A method for orbit determination of spatial non-cooperative maneuvering spacecraft under non-gaussian noise

Abstract

The application relates to a kind of non-gaussian noise under the orbit determination method of spatial non-cooperative maneuvering spacecraft, including obtaining the state prediction value and measurement prediction value of target at current time, construct based on adaptive robust attenuation memory filter;Minimize cost function to obtain modified measurement noise covariance matrix, introduce adaptive fading factor to monitor the residual change in filter in real time, detect whether residual exists impulse maneuver or measurement outlier;According to the deviation degree of standardized measurement residual compared with adjustment parameter and adaptive fading factor, calculate discrimination index, and discriminate maneuver and measurement outlier according to discrimination index;Covariance matrix is corrected by discrimination index;Calculate the Kalman gain matrix at current time, and obtain the state and state covariance estimation value of target according to the measurement information at current time, until the end of task;Make up the existing method under non-gaussian noise filter tracking performance decline, prone to maneuver false detection and other problems.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and more specifically to a method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise. Background Technology

[0002] Orbit determination for non-cooperative spacecraft is crucial for various space missions, including space cataloging, collision avoidance, and rendezvous and docking. Traditional Kalman filters provide a direct method for orbit determination. However, when the target spacecraft is non-cooperative and performs unknown maneuvers, traditional filters cannot compensate for the mismatch between the nominal dynamics model and the actual maneuvers, leading to degraded tracking performance and even divergence. Furthermore, traditional Kalman filters are derived under the assumption of Gaussian noise, while sensor measurements often deviate from this assumption. In practical applications, measurement noise often exhibits heavy-tailed non-Gaussian characteristics and generates measurement anomalies. Because the assumed measurement model differs from the actual measurement model, the accuracy of filters based on the Gaussian assumption is significantly reduced. Moreover, existing orbit determination methods struggle to distinguish between measurement anomalies and maneuvers, easily leading to false maneuver detections. Misclassifying measurement anomalies as maneuvers reduces the accuracy of the filtering method and may even cause divergence. Therefore, accurately determining the orbit of a non-cooperative maneuvering spacecraft when prior information about the target spacecraft's maneuvers is lacking, measurement anomalies exist, and measurements are contaminated by non-Gaussian noise becomes a significant challenge.

[0003] Currently, both domestic and international research has explored orbit determination for noncooperative maneuvering spacecraft from various perspectives. Existing literature, such as Gui, J., Li, S., and Xin, M., “Adaptive Fading Factor-Based Nonlinear Filter for Tracking Noncooperative Maneuvering Spacecraft,” Journal of Guidance, Control, and Dynamics, 2025, pp. 1–11, proposes a nonlinear filter based on an adaptive fading factor, achieving orbit determination for noncooperative impulsive maneuvering spacecraft. However, this method assumes that the sensor measurement noise follows a Gaussian distribution. When the measurement noise is contaminated and exhibits a non-Gaussian distribution, frequent false maneuvers occur, leading to a decrease in orbit determination accuracy. Existing literature, Li, S., TAN, P., LIU, W., and CUI, N., “RobustRecursive Sigma Point Kalman Filtering for Huber-Based Generalized M-Estimation,” Chinese Journal of Aeronautics, Vol. 38, No. 5, 2024, p. 103215, introduces a recursive update strategy into a nonlinear filtering framework and proposes a robust recursive Kalman filter based on Huber M-estimation, achieving accurate orbit determination of spacecraft under non-Gaussian measurement noise. However, this method can only suppress the influence of non-Gaussian measurement noise and measurement outliers on the orbit determination process. When the target spacecraft undergoes pulse maneuvers, the filter rapidly diverges and loses its orbit determination capability. Existing literature, such as Chang, L., Hu, B., Chang, G., and Li, A., “Multiple Outliers Suppression Derivative-Free Filter Based on Unscented Transformation,” Journal of Guidance, Control, and Dynamics, proposes an outlier-robust unscented Kalman filter that simultaneously handles state and measurement outliers during target tracking. However, this method has limited robustness to state outliers. When the target undergoes large-amplitude maneuvers, the filter struggles to withstand the uncertainties introduced by the maneuvers, leading to filter divergence. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise conditions. This method enables orbit determination of non-cooperative maneuvering spacecraft under non-Gaussian noise conditions, and solves the problems of existing technologies that make it difficult to distinguish between measurement anomalies and maneuvers under non-Gaussian noise conditions, easily leading to false detections of maneuvers, and causing degradation or even divergence in filter tracking performance.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise, comprising:

[0006] Construct an adaptive robust decay memory filter: use generalized M-estimation as the weighted least squares estimate in the replacement filter, and replace the L2 cost function with a robust Huber cost function;

[0007] Calculate and obtain the target's current state prediction value and measurement prediction value;

[0008] The modified measurement noise covariance matrix is ​​obtained by minimizing the cost function in the filter. The following operation is repeated recursively at each time step during the filtering process until the filtering process ends:

[0009] An adaptive fading factor is introduced to monitor the change in measurement residuals in the filter in real time. When the adaptive fading factor is greater than a threshold, it indicates that there is a measurement anomaly or impulse maneuver at the current moment; and

[0010] Calculate the discrimination index to distinguish between measurement anomalies and impulse maneuvers, and adjust the adaptive fading factor based on the discrimination results;

[0011] Adjustments are made to the state estimation covariance, cross-covariance, and measurement residual covariance based on the discriminant index;

[0012] The Kalman gain matrix at the current time is calculated, and the target's state and state covariance estimate are obtained by updating the measurement information at the current time.

[0013] Preferably, a nonlinear system for the spacecraft is established, and the ranging of the non-cooperative target spacecraft is obtained from the ground station. Azimuth A, Pitch E, Velocity Information The sigma sample points at time k-1 are calculated based on the unscented transformation, and the predicted state value of the target at time k is obtained through nonlinear state equation propagation. State covariance predicted values The predicted measurement value is calculated based on the measurement model. And the predicted values ​​of the measurement covariance matrix .

[0014] Preferably, the ground station collects measurement values ​​of the space non-cooperative pulse maneuvering spacecraft in an East-North-Sky coordinate system, and the measurement noise in the measurement values ​​is... It is zero-mean Gaussian white noise, which satisfies ,in To measure the noise covariance matrix.

[0015] Preferably, the standardized state error is defined as... and standardized measurement residuals are , The cost function constructed by replacing the L2 norm cost function with the robust Huber cost function, representing the measurement mapping matrix, is as follows:

[0016] ;

[0017] in, for The i-th component, for The j-th component, Here, n represents the dimension of the state vector, and m represents the dimension of the observation vector.

[0018] Preferably, the modified measurement noise covariance matrix :

[0019] ;

[0020] ;

[0021] ;

[0022] Where T / 2 represents the transpose of the square root of the matrix; Represents Huber function The derivative; This represents the Huber weight function.

[0023] Preferably, the actual measurement value at the current time is obtained through a ground station. And the predicted value measured at the current time The difference is used to obtain the measurement residual of the filter. ;

[0024] Based on measurement residuals The residual covariance matrix is ​​obtained by approximate calculation. ;

[0025] 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 time. The formula is:

[0026] ;

[0027] ;

[0028] Where β is the softening factor;

[0029] The suboptimal fading 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 adaptive fading factor. The formula is:

[0030] ;

[0031] ;

[0032] ;

[0033] in, Representation matrix and The ratio of each diagonal component.

[0034] Preferably, based on discriminant indicators The following steps are taken to distinguish between measurement anomalies and pulse maneuvers:

[0035] When the velocity component in the standardized measurement residual deviates to a certain degree When the value is significantly greater than other components, it is determined to be an impulsive maneuver, and the adaptive fading factor remains unchanged;

[0036] Otherwise, it is judged as a measurement outlier, and the adaptive fading factor is reset to 1.

[0037] Preferably, the discriminant index is calculated. Identifying pulse maneuvers and measuring outliers:

[0038] ;

[0039] ;

[0040] in Represents standardized measurement residuals Each component Compared to adjusting parameters The relative degree of deviation, This indicates the discrimination threshold.

[0041] Preferably, the Kalman gain matrix at the current time is calculated. The posterior state estimate is updated based on the measurement information. Posterior estimate of state covariance The formula is:

[0042] ;

[0043] ;

[0044] .

[0045] Beneficial Effects: This invention constructs an adaptive robust attenuation memory filter and employs the Huber robust cost function in generalized M-estimation to limit the contribution of measurement outliers to the cost function. By minimizing the cost function in the filter, a modified measurement noise covariance matrix is ​​obtained, thus suppressing the impact of measurement outliers and non-Gaussian measurement noise on filtering performance. Furthermore, by utilizing an adaptive fading factor to detect abrupt changes in the measurement residuals and using a discrimination index to distinguish whether these changes are caused by measurement outliers or maneuvers, the problem of false maneuver detection common in existing orbit determination methods is avoided. By adopting different compensation measures for measurement outliers and maneuvers, the impact of errors in the dynamic and measurement models on orbit determination performance is reduced, effectively solving the problem of decreased accuracy and even filter divergence of existing Kalman filters when determining the orbits of maneuvering spacecraft under non-Gaussian measurement noise conditions. The overall approach is novel and has strong innovativeness and engineering application prospects. Attached Figure Description

[0046] Figure 1 This is a flowchart of the method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to the present invention;

[0047] Figure 2 This diagram illustrates a comparison of the position estimation errors of the method of this invention with existing outlier robust unscented Kalman filters (ORUKF), adaptive robust unscented Kalman filters (ARUKF), and robust recursive Kalman filters (RRSPKF) during the orbit determination process.

[0048] Figure 3 This diagram illustrates a comparison of the velocity estimation errors of the method of this invention with existing outlier robust unscented Kalman filters (ORUKF), adaptive robust unscented Kalman filters (ARUKF), and robust recursive Kalman filters (RRSPKF) during the tracking process.

[0049] Figure 4 This is a schematic diagram illustrating the change in the adaptive reduction factor obtained by the method of the present invention during the tracking process. Detailed Implementation

[0050] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0051] Example: Figure 1 As shown, a method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise includes the following steps:

[0052] Step 1: Establish the nonlinear system of the spacecraft and obtain the ranging of the non-cooperative target spacecraft from the ground station. Azimuth A, Pitch E, Velocity The information is obtained by calculating the sigma sample points of the previous time step based on the unscented transformation, and by propagating the nonlinear state equation to obtain the state prediction value of the target at the current time step. The measurement prediction value is then calculated based on the measurement model.

[0053] Step 2: Use generalized M-estimation instead of weighted least squares estimation in traditional filters, and replace the L2 cost function with a robust cost function to limit the contribution of measurement outliers to the cost function;

[0054] Step 3: The modified measurement noise covariance matrix is ​​obtained by minimizing the Huber robust cost function in the generalized M-estimation to correct the measurement covariance in the standard filter;

[0055] Step 4: Introduce an adaptive fading factor to monitor the change of measurement residuals in the filter in real time. When the adaptive fading factor is greater than the threshold, it indicates that there is a measurement anomaly or pulse maneuver at the current moment.

[0056] Step 5: Calculate the discrimination index based on the deviation of the standardized measurement residual from the adjustment parameter and the adaptive fading factor. Based on the discrimination index, distinguish between measurement outliers and impulse maneuvers, and correct the adaptive fading factor based on the discrimination results.

[0057] Step 6: Adjust the state estimation covariance, cross-covariance, and measurement residual covariance based on the discriminant index;

[0058] Step 7: Calculate the Kalman gain matrix at the current time, and update the target's state and state covariance estimate based on the measurement information at the current time.

[0059] In another exemplary embodiment of this application, establishing a simulation scenario requires determining the pre-maneuver trajectory of the non-cooperative spacecraft, identifying the moment of abrupt change in the measurement residual, determining whether the change is due to a measurement anomaly or a maneuver, and determining the trajectory after the maneuver. A state-space model of the following nonlinear system is established:

[0060] ;

[0061] in This indicates the spacecraft's status, including its position in the J2000 coordinate system. and speed Where x, y, and z represent the positions of the three axes. , , Indicates the three-axis velocity. The nominal dynamic model of the target spacecraft. For measurement model, 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;

[0062] In another exemplary embodiment of this application, the ground station collects measurements of a space non-cooperative pulse maneuvering spacecraft in the East-North-Sky (ENU) coordinate system, specifically including:

[0063] ;

[0064] ;

[0065] in, The measurement value at time k includes the distance measurement ( ), Azimuth (A), Pitch (E), Velocity ( ), This represents the spacecraft's position vector in the East-North-Sky coordinate system of the station. The velocity vector of the spacecraft in the East-North-Sky coordinate system is represented as follows:

[0066] ;

[0067] in, and This represents the spacecraft's position and velocity vectors in the J2000 coordinate system. This represents the position vector of the station in the Earth-fixed coordinate system. This is the transformation matrix from the J2000 coordinate system to the Earth-fixed coordinate system. This is the transformation matrix from the Earth-Fixed Coordinate System to the East-North-Sky Coordinate System.

[0068] Choose the unscented transformation sampling points at time k-1; the system's state vector has a dimension of n, so p = 2n+1 sampling points (sigma points) need to be selected. The sampling points at time k-1 are selected as follows:

[0069] ;

[0070] in, This represents the state estimate at time k-1. Represents the matrix within brackets The i-th column of the square root matrix; because It is always a real symmetric positive definite matrix, and its square root matrix is ​​calculated using Cholesky decomposition; the weights of the mean and covariance are as follows:

[0071] ;

[0072] ;

[0073] in, Used to control the distribution of sigma points, its value is between 0 and 1. α is the principal scaling factor, which affects the distribution range of sampling points. In this embodiment, α = 0.5 is taken; β is the secondary scaling factor, which affects the weight of the estimation result of the previous step on the subsequent variance matrix calculation. In this embodiment, β = 2 is taken. The range of values ​​is In this embodiment, we take , where n represents the dimension of the state vector. Indicates the covariance weights of the sampling points. This represents the covariance weight of the sampling points.

[0074] Calculate the predicted sample points at time k State prediction value State covariance predicted values :

[0075] ;

[0076] ;

[0077] ;

[0078] in This represents the process noise covariance matrix.

[0079] The sigma point at time k is transformed using the measurement equation, and the predicted measurement value is calculated. And the predicted values ​​of the measurement covariance matrix :

[0080] ;

[0081] ;

[0082] ;

[0083] in This represents time k.

[0084] In another exemplary embodiment of this application, considering the non-Gaussian nature of measurement noise, a generalized M-estimation is used instead of the weighted least squares estimation in the traditional filter. A robust Huber cost function replaces the L2 norm cost function, limiting the contribution of measurement outliers to the cost function. The Huber function is a combination of the L1 and L2 norms. When the residuals are within the Huber threshold range, the Huber function exhibits the L2 norm, and the robust Huber-based estimator is a weighted least squares estimator. When the residuals exceed the Huber threshold, the Huber function exhibits the L1 norm, and the robust Huber estimator is an L1 norm estimator. The standardized state error is denoted as... and standardized measurement residuals are The following robust cost function can be constructed:

[0085] ;

[0086] in, for The i-th component, for The j-th component, The Huber function is defined as follows:

[0087] ;

[0088] in The independent variable of the function, This is an adjustable parameter, set to 1.345.

[0089] In another exemplary embodiment of this application, the modified measurement noise covariance matrix is ​​obtained by minimizing the Huber robust cost function in the generalized M-estimation, as follows:

[0090] By differentiating the cost function, the following implicit equation can be obtained:

[0091] ;

[0092] in, Represents Huber function The derivative, Define Huber weight function The corresponding matrix is The above formula can be rewritten in matrix form:

[0093] ;

[0094] The j-th component at time k The expression is as follows:

[0095] ;

[0096] Will and Substituting the values, we obtain the following implicit equation:

[0097] ;

[0098] The modified measurement noise covariance matrix can be obtained. :

[0099] ;

[0100] In another exemplary embodiment of this application, the predicted value is measured 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:

[0101] ;

[0102] Based on the measured residuals The residual covariance matrix is ​​obtained by approximate calculation. The formula is:

[0103] ;

[0104] in, The forgetting factor is set to 0.95 in this embodiment;

[0105] 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:

[0106] ;

[0107] ;

[0108] Where β is the softening factor;

[0109] The suboptimal fading 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 adaptive fading factor. The formula is:

[0110] ;

[0111] ;

[0112] ;

[0113] in, Representation matrix and The ratio of each diagonal component. When the adaptive fading 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 occurred;

[0114] In another exemplary embodiment of this application, a discrimination index is calculated. To distinguish between pulse maneuvers and measurement anomalies:

[0115] ;

[0116] ;

[0117] in, Represents standardized measurement residuals Each component Compared to adjusting parameters The relative degree of deviation, Indicates the discrimination threshold; the degree of deviation of the velocity component in the standardized measurement residual. If the value is significantly greater than the other three components, the mutation is considered to be caused by a maneuver; otherwise, the mutation is considered to be caused by a measurement outlier. When the mutation is determined to be a maneuver, the adaptive fading factor remains unchanged; when it is determined to be a measurement outlier, the adaptive fading factor is reset to 1.

[0118] In another exemplary embodiment of this application, by discriminant indicators State estimation covariance Covariance and measurement residual covariance Adjustments will be made:

[0119] ;

[0120] ;

[0121] ;

[0122] The Kalman gain matrix at the current time step is calculated. The posterior state estimate is updated based on the measurement information. Posterior estimate of state covariance The formula is:

[0123] ;

[0124] ;

[0125] ;

[0126] For each step in the filtering process, the adaptive fading factor corresponding to the current step needs to be calculated. The system identifies whether there are any abnormal mutations in the current step. If abnormal mutations are found, they need to be identified through discrimination indicators. Distinguish between measurement outliers and maneuvers, and process the covariance based on the distinction results until the filtering process is complete.

[0127] This application also provides an embodiment that comprehensively analyzes the above-mentioned method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise; the following calculation conditions and technical parameters are set:

[0128] 1. The initial position and velocity of the non-cooperative target spacecraft in the J2000 coordinate system are [-5726510.59, -3472068.72, 1156512.92] m and [-1594.7645, -150.6295, -7498.2957] m / s, respectively;

[0129] 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;

[0130] 3. The ground station is located at longitude 24.6°, latitude 118.0°, and altitude 50.0 m in the geodetic coordinate system;

[0131] 4. 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.

[0132] 5. The measured noise conforms to a non-Gaussian noise distribution. The probability density function of non-Gaussian noise is defined as follows:

[0133] ;

[0134] in, and These are the standard deviations of independent Gaussian distributions. Set as , Here, represents the disturbance parameter, indicating the degree of noise pollution. .

[0135] 6. The tracking process started at 00:10:00 on September 12, 2025, and lasted for 1000 seconds.

[0136] 7. A measurement outlier exists at 300 s, specifically... ;

[0137] 8. At 500 s, the target spacecraft generates a pulse maneuver with an amplitude of 10 m / s along the velocity direction.

[0138] Figure 2 , Figure 3 , Figure 4 The simulation results of the present invention are given below:

[0139] Figure 2 and Figure 3 The target position estimation error and velocity estimation error obtained by the maneuvering spacecraft orbit determination method based on the adaptive robust decay memory filter described in this invention are presented respectively. It can be seen that, compared with the existing outlier robust unscented Kalman filter (ORUKF), adaptive robust unscented Kalman filter (ARUKF), and robust recursive Kalman filter (RRSPKF), the tracking algorithm of this invention has higher estimation accuracy. Compared with the existing ORUKF, ARUKF, and RRSPKF methods, the orbit determination method disclosed in this invention reduces the orbit determination error by approximately 96.6%, 81.4%, and 77.1% respectively throughout the mission, indicating that it has higher orbit determination accuracy and better filtering performance, demonstrating the superiority of the algorithm described in this invention.

[0140] Figure 4 The changes in the adaptive fading factor obtained by the tracking algorithm described in this invention are presented. It can be seen that when measurement anomalies exist, the adaptive fading factor described in this invention does not exceed the detection threshold, and the discrimination index successfully identifies it as a measurement anomaly. After a maneuver occurs, the proposed filter detects the maneuver promptly and accurately, and there are no false detections of maneuvers during periods when no maneuvers occur.

[0141] Therefore, by using the method proposed in this invention, the orbit determination of a spacecraft with non-cooperative pulse maneuvering under non-Gaussian measurement noise conditions can be achieved using only ground station measurement data. Moreover, the orbit determination accuracy is significantly improved compared to the three existing methods. It successfully distinguishes between measurement anomalies and maneuvers, does not cause false detections of maneuvers in the non-maneuvering segment, and accurately detects the timing of maneuvers.

[0142] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise, characterized in that: include: Construct an adaptive robust decay memory filter: use generalized M-estimation as the weighted least squares estimate in the replacement filter, and replace the L2 cost function with a robust Huber cost function; Calculate and obtain the target's current state prediction value and measurement prediction value; The modified measurement noise covariance matrix is ​​obtained by minimizing the cost function in the filter. The following operation is repeated recursively at each time step during the filtering process until the filtering process ends: An adaptive fading factor is introduced to monitor the change of measurement residuals in the filter in real time. When the adaptive fading factor is greater than the threshold, it is indicated that there is a measurement anomaly or pulse maneuver at the current moment. The current measurement value is obtained from the ground station. And the predicted value measured at the current time The difference is used to obtain the measurement residual of the filter. ; Based on measurement residuals The residual covariance matrix is ​​obtained by approximate calculation. ; 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 time. The formula is: ； ； Where β is the softening factor. To measure the noise covariance matrix, These are the predicted values ​​of the covariance matrix; The suboptimal fading 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 adaptive fading factor. The formula is: ； ； ； in, Representation matrix and The ratios of the diagonal components, For ranging of non-cooperative target spacecraft, A is the azimuth angle and E is the elevation angle. For speed measurement information; and Calculate the discrimination index to distinguish between measurement anomalies and impulse maneuvers, and adjust the adaptive fading factor based on the discrimination results; Adjustments are made to the state estimation covariance, cross-covariance, and measurement residual covariance based on the discriminant index; The Kalman gain matrix at the current time is calculated, and the target's state and state covariance estimate are obtained by updating the measurement information at the current time.

2. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 1, characterized in that: Establish a nonlinear system for the spacecraft and obtain ranging data from non-cooperative target spacecraft based on ground station data. Azimuth A, Pitch E, Velocity Information The sigma sample points at time k-1 are calculated based on the unscented transformation, and the predicted state value of the target at time k is obtained through nonlinear state equation propagation. State covariance predicted values The predicted measurement value is calculated based on the measurement model. And the predicted values ​​of the measurement covariance matrix .

3. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 2, characterized in that: The ground station collects measurement values ​​of the non-cooperative pulse maneuvering spacecraft in the East-North-Sky coordinate system, and the measurement noise in the measurement values ​​is... It is zero-mean Gaussian white noise, which satisfies ,in To measure the noise covariance matrix.

4. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 3, characterized in that: Define the standardized state error as and standardized measurement residuals are , The cost function constructed by replacing the L2 norm cost function with the robust Huber cost function, representing the measurement mapping matrix, is as follows: ； in, for The i-th component, for The j-th component, Here, n represents the dimension of the state vector, and m represents the dimension of the observation vector.

5. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 4, characterized in that: The modified measurement noise covariance matrix : ； ； ； Where T / 2 represents the transpose of the square root of the matrix; Represents Huber function The derivative; This represents the Huber weight function.

6. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 5, characterized in that: Based on discriminant indicators The following steps are taken to distinguish between measurement anomalies and pulse maneuvers: When the velocity component in the standardized measurement residual deviates to a certain degree When the value is significantly greater than other components, it is determined to be an impulsive maneuver, and the adaptive fading factor remains unchanged; Otherwise, it is judged as a measurement outlier, and the adaptive fading factor is reset to 1.

7. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 6, characterized in that: Calculate the discriminant index Identifying pulse maneuvers and measuring outliers: ； ； in Represents standardized measurement residuals Each component Compared to adjusting parameters The relative degree of deviation, This indicates the discrimination threshold.

8. The method for determining the orbit of a non-cooperative maneuvering spacecraft under non-Gaussian noise according to claim 7, characterized in that: The Kalman gain matrix at the current time step is calculated. The posterior state estimate is updated based on the measurement information. Posterior estimate of state covariance The formula is: ； ； 。

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