A method for tracking a spatial non-cooperative impulsive maneuvering target satellite under wild value interference

Abstract

This invention discloses a method for tracking a non-cooperative pulse-maneuvering target satellite under outlier interference, specifically relating to the field of aerospace technology. Based on measurement data of the non-cooperative target satellite obtained from a ground station and an assumed nominal dynamic model, the method uses the spherical-radial volume rule to calculate the target's current state prediction and measurement prediction. It monitors the changes in the measurement residuals in the filter in real time based on the maneuver sensitivity factor calculated by the ASTCKF filter to detect the presence of pulse maneuvers or measurement outliers during the tracking process. The ASTCKF filter is used to process measurement outliers, distinguishing between outliers and maneuvers. If a pulse maneuver occurs at the current moment, the covariance is expanded using the maneuver sensitivity factor; if it is a measurement outlier, it degenerates into a normal CKF. The Kalman gain matrix is ​​calculated and the state estimate is updated. The method determines whether a maneuver or measurement outlier exists at each moment during the filtering process until the filtering process ends.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and specifically to a method for tracking a space-based non-cooperative pulse-maneuvering target satellite under outlier interference. Background Technology

[0002] Because unknown maneuvers increase the uncertainty of the dynamics model, causing a mismatch between the nominal and actual dynamics models, failure to compensate the dynamics model in a timely and effective manner can lead to a decline in target tracking performance and even filter divergence. However, when the maneuver amplitude is small, existing tracking methods struggle to detect the maneuver and therefore cannot quickly compensate the dynamics model after it occurs. Furthermore, measurement outliers may exist during target tracking, and existing tracking methods struggle to distinguish between measurement outliers and maneuvers, easily leading to false maneuver detections. Therefore, accurately tracking non-cooperative targets in the absence of prior maneuver information and the presence of measurement outliers remains a significant challenge.

[0003] Current non-cooperative maneuvering satellite tracking methods can be mainly divided into three categories: re-initialization orbit determination process methods, maneuver reconstruction methods, and filtering methods. Existing literature, Ko, HC, and Scheeres, DJ, “Event Representation-Based Orbit Determination across Unknown Space Events.” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 12, 2015, pp. 2351–2365, models unknown maneuvers by inferring Fourier coefficients to improve conventional batch filtering, providing a more accurate initial state for restarted filters and improving tracking performance after maneuvers. However, the tracking performance of this method heavily depends on accurate maneuver detection and the chosen expansion coefficient. Therefore, this method is unsatisfactory in scenarios requiring high precision.

[0004] Existing literature, Holzinger, MJ, Scheeres, DJ, and Alfriend, KT, “Object Correlation, Maneuver Detection, and Characterization Using ControlDistance Metrics.” Journal of Guidance, Control, and Dynamics, Vol. 35, No.4, 2012, pp. 1312–1325, proposes a maneuvering target tracking method based on optimal control estimation, allowing maneuver reconstruction in the absence of prior information. Existing literature, Goff, GM, Showalter, D., Black, JT, and Beck, JA, “Parameter Requirements for Noncooperative Satellite Maneuver Reconstruction Using Adaptive Filters.” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 3, 2015, investigates the impact of typical parameters on known noncooperative satellite maneuver reconstruction methods. However, maneuver reconstruction methods are highly sensitive to orbit estimates before and after maneuvers, and these methods are typically computationally expensive.

[0005] The existing literature Wang, Y., Sun, S., and Li, L. “Adaptively Robust Unscented Kalman Filter for Tracking a Maneuvering Vehicle.” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 5, 2014, pp. 1696–1701 proposes an adaptive robust unscented Kalman filter that employs a strong tracking filter (STF) structure to reduce the impact of errors in the dynamics and measurement models on tracking accuracy. Existing literature (Jiang, Y., Ma, P., and Baoyin, H., “Residual-Normalized Strong Tracking Filter for Tracking a Noncooperative Maneuvering Spacecraft.” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 10, 2019, pp. 2304–2309) proposes a residual normalized strong tracking filter (RNSTF), which enhances the strong tracking filter's ability to detect pulse maneuvers with amplitudes less than 10 m / s. However, when the pulse maneuver amplitude is too small, such as less than 1 m / s, existing STF methods and their variants cannot detect the maneuver in a timely manner. Furthermore, when measurement outliers exist, existing STF methods and their variants cannot distinguish between maneuvers and measurement outliers, easily leading to false detections of maneuvers, resulting in reduced tracking accuracy and decreased filter divergence. Therefore, it can be seen that there is still room for improvement in current satellite tracking technology. Summary of the Invention

[0006] Therefore, the present invention provides a method for tracking a space non-cooperative pulse maneuvering target satellite under outlier interference, in order to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for tracking a space non-cooperative pulse maneuvering target satellite under outlier interference, comprising the following steps:

[0008] Step 1: Based on the ranging, azimuth, elevation, and velocity information of the non-cooperative target satellite obtained from the ground station, forward prediction is performed using the Adaptive Strong Tracking Volumetric Kalman Filter (ASTCKF). Volume points are created according to the third-order volume principle, and the current state prediction and measurement prediction values ​​are obtained through the spherical-radial volume rule and the assumed nominal dynamic model.

[0009] Step 2: Obtain the measurement residual of the Adaptive Strong Tracking Volumetric Kalman Filter (ASTCKF) by combining the predicted value at the current moment with the actual measurement value obtained from the ground station, and calculate the motion sensitivity factor accordingly; monitor the changes in the measurement residual of the ASTCKF in real time based on the motion sensitivity factor in the ASTCKF, and detect whether there are pulse maneuvers or measurement outliers in the target during the tracking process. When the motion sensitivity factor is greater than the threshold, it indicates that there is an abnormal change in the measurement residual;

[0010] Step 3: Use an adaptive strong tracking capacitive Kalman filter (ASTCKF) to process measurement outliers, distinguish between outliers and maneuvers, and avoid false detections of maneuvers caused by measurement outliers; when an abnormal change is determined to be a maneuver, keep the maneuver sensitivity factor unchanged; when an abnormal change is determined to be a measurement outlier, reset the maneuver sensitivity factor to 1.

[0011] Step 4: When the maneuver sensitivity factor is greater than 1, i.e. when the abnormal change is determined to be a maneuver, the covariance is expanded according to the value of the maneuver sensitivity factor; when the maneuver sensitivity factor is less than or equal to 1, i.e. when the abnormal change is determined to be a measurement outlier, the adaptive strong tracking capacitive Kalman filter (ASTCKF) degenerates into a regular capacitive Kalman filter (CKF).

[0012] Step 5: Calculate the Kalman gain matrix and update the state estimate and the posterior estimate of the state covariance; calculate the maneuver sensitivity factor corresponding to the current time at each time step in the filtering process, identify whether there is an abnormal change at the current time, and determine whether the abnormal change is a pulse maneuver or a measurement outlier until the filtering process ends.

[0013] Preferably, step one specifically includes:

[0014] Step 1.1: The ground station collects measurements of the non-cooperative pulse-maneuvering target in space. ,in The measurement value at time k includes the distance measurement. Azimuth A, Pitch E, Velocity Ground stations collect range, azimuth, elevation, and velocity information of the target satellite in the North-Sky-East coordinate system. Let K be the measurement noise of the ground station at time k. The measurement noise is zero-mean Gaussian white noise, which satisfies the following conditions: ,in To measure the noise covariance matrix;

[0015] Step 1.2, the nonlinear system state-space model of the target satellite is represented as follows:

[0016] ;

[0017] The target state is The target state includes its position in the J2000 coordinate system. and speed Where x, y, and z represent the three-axis position coordinates of the non-cooperative target satellite in the J2000 coordinate system, and v x v y v z This represents the three-axis velocity of the non-cooperative target satellite in the J2000 coordinate system. The nominal dynamic model of the target satellite. For measurement model;

[0018] Step 1.3: Create 2n volume points according to the third-order volume principle, where n is the dimension of the state vector, and obtain the predicted state value at the current moment through the spherical-radial volume rule and the assumed nominal dynamic model. and measurement prediction values The formula is:

[0019] Decomposition of state estimation error covariance matrix Based on this, the volume point is calculated and a nonlinear transformation is performed:

[0020] ;

[0021] ;

[0022] In the formula, S is the square root coefficient of the covariance matrix; and Let x be the volume point; m is the total number of volume points. According to the third-order volume principle, m is twice the dimension n of the state vector, that is, m = 2n; n is the dimension of the state vector x. , The set of points generated by permuting or inverting unit vectors in n-dimensional space, satisfying:

[0023] ;

[0024] Calculate state prediction value and the predicted covariance matrix :

[0025] ;

[0026] ;

[0027] in Represents the process noise covariance matrix;

[0028] Decompose the prediction error covariance matrix Predict the volume point at the next moment. And according to the measurement model A nonlinear transformation is performed to calculate the predicted measurement value. :

[0029] ;

[0030] ;

[0031] .

[0032] Preferably, the nominal dynamic model assumed in the filtering process in step 1.3 is a two-body dynamic model. Specifically:

[0033] ;

[0034] Where μ is the Earth's gravitational coefficient.

[0035] Preferably, step two specifically includes:

[0036] Step 2.1, Measure the predicted value at the current time. Obtain the actual measurement value at the current time from the ground station. Obtain the measurement residual of the filter The formula is:

[0037] ;

[0038] Step 2.2, based on the measurement residuals The residual covariance matrix is ​​obtained by approximate calculation. The formula is:

[0039] ;

[0040] in, This is the forgetting factor, usually taken as 0.95;

[0041] Calculate the covariance matrix of the measurement residuals after eliminating the influence of measurement errors. The nominal value of the measurement residual variance matrix at the current moment, obtained by extrapolating the target state from the previous step. The formula is:

[0042] ;

[0043] ;

[0044] Step 2.3: Calculate the suboptimal sensitivity factor corresponding to all measurement residual components at the current time using an approximate calculation method. Choose different residual components The maximum value in is used as the maneuver sensitivity factor. The formula is:

[0045] ;

[0046] ;

[0047]

[0048] When the motion-sensitive factor When the value is greater than the threshold (threshold set to 1), it indicates that the measured residual at the current time is... An abnormal mutation occurs, with pulsed maneuvering or measurement outliers.

[0049] Preferably, step three specifically includes:

[0050] Step 3.1, when the maneuver sensitivity factor calculated in step two... When the value exceeds the threshold, the predicted state value is calculated using the spherical-radial volume rule and the nominal dynamic model from step one. and the predicted covariance matrix The predicted state, covariance, and measurement at the next time step; As input to the auxiliary filter, the maneuver sensitivity factor at time k+2 is obtained through the calculation step in step two. The formula is:

[0051] ;

[0052] ;

[0053] in This indicates the suboptimal sensitivity factor corresponding to the measured residual component at the next time step;

[0054] Step 3.2, the maneuver sensitivity factor at time k+2 If the value is still greater than the threshold, it indicates that the abnormal change at time k+1 is a maneuver, and the maneuver sensitivity factor at time k+1 remains unchanged; when the maneuver sensitivity factor at time k+2 is less than or equal to 1, it indicates that the abnormal change at time k+1 is a measurement field value, and the maneuver sensitivity factor at time k+1 is reset to 1, as shown in the formula:

[0055] .

[0056] Preferably, step four specifically includes:

[0057] The maneuverability sensitivity factor calculated in steps two and three State estimation covariance Covariance and measurement residual covariance The expansion is performed using the following formula:

[0058] ;

[0059] ;

[0060] .

[0061] Preferably, step five specifically includes:

[0062] The Kalman gain matrix at the current time step is calculated. Update the posterior estimate of the state. Posterior estimate of state covariance The formula is:

[0063] ;

[0064] ;

[0065] ;

[0066] For each step in the filtering process, calculate the motion sensitivity factor corresponding to the current step. The system identifies whether there are any abnormal mutations in the current step. If abnormal mutations are found, the system calculates the motion sensitivity factor for the next step using an auxiliary filter. The system determines whether the abnormal mutation is due to pulse motion or a measurement outlier, and takes appropriate measures until the filtering process ends.

[0067] This invention is based on an adaptive strong-tracking capacitive Kalman filter. By utilizing a maneuver sensitivity factor, it can detect small-amplitude pulse maneuvers in a timely and accurate manner, effectively solving the problem of performance degradation and filter divergence in standard Kalman filters when tracking maneuvering targets. The maneuver sensitivity factor improves the filter's sensitivity to abrupt changes in various measurement residual components, addressing the issue that standard strong-tracking filters are primarily affected by range residual components and cannot detect small-amplitude pulse maneuvers. After successful maneuver detection, the maneuver sensitivity factor is used to expand the filter's covariance, enhancing the ability of new measurements to correct the state, thereby reducing the mismatch between the nominal and actual dynamic models caused by pulse maneuvers and improving the filter's convergence. Real-time tracking of pulse maneuvering targets is achieved by updating the state posterior estimate and the state covariance posterior estimate using the Kalman gain matrix. The overall approach is novel and has strong innovation and engineering application prospects. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the simulation test scenario of the present invention.

[0069] Figure 2This is a schematic diagram illustrating the relationship between the propagation error of the nominal track, the real track, the nominal dynamic model, and the error caused by the pulse maneuver in the simulation scenario of this invention.

[0070] Figure 3 This is a flowchart of the pulse maneuvering target tracking method proposed in this invention.

[0071] Figure 4 This is a schematic diagram illustrating the position estimation errors of the tracking method and comparison method described in this invention during the tracking process.

[0072] Figure 5 This is a schematic diagram illustrating the speed estimation error of the tracking method and comparison method described in this invention during the tracking process.

[0073] Figure 6 This is a schematic diagram showing the change of the measurement residual of the tracking method described in this invention during the tracking process.

[0074] Figure 7 This is a schematic diagram showing the changes in the sensitivity factors corresponding to each measurement residual component in the tracking method described in this invention during the tracking process. Detailed Implementation

[0075] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] like Figure 3 As shown, this invention proposes a method for tracking non-cooperative pulse maneuvering targets in space under outlier interference, comprising the following steps:

[0077] Step 1: Based on the ranging, azimuth, elevation, and velocity information of the non-cooperative target satellite obtained from the ground station, forward prediction is performed using an Adaptive Strong Tracking Cumulative Kalman Filter (ASTCKF). 2n volume points are created according to the third-order volume principle, and the current state prediction value is obtained through the spherical-radial volume rule and the assumed nominal dynamic model. and measurement prediction values ;

[0078] Step 2: Obtain the measurement residual of the Adaptive Strong Tracking Volumetric Kalman Filter (ASTCKF) by combining the predicted value at the current time with the actual measurement value obtained from the ground station, and then calculate the computer's dynamic sensitivity factor accordingly. Based on the real-time monitoring of the change in the measurement residual in the adaptive strong tracking capacitive Kalman filter ASTCKF using the maneuver sensitivity factor in ASTCKF, it is possible to detect whether there is pulse maneuvering or measurement outlier of the target during the tracking process. When the maneuver sensitivity factor is greater than the threshold, it indicates that there is an abnormal change in the measurement residual.

[0079] Step 3: Use an adaptive strong tracking capacitive Kalman filter (ASTCKF) to process measurement outliers, distinguish between outliers and maneuvers, and avoid false detections of maneuvers caused by measurement outliers; when an abnormal change is determined to be a maneuver, keep the maneuver sensitivity factor unchanged; when an abnormal change is determined to be a measurement outlier, reset the maneuver sensitivity factor to 1.

[0080] Step 4: When the maneuver sensitivity factor is greater than 1, i.e. when the abnormal change is determined to be a maneuver, the covariance is expanded according to the value of the maneuver sensitivity factor; when the maneuver sensitivity factor is less than or equal to 1, i.e. when the abnormal change is determined to be a measurement outlier, the adaptive strong tracking capacitive Kalman filter ASTCKF degenerates into a regular capacitive Kalman filter CKF.

[0081] Step 5: Calculate the Kalman gain matrix And update the obtained state estimate. Posterior estimate of state covariance At each moment in the filtering process, it is necessary to calculate the maneuver sensitivity factor corresponding to the current moment, identify whether there is an abnormal change at the current moment, and determine whether the abnormal change is a pulse maneuver or a measurement outlier until the filtering process ends.

[0082] The following will provide a detailed analysis and explanation of each step:

[0083] Step 1: Establish such Figure 1 The simulation scenario shown includes the pre-maneuver orbit of the non-cooperative target satellite, the moment of the pulse maneuver, the post-maneuver orbit, and the nominal orbit. The relationship between the nominal orbit, the actual orbit, the propagation error of the nominal dynamics model, and the error caused by the pulse maneuver is as follows: Figure 2 As shown. Measurements obtained from ground stations of non-cooperative target satellites include... ,in The measurement value at time k includes the distance measurement ( ), Azimuth (A), Pitch (E), Velocity ( The ground station collects the target satellite's range, azimuth, elevation, and velocity information in the North-Sky-East coordinate system. Let K be the measurement noise of the ground station at time k. The measurement noise is zero-mean Gaussian white noise, which satisfies the following conditions: ,in To measure the noise covariance matrix.

[0084] The established nonlinear system state-space model of the target satellite is represented as follows:

[0085] ;

[0086] The target state is The target state includes its position in the J2000 coordinate system. and speed Where x, y, and z represent the three-axis position coordinates of the non-cooperative target satellite in the J2000 coordinate system, and v x v y v z This represents the three-axis velocity of the non-cooperative target satellite in the J2000 coordinate system. The nominal dynamic model of the target satellite. For unknown maneuver acceleration, The input coefficient matrix for acceleration. For measurement model.

[0087] Based on the third-order volume principle, 2n volume points are created, where n is the dimension of the state vector. The predicted state value at the current moment is obtained through the spherical-radial volume rule and the assumed nominal dynamic model. and measurement prediction values The formula is:

[0088] Decompose the state estimation error covariance matrix, calculate the volume points based on it, and perform a nonlinear transformation:

[0089] ;

[0090] ;

[0091] In the formula, S is the square root coefficient of the covariance matrix; and Let x be the volume point; m is the total number of volume points. According to the third-order volume principle, m is twice the dimension n of the state vector, that is, m = 2n; n is the dimension of the state vector x. , The set of points generated by permuting or inverting unit vectors in n-dimensional space, satisfying:

[0092] ;

[0093] Calculate state prediction value and the predicted covariance matrix :

[0094] ;

[0095] ;

[0096] in, This represents the process noise covariance matrix.

[0097] Decompose the prediction error covariance matrix Predict the volume point at the next moment. And according to the measurement model A nonlinear transformation is performed to calculate the predicted measurement value. :

[0098] ;

[0099] ;

[0100] ;

[0101] The nominal dynamic model assumed during the filtering process is a two-body dynamic model. Specifically:

[0102] ;

[0103] Where μ is the Earth's gravitational coefficient.

[0104] Step 2: Measure the predicted value at the current time. Obtain the actual measurement value at the current time from the ground station. Obtain the measurement residual of the filter The formula is:

[0105] ;

[0106] Based on the measured residuals The residual covariance matrix is ​​obtained by approximate calculation. The formula is

[0107] ;

[0108] in The forgetting factor is usually set to 0.95.

[0109] Calculate the covariance matrix of the measurement residuals after eliminating the influence of measurement errors. The nominal value of the measurement residual variance matrix at the current moment, obtained by extrapolating the target state from the previous step. The formula is:

[0110] ;

[0111] ;

[0112] The suboptimal sensitivity factor corresponding to all measurement residual components at the current moment is calculated using an approximate calculation method. Choose different residual components The maximum value in is used as the maneuver sensitivity factor. The formula is:

[0113] ;

[0114] ;

[0115]

[0116] When the motion-sensitive factor When the value is greater than the threshold (threshold set to 1), it indicates that the measured residual at the current time is... An abnormal mutation occurs, with pulsed maneuvering or measurement outliers.

[0117] Step 3: When the maneuver sensitivity factor calculated in Step 2 is... When the value exceeds the threshold, the predicted state value is calculated using the spherical-radial volume rule and the nominal dynamic model from step one. and the predicted covariance matrix The predicted state, covariance, and measurement at the next time step. As input to the auxiliary filter, the maneuver sensitivity factor at time k+2 is obtained through the calculation step in step two. The formula is:

[0118] ;

[0119] ;

[0120] in This indicates the suboptimal sensitivity factor corresponding to the measured residual component at the next time step.

[0121] The mobility sensitivity factor at time k+2 If the value is still greater than the threshold, it indicates that the abnormal change at time k+1 is a maneuver, and the maneuver sensitivity factor at time k+1 remains unchanged; when the maneuver sensitivity factor at time k+2 is less than or equal to 1, it indicates that the abnormal change at time k+1 is a measurement field value, and the maneuver sensitivity factor at time k+1 is reset to 1, as shown in the formula:

[0122] ;

[0123] Step 4: Using the maneuver sensitivity factors calculated in Steps 2 and 3 State estimation covariance Covariance and measurement residual covariance The expansion is performed using the following formula:

[0124] ;

[0125] ;

[0126] ;

[0127] Step 5: Calculate the Kalman gain matrix at the current time. Update the posterior estimate of the state. Posterior estimate of state covariance The formula is:

[0128] ;

[0129] ;

[0130] ;

[0131] For each step in the filtering process, it is necessary to calculate the motion sensitivity factor corresponding to the current step. The system identifies whether there are any abnormal mutations in the current step. If abnormal mutations are found, the auxiliary filter is used to calculate the motion sensitivity factor for the next step. The system determines whether the abnormal mutation is due to pulse motion or a measurement outlier, and takes appropriate measures until the filtering process ends.

[0132] The feasibility of this invention is illustrated by the following examples.

[0133] The following calculation conditions and technical parameters are set:

[0134] 1. The initial position and velocity of the non-cooperative target satellite in the J2000 coordinate system are [3345389.980, 4971415.937, 5685848.830] m and [4428.731, 3820.477, -4494.853] m / s, respectively;

[0135] 2. The initial position estimation error of the target is [1000, 1000, 1000] m, and the initial velocity estimation error is [1, 1, 1] m / s;

[0136] 3. The standard deviation of the noise in the distance measurement at the ground station is 10 m, the standard deviation of the noise in the azimuth and elevation angle measurement is 0.01 °, the standard deviation of the noise in the velocity measurement is 0.1 m / s, and the measurement interval is 1 s;

[0137] 4. The tracking process started at 00:19:00 on October 15, 2024, and lasted for 2500 seconds.

[0138] 5. A measurement outlier exists at 500 s, specifically... ;

[0139] 6. At 1000 s, the target satellite generates a pulse maneuver with an amplitude of 0.5 m / s along the velocity direction.

[0140] Figure 4 , Figure 5 , Figure 6 , Figure 7 Simulation results for the present invention are presented respectively.

[0141] Figure 4 and Figure 5 The target position estimation error and velocity estimation error obtained by the maneuvering target tracking method described in this invention are presented respectively. It can be seen that, compared with the standard Strong Tracking Filter (STF), Strong Tracking Unscented Kalman Filter (STUKF), and Residual Normalized Strong Tracking Filter (RNSTF), the tracking algorithm described in this invention has higher estimation accuracy. Compared with existing STF, STUKF, and RNSTF, the tracking error of the maneuvering satellite tracking method disclosed in this invention is reduced by approximately 65.7%, 63.3%, and 66.2%, respectively, indicating higher tracking accuracy and better filtering performance, demonstrating the superiority of the algorithm described in this invention.

[0142] Figure 6 The changes in measurement residuals obtained using the tracking algorithm described in this invention are presented. It can be seen that after the measurement outlier and the maneuver, none of the residual components changed significantly, and after briefly exceeding the 3σ boundary, they quickly returned to the 3σ range.

[0143] Figure 7 The changes in the sensitivity factors corresponding to each residual component obtained by the tracking algorithm described in this invention are presented. It can be seen that at outlier locations, the sensitivity factors described in this invention do not exceed the detection threshold (threshold is 1), and no false detection of maneuvers occurs. After a maneuver occurs, the sensitivity factors described in this invention change significantly and exceed the detection threshold, indicating that the algorithm described in this invention can accurately distinguish between outliers and maneuvers and detect the occurrence of the maneuver.

[0144] Therefore, by using the method proposed in this invention, tracking of non-cooperative pulse maneuvering target satellites in space can be achieved using only ground station measurement data, and the tracking accuracy is significantly improved compared to existing methods, especially when the pulse maneuver amplitude is small and measurement outliers exist.

[0145] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for tracking a spatial non-cooperative impulsive maneuvering target satellite under wild value interference, characterized in that: It comprises the following steps: Step one: according to the ground station to get the non-cooperative target satellite ranging, azimuth, elevation angle, speed information, using adaptive strong tracking cubature Kalman filter ASTCKF for forward prediction, according to the three order volume principle to create volume point, and through the spherical-radial volume rule and the assumed nominal dynamic model to get the state prediction value and measurement prediction value at the current time; The step one specifically comprises: Step 1.1, the ground station collects the measurement values of the space non-cooperative impulsive maneuvering target wherein is the measurement value at time k, which includes the range , the azimuth angle A, the elevation angle E, and the velocity ; the ground station collects the range, the azimuth angle, the elevation angle, and the velocity information of the target satellite in the north-sky-east coordinate system; is the measurement noise of the ground station at time k, the measurement noise is zero-mean Gaussian white noise, which satisfies wherein is the measurement noise covariance matrix; Step 1.2, the nonlinear system state space model of target satellite is expressed as follows: ； wherein the target state is ; the target state comprises its position and velocity in the J2000 coordinate system x , v y , v z , wherein x, y, z denote the three-axis position coordinates of the non-cooperative target satellite in the J2000 coordinate system, v x , v y , v z denote the three-axis velocity of the non-cooperative target satellite in the J2000 coordinate system, is a nominal dynamic model of the target satellite, is a measurement model; Step 1.

3. Create 2n volume points according to the third-order volume principle, n is the dimension of the state vector, and get the state prediction value at the current time through the spherical-radial volume rule and the assumed nominal dynamic model and the measurement prediction value , the formula is: Decomposed state estimation error covariance matrix From which the volume points are computed and nonlinearly transformed: ； ； where S is the square root coefficient of the covariance matrix; and is the volume point; m is the total number of volume points, according to the third-order volume principle, m is twice the dimension n of the state vector, that is, m = 2n; n is the dimension of the state vector x; , is the point set generated by full permutation or negation of the unit vector in n-dimensional space, which satisfies: ； Computing state prediction values and prediction covariance matrix : ； ； wherein denotes the process noise covariance matrix; Decompose the prediction error covariance matrix , predict the volume point at next time And according to the measurement model Nonlinear transformation is carried out to calculate the measurement prediction value : ； ； ； Step two: through the current time measurement prediction value and the ground station to get the current time measurement real value to get the measurement residual of adaptive strong tracking cubature Kalman filter ASTCKF, and calculate the maneuvering sensitive factor accordingly; according to the maneuvering sensitive factor in ASTCKF, the change of measurement residual in adaptive strong tracking cubature Kalman filter ASTCKF is monitored in real time, whether the target exists pulse maneuvering or measurement outliers in the tracking process is detected, when the maneuvering sensitive factor is greater than the threshold value, it is explained that the measurement residual exists abnormal mutation; The step two specifically comprises: Step 2.1, prediction of current time measurement value and the ground station obtain the current time measurement true value obtain the measurement residual of the filter , the formula is: ； Step 2.2, compute the measurement residual Approximate the residual covariance matrix , which is ； wherein are the forgetting coefficients; a covariance matrix of the measurement residuals after the influence of measurement errors has been excluded and a nominal value of the measurement residual covariance matrix at the current time instant extrapolated from the target state of the previous step , which is given by ； ； Step 2.3, calculate the suboptimal sensitivity factor corresponding to all measurement residual components at current time by approximate calculation method , select the maximum value in different residual components as the maneuvering sensitivity factor , the formula is: ； ； When the maneuver-sensitive factor is greater than the threshold value, it indicates that the measurement residual at the current time abnormal mutation occurs, there is a pulse maneuver or measurement outliers; Step three: through adaptive strong tracking cubature Kalman filter ASTCKF to process measurement outliers, distinguish outliers and maneuvering, avoid the false detection of maneuvering caused by measurement outliers; when the abnormal mutation is determined to be maneuvering, the maneuvering sensitive factor is kept unchanged, when the abnormal mutation is determined to be measurement outliers, the maneuvering sensitive factor is reset to 1; Step four: when the maneuvering sensitive factor is greater than 1, that is, when the abnormal mutation is determined to be maneuvering, the covariance is inflated according to the value of the maneuvering sensitive factor; when the maneuvering sensitive factor is less than or equal to 1, that is, when the abnormal mutation is determined to be measurement outliers, the adaptive strong tracking cubature Kalman filter ASTCKF is degraded to ordinary cubature Kalman filter CKF; Step five: the Kalman gain matrix is calculated, and the state estimation value and the state covariance posteriori estimation value are updated; the maneuvering sensitive factor corresponding to the current time is calculated at each time in the filtering process, whether the abnormal mutation exists at the current time is identified, whether the abnormal mutation is pulse maneuvering or measurement outliers is judged until the filtering process is finished.

2. The tracking method of a spatial non-cooperative impulsive maneuvering target satellite under outliers interference according to claim 1, characterized in that: The nominal dynamics model assumed in the filtering process in step 1.3 is a two-body dynamics model , in particular: ； Wherein μ is the earth gravity coefficient.

3. The method of claim 1, wherein: The step three specifically comprises: Step 3.1, when the maneuver-sensitivity factor calculated in Step 2 is greater than a threshold value, compute the state prediction and the prediction covariance matrix by the spherical-radial cubature rule and the nominal dynamics model in Step 1 Step 3.2, use the predicted state and covariance and the measurement at the next time step as the inputs to the auxiliary filter, and obtain the maneuver-sensitivity factor at time k+2 by the computation in Step 2 Step 3.3, compute the state prediction and the prediction covariance matrix by the spherical-radial cubature rule and the nominal dynamics model in Step 1 Step 3.4, use the predicted state and covariance and the measurement at the next time step as the inputs to the auxiliary filter, and obtain the maneuver-sensitivity factor at time k+2 by the computation in Step 2 Step 3.5, compute the state prediction and the prediction covariance matrix by the spherical-radial cubature rule and the nominal dynamics model in Step 1 Step 3.6, use the predicted state and covariance and the measurement at the next time step as the inputs to the auxiliary filter, and obtain the maneuver-sensitivity factor at time k+2 by the computation in Step 2 ； ； wherein denotes the suboptimal sensitivity factor corresponding to the measurement residual component at the next time instant; Step 3.2, when the maneuver sensitive factor at k+2 time If the maneuver sensitive factor at k+2 time is still greater than the threshold value, it indicates that the abnormal mutation at k+1 time is a maneuver, and the maneuver sensitive factor at k+1 time is kept unchanged; when the maneuver sensitive factor at k+2 time is less than or equal to 1, it indicates that the abnormal mutation at k+1 time is a measurement outlier, and the maneuver sensitive factor at k+1 time is reset to 1, and the formula is: 。 4. The tracking method of a spatial non-cooperative impulsive maneuvering target satellite under outliers according to claim 3, characterized in that: The step four specifically comprises: manipulation sensitive factor calculated in step two and step three state estimation covariance cross covariance and measurement residual covariance is inflated by the formula ； ； 。 5. The method of claim 4, wherein: The step five specifically comprises: The Kalman gain matrix at the current time is calculated The state posterior estimate value and the state covariance posterior estimate value are updated, and the formula is ； ； ； calculating the maneuver-sensitive factor corresponding to the current step for each step in the filtering process identifying whether there is an abnormal mutation in the current step, and if there is an abnormal mutation, calculating the maneuver-sensitive factor corresponding to the next step through an auxiliary filter judging whether the abnormal mutation is a pulse maneuver or a measurement outlier, and taking a corresponding processing mode until the filtering process ends.

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