of the polynomial. .

[0053] The satellite orbit equations using SG filtering are:

[0054] (1)

[0055] in Indicates the current epoch. Observation coordinates of low Earth orbit satellites Window length The relative time index within, , , …、 These are the fitting coefficients for the satellite orbit equations.

[0056] Formula (1) can be written in matrix form. Its formula is expressed as shown in equation (2);

[0057] (2)

[0058] Specifically: , It is the Vandermonde matrix. , .

[0059] Solve the matrix using the least squares rule. The solution is:

[0060] ;

[0061] That is, .

[0062] Let the projection matrix for:

[0063] .

[0064] Since only the solution needs to be found That is, the current epoch If the location information is known, then only the solution needs to be obtained. Therefore, the solution is... The first line is sufficient. Let... The first row vector Then the smoothed value The formula is:

[0065] (3)

[0066] Smoothed coordinates of the current epoch after SG filtering of low-Earth orbit satellites Equal to the fitting coefficient of the satellite orbit equation .

[0067] Step 3. High-precision numerical differential acceleration solution based on a five-point template.

[0068] Both the orbital data after SG filtering in step 2 above and the original orbital data need to be processed by numerical differentiation to extract acceleration information from the discrete position sequence.

[0069] To further reduce the truncation error introduced by numerical differentiation and to more accurately capture instantaneous acceleration changes, this invention adopts the more accurate five-point central difference stencil.

[0070] Compared to traditional second-order precision The three-point difference method, and the five-point central difference method used in this embodiment, make full use of the position information of the current epoch and the two epochs before and after it (a total of 5 points).

[0071] Through Taylor series expansion, it can be seen that the truncation error of the five-point central difference method can be reduced to [missing value]. This significantly improves the mathematical accuracy of acceleration calculations.

[0072] Specifically, based on the original orbit of the low-Earth orbit satellite and the orbit smoothed by SG filtering, the five-point center difference method is used to extract acceleration information from the discrete position sequence and calculate the original acceleration and the reference background acceleration.

[0073] The original orbit is the three-dimensional position coordinates of the low-orbit satellite in the J2000 geocentric inertial coordinate system. The trajectory after SG filtering is a smoothed coordinate system. The formula for estimating the instantaneous acceleration of low-Earth orbit satellites is as follows:

[0074] (4)

[0075] in for The acceleration vector calculated from the epoch; for The orbital position coordinates of the epoch, including , , Three components; The epoch sampling interval; coefficient With denominator These are the standard coefficients of the five-point difference template.

[0076] The higher-order differential steps shown in formula (4) are based on the original orbits respectively. and the track after SG filtering smoothing The original acceleration was calculated. and reference background acceleration .

[0077] Step 4. Transform the original acceleration and background reference acceleration to the satellite body coordinate system (SRF).

[0078] To analyze the components of the nonconservative forces generated by the thrusters in the satellite body direction (along-track, radial, and cross-track), the obtained inertial frame accelerations are converted to the satellite scientific reference coordinate system (SRF).

[0079] This invention utilizes attitude quaternion data provided by low-Earth orbit satellites. This enables the coordinate transformation of the motor force from the J2000 geocentric inertial coordinate system to the SRF coordinate system.

[0080] Based on Euler's rotation theorem, a rotation matrix from the satellite body frame (SRF) to the inertial coordinate system (J2000) is constructed using quaternions, expressed as follows:

[0081] (5)

[0082] in Represents the epoch The rotation matrix below, where For this Quaternions under an epoch This is used to rotate and scale vectors in three-dimensional space. Since the rotation matrix is ​​an orthogonal matrix, its inverse is equal to its transpose.

[0083] Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system. Therefore, the acceleration formula from the J2000 geocentric inertial coordinate system to the SRF coordinate system is:

[0084] (6)

[0085] in Ephemeris of the J2000 geocentric inertial coordinate system The original acceleration or reference background acceleration is below. To convert to the corresponding acceleration in the SRF coordinate system, Rotation matrix The transpose of .

[0086] , , They represent the original accelerations. Or refer to background acceleration Components in the X, Y, and Z directions.

[0087] Step 5. Extract the high-frequency acceleration residual and realize track motion detection.

[0088] The core of step 5 lies in separating the high-frequency non-conservative force signal through the "background removal method".

[0089] A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration to eliminate the influence of the background field and extract the high-frequency residual containing information of both the orbital control maneuver signal and the residual high-frequency noise.

[0090] Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

[0091] Let the original acceleration and the reference background acceleration after coordinate transformation be respectively and .

[0092] It includes low-frequency signals of Earth's gravity, air resistance, light pressure, instantaneous thrust generated by the orbital control thruster OCT, and high-frequency measurement noise. The results are calculated based on SG filtering.

[0093] Because SG filtering has extremely strong smoothing characteristics, the high-frequency pulse signal generated by the orbit control thruster OCT is filtered out. The term primarily characterizes the Earth's gravitational field and the slowly changing nonconservative background force field.

[0094] based on and A difference sequence is constructed to eliminate the influence of the background field and extract high-frequency residuals. The formula is:

[0095] (7)

[0096] The calculated residuals It contains the following two parts of information: track control maneuver signals and residual high-frequency noise.

[0097] The orbit control maneuver signal manifests as significant pulses or steps in the time series, corresponding to the thrust acceleration when OCT is activated; the residual high-frequency noise, i.e. the kinematic orbit positioning error that has not been completely separated, manifests as background noise.

[0098] Through analysis The components on each axis of the SRF coordinate system are used to accurately identify the time, duration, and thrust direction of satellite maneuvers.

[0099] Example 2

[0100] This embodiment 2 describes an orbital maneuver detection system based on the difference between kinematic orbital epochs. This system is based on the same inventive concept as the orbital maneuver detection method based on the difference between kinematic orbital epochs in embodiment 1 above.

[0101] The orbital maneuver detection system based on the difference between kinematic orbital epochs in this embodiment includes the following modules:

[0102] The kinematic orbit acquisition module is used to obtain the kinematic orbit data of the low-Earth orbit satellite through precise single-point positioning calculation, and records the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system.

[0103] The Savitzky-Golay filtering and smoothing module is used to filter and smooth the obtained low-Earth orbit satellite position data.

[0104] The numerical differential acceleration calculation module is used to extract acceleration information from the discrete position sequence based on the original trajectory and the trajectory smoothed by SG filtering, and to calculate the original acceleration and the reference background acceleration using the five-point center difference method.

[0105] The five-point central difference method utilizes the positional information of a total of five points, including the current epoch and the two epochs before and after it.

[0106] The coordinate transformation module is used to transform the original acceleration and background reference acceleration to the satellite body coordinate system (SRF).

[0107] Using attitude quaternion data provided by low-orbit satellites, the coordinate transformation of the maneuvering force from the inertial coordinate system to the SRF coordinate system is realized, and the rotation matrix from the SRF coordinate system to the inertial coordinate system is constructed according to Euler's rotation theorem.

[0108] Since the rotation matrix is ​​an orthogonal matrix, its inverse matrix is ​​equal to its transpose matrix;

[0109] Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system;

[0110] And a track motion detection module, used to extract high-frequency acceleration residuals and realize track motion detection;

[0111] A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration to eliminate the influence of the background field and extract the high-frequency residual containing information of both the orbital control maneuver signal and the residual high-frequency noise.

[0112] Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

[0113] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0114] Example 3

[0115] This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the orbital maneuver detection method based on the difference between kinematic orbital epochs in embodiment 1 above.

[0116] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0117] Example 4

[0118] This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the orbital maneuver detection method based on the difference between kinematic orbital epochs in embodiment 1 above.

[0119] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0120] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for detecting orbital maneuvers based on the difference between kinematic orbital epochs, characterized in that, Includes the following steps: Step 1. Use the kinematic orbit data of the low-Earth orbit satellite, which is obtained through precise single-point positioning calculation, to record the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system; Step 2. Perform SG filtering smoothing on the low-Earth orbit satellite position data; Step 3. Based on the original orbit of the low-Earth orbit satellite and the orbit smoothed by SG filtering, the five-point center difference method is used to extract acceleration information from the discrete position sequence and calculate the original acceleration and the reference background acceleration. The five-point central difference method utilizes the positional information of five points, including the current epoch and the two epochs before and after it; Step 4. Transform the original acceleration and background reference acceleration to the satellite body coordinate system (SRF); Using attitude quaternion data provided by low-orbit satellites, the coordinate transformation of the maneuvering force from the inertial coordinate system to the SRF coordinate system is realized, and the rotation matrix from the SRF coordinate system to the inertial coordinate system is constructed according to Euler's rotation theorem. Since the rotation matrix is ​​an orthogonal matrix, its inverse matrix is ​​equal to its transpose matrix; Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system; Step 5. Extract high-frequency acceleration residuals and perform track motion detection; A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration to eliminate the influence of the background field and extract the high-frequency residual containing information of both the orbital control maneuver signal and the residual high-frequency noise. Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

2. The orbital maneuver detection method based on the difference between kinematic orbital epochs according to claim 1, characterized in that, In step 2, the SG filtering smoothing process is as follows: For high-frequency sampling data from low-Earth orbit satellites, select the current epoch. The small orbital arc segment, including the two epochs before and after it, was fitted using a 6th-order polynomial to remove observation noise. Therefore, set the window length. ,in Represents the half-length of the sliding window and the order of the polynomial. ; The satellite orbit equations using SG filtering are: (1) in Indicates the current epoch. Observation coordinates of low Earth orbit satellites Window length Relative index within, , , …、 These are the fitting coefficients for the satellite orbit equations; Rewrite formula (1) in matrix form Its formula is shown in equation (2); (2) in , It is the Vandermonde matrix. , ; Solve the matrix using the least squares rule. Solution for: ； Right now ; Let the projection matrix for: ； Since only the solution needs to be found That is, the current epoch If the location information is not available, then only the solution needs to be found. Therefore, the solution is... The first line is sufficient; let's assume... The first row vector Then the smoothed value The formula is: (3) That is, the smoothed coordinates of the current epoch after SG filtering of low-Earth orbit satellites. Equal to the fitting coefficient of the satellite orbit equation .

3. The orbital maneuver detection method based on the difference between kinematic orbital epochs according to claim 1, characterized in that, In step 3, the instantaneous acceleration estimation formula for low-orbit satellites is as follows: (4) in for The acceleration vector calculated from the epoch; for The orbital position coordinates of the epoch, including , , Three components; The epoch sampling interval; coefficient With denominator The standard coefficients of the five-point difference template; The higher-order differential steps shown in formula (4) are based on the original orbits respectively. and the track after SG filtering smoothing The original acceleration was calculated. and reference background acceleration .

4. The orbital maneuver detection method based on the difference between kinematic orbital epochs according to claim 1, characterized in that, In step 4, the rotation matrix from the SRF coordinate system to the inertial coordinate system is expressed by the following formula: (5) wherein represents the rotation matrix at the epoch , is the quaternion at the epoch , for implementing a rotation scaling of a vector in three-dimensional space; Therefore, the acceleration formula for transforming from the inertial coordinate system to the SRF coordinate system is: (6) wherein is the original acceleration or reference background acceleration in the J2000 epoch of the geocentric inertial coordinate system, is the corresponding acceleration in the SRF coordinate system, is the rotation matrix transpose of the rotation matrix; , , respectively represent the original acceleration or the reference background acceleration in the X, Y, Z directions.

5. The orbital maneuver detection method based on the difference between kinematic orbital epochs according to claim 1, characterized in that, Step 5 specifically involves: Let the coordinate-transformed original acceleration and the reference background acceleration be respectively and ; Based on and , the differential sequence is constructed to eliminate the influence of the background field and extract the high-frequency residual , the formula is: (7) in It includes low-frequency signals of Earth's gravity, air resistance, light pressure, instantaneous thrust generated by the orbital control thruster OCT, and high-frequency measurement noise; The results are based on SG filtering. The calculated residuals It contains the following two parts of information: track control maneuver signals and residual high-frequency noise; The orbit control maneuver signal manifests as significant pulses or steps in the time series, corresponding to the thrust acceleration when OCT is activated; the residual high-frequency noise, i.e. the kinematic orbit positioning error that has not been completely separated, manifests as the background noise. Through analysis The components on each axis of the SRF coordinate system are used to identify the time, duration, and thrust direction of the satellite maneuver.

6. A trajectory maneuver detection system based on the difference between kinematic trajectory epochs, characterized in that, Includes the following modules: The kinematic orbit acquisition module is used to obtain the kinematic orbit data of the low-Earth orbit satellite through precise single-point positioning calculation, and records the three-dimensional position coordinates of the low-Earth orbit satellite in the J2000 geocentric inertial coordinate system. The Savitzky-Golay filtering and smoothing module is used to filter and smooth the position data of low-Earth orbit satellites. The numerical differential acceleration calculation module is used to extract acceleration information from the discrete position sequence based on the original trajectory and the trajectory smoothed by SG filtering, and to calculate the original acceleration and the reference background acceleration using the five-point center difference method. The five-point central difference method utilizes the positional information of a total of five points, including the current epoch and the two epochs before and after it. The coordinate transformation module is used to transform the raw acceleration and background reference acceleration to the satellite body coordinate system (SRF). Using attitude quaternion data provided by low-orbit satellites, the coordinate transformation of the maneuvering force from the inertial coordinate system to the SRF coordinate system is realized, and the rotation matrix from the SRF coordinate system to the inertial coordinate system is constructed according to Euler's rotation theorem. Since the rotation matrix is ​​an orthogonal matrix, its inverse matrix is ​​equal to its transpose matrix; Based on this transpose matrix, the original acceleration and background reference acceleration are transformed from the inertial coordinate system to the SRF coordinate system; And a track motion detection module, used to extract high-frequency acceleration residuals and realize track motion detection; A difference sequence is constructed based on the original acceleration after coordinate transformation and the reference background acceleration to eliminate the influence of the background field and extract the high-frequency residual containing information of both the orbital control maneuver signal and the residual high-frequency noise. Analyze the components of the high-frequency residuals on each axis of the SRF coordinate system to identify the time, duration, and thrust direction of satellite maneuvers.

7. A computer device, comprising a memory and one or more processors; characterized in that, The memory stores executable code, which, when executed by the processor, is used to implement the orbital maneuver detection method based on the difference between kinematic orbital epochs as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a program stored thereon; characterized in that, When executed by the processor, the program is used to implement the orbital maneuver detection method based on the difference between kinematic orbital epochs as described in any one of claims 1 to 5.

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