A space-based adaptive filtering method for near space flight targets

Abstract

The present disclosure provides a space-based adaptive filtering method for near space flight targets, state detection tracking of near space targets is performed by a satellite networking system composed of multiple space-based satellites, Kalman filtering is used to filter measurement data to obtain target state estimation; in the Kalman filtering process, the maneuvering frequency of the process noise covariance matrix in the one-step prediction link is corrected according to the maneuvering frequency estimation; the first error factor of the satellite networking system for target positioning is determined according to the networking geometry of the satellite networking system, and the second error factor of the measurement model of the satellite networking system is determined according to the innovation; the correction factor is determined according to the first error factor and the second error factor, and the measurement noise covariance matrix in the time update link of the Kalman filtering is corrected. Using the present application can improve the tracking accuracy of space-based satellites on targets.

Description

Technical Field

[0001] This invention relates to the field of aerospace science and technology, specifically to a space-based adaptive filtering method for near-space flight targets. Background Technology

[0002] In long-range interception missions targeting high-speed gliding vehicles in near space, traditional ground-based radar detection methods are difficult to achieve effective network deployment for continuous detection of targets due to geographical constraints and complex electromagnetic interference on the battlefield. With the continuous enhancement of space delivery capabilities of various countries, medium and low orbit satellite constellations have provided a new approach for long-range continuous tracking.

[0003] Currently, there are many filtering methods for target tracking, such as Kalman filtering (KF) for linear systems, and Extended Kalman Filter (EKF), Uncented Kalman Filter (UKF), and Cubature Kalman Filter (CKF) for nonlinear systems. Most existing filtering methods for tracking gliding targets in near space are improvements on these methods, mainly focusing on the construction of the tracking model and the correction of the prediction model.

[0004] Some scholars have conducted research on the impact of sensor measurements on estimation accuracy. For example, Yang Yueshuang et al. addressed the issue of sensor measurement error characteristics changing over time by improving the measurement noise estimator based on Sage-Husa filtering and utilizing local dynamic statistics of innovation. This improved the accuracy and stability of noise estimation and enhanced target tracking performance when the statistical characteristics of measurement noise are unknown. However, existing research on reducing the impact of measurement errors still largely focuses on optimizing and correcting prediction models, lacking systematic research on the error compensation mechanisms of the measurement models themselves.

[0005] Adaptive adjustment of the noise covariance matrix is ​​a common approach in Kalman filter tracking. Li et al. addressed the problems of prediction model mismatch caused by unknown maneuvers of near-space gliding targets and unstable detection performance due to potential interference or blockage of sensor signals. They proposed a noise-adaptive EKF filtering method based on Deep Deterministic Policy Gradient (DDPG). By using multi-sensor fusion to detect unknown target maneuvers and inaccurate measurement models, and selectively adjusting the process and measurement models, the robustness of the filtering was improved.

[0006] Existing research on filtering and tracking techniques for high-speed near-space targets using space-based infrared satellites largely overlooks the impact of the relatively poor detection accuracy of space-based satellites on target tracking accuracy. While radar typically provides tracking accuracy at the hundred-meter level for near-space targets, space-based infrared satellites achieve accuracy at the kilometer level, making it difficult to meet the requirements for continuous and effective tracking of high-speed near-space targets. Summary of the Invention

[0007] In view of this, the present invention provides a space-based adaptive filtering method for near-space flying targets, which is used for adaptive tracking of space-based satellites of high-speed gliding targets in near space, thereby improving the tracking accuracy of space-based satellites of targets.

[0008] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0009] A space-based adaptive filtering method for near-space flying targets includes:

[0010] The near-space target is detected and tracked by a satellite network system composed of multiple space-based satellites. Kalman filtering is used to filter the measurement data to obtain the target state estimate.

[0011] The maneuver frequency of the process noise covariance matrix in the one-step prediction stage of the Kalman filter is corrected based on the maneuver frequency estimation.

[0012] The first error factor for target positioning of the satellite networking system is determined based on the networking geometry of the satellite networking system, and the second error factor for the measurement model of the satellite networking system is determined based on the new information. The correction factor is determined based on the first error factor and the second error factor to correct the measurement noise covariance matrix in the Kalman filter time update stage.

[0013] Preferably, the correction of the maneuver frequency of the process noise covariance matrix in the one-step prediction stage of the Kalman filter based on the maneuver frequency estimation is as follows:

[0014] Normalized distance d using filtered information k As a variable for motion detection;

[0015] If the normalized distance d of the filtered innovation k If the probability exceeds the threshold δd corresponding to the allowable false alarm, the target is considered to have maneuvered, increasing the prediction error. Therefore, the maneuver frequency is estimated and substituted into the process noise covariance matrix Q at the next time step. k The maneuver frequency is corrected and then filtered.

[0016] If the normalized distance d of the filtered innovation k If not greater than, then the process noise covariance matrix Q is not considered. k Make corrections.

[0017] Preferably, the estimated maneuver frequency is:

[0018] Normalize the distance d using filtered innovation k The maneuver frequency at time k is estimated using the following formula.

[0019]

[0020] in, and , respectively, are the estimated maneuver frequencies at time k and time k-1; D, T, and C represent the three dimensions of drag, turning force, and climb force, respectively.

[0021] Preferably, the first error factor for target positioning by the satellite networking system, determined based on the networking geometry of the satellite networking system, is:

[0022] For a satellite constellation system containing two satellites, the line-of-sight angle α between the two satellites is used. ts Determine the first error factor; the angle α between the lines of sight of the two stars. ts The closer to 90°, the better the network geometry and the smaller the first error factor.

[0023] Preferably, the method of utilizing the angle α between the two stars' lines of sight ts The first error factor is determined as:

[0024]

[0025] Among them, c 1,k It is the first error factor at time k.

[0026] Preferably, the first error factor for target positioning by the satellite networking system, determined based on the networking geometry of the satellite networking system, is:

[0027] For containing n s A satellite constellation system of n satellites s >2, using n s Geometric precision factor I of each satellite PDOP Determine the first error factor; geometric precision factor I PDOP The smaller the value, the higher the positioning accuracy of the satellite network, and the smaller the first error factor.

[0028] Preferably, the geometric precision factor I of m satellites is used. PDOP The first error factor is determined as:

[0029]

[0030] Among them, c 1,k I is the first error factor at time k; minand I max For I PDOP The set extreme value.

[0031] Preferably, the second error factor for determining the satellite networking system measurement model based on the new information is:

[0032] Determine the theoretical covariance matrix estimate of the innovation

[0033] The Kalman filter employs an unscented Kalman filter to construct the measurement noise covariance matrix R. k Adaptive matrix for:

[0034]

[0035] Where n is the dimension of the target state space; These are the weighting coefficients of the Sigma point covariance during the UKF filtering process; The Sigma point is predicted by the measurement model at time k. Predict the state value for the target Projection in the measurement model; (·) ii To indicate taking the diagonal elements of the matrix, the superscript (i) indicates the measurement dimension;

[0036] Extracting the adaptive matrix Λ k elements on the middle diagonal Calculate the second error factor for each measurement dimension i.

[0037]

[0038] Where, λ max and λ min These are the upper and lower limits of the pre-set second error factor, respectively.

[0039] Preferably, the step of determining the correction factor based on the first error factor and the second error factor to correct the measurement noise matrix in the Kalman filter time update stage is as follows:

[0040] For the measurement noise covariance matrix R k The correction method is as follows:

[0041]

[0042] In the formula, R k The measurement noise covariance matrix before correction. This is the corrected measurement noise covariance matrix; U k This is the correction factor matrix; the subscript k indicates time k.

[0043] Correction factor matrix For the correction factor of different measurement dimensions i The diagonal matrix formed, i = 1, ..., 2n s ;

[0044] Correction factor The determination method is as follows: a fuzzy controller is used to construct the first error factor, the second error factor, and the correction factor. The fuzzy relationship between them; based on the first error factor and the second error factor of measurement dimension i, input to the fuzzy controller to obtain the correction factor of measurement dimension i.

[0045] Preferably, the fuzzy controller is configured as follows:

[0046] Let the membership functions of the first and second error factors be trigonometric functions defined in the range [0,1], and the correction factor... The membership function is a trigonometric function defined within a specified range;

[0047] The fuzzy set of the fuzzy controller is {VS,S,M,B,VB}, which represent very small, small, medium, large, and very large, respectively.

[0048] The fuzzy controller rules are as follows:

[0049]

[0050]

[0051] Among them, c 1,k This represents the first error factor at time k. This represents the second error factor of measurement dimension i at time k.

[0052] Beneficial effects:

[0053] (1) For the problem of tracking near-space flying targets, this invention uses a multi-satellite networking system to continuously track them. To address the problem of poor measurement accuracy of space-based infrared satellites, the filtering tracking accuracy is improved by adaptively correcting the noise covariance matrix.

[0054] (2) The satellite configuration weight and the novel orthogonal weight are used to judge the accuracy of satellite measurement, and the measurement noise covariance matrix R is adaptively adjusted to dynamically adjust the influence of the measurement value on the estimation result and improve the tracking accuracy of the space-based satellite on the target.

[0055] (3) In a preferred embodiment, the satellite configuration weights and novel orthogonal weights are converted into correction factors by a fuzzy controller. On the basis of adaptive correction of the measurement noise covariance matrix, the extreme weights are avoided from over-adjusting the noise matrix, thereby improving the filtering accuracy and ensuring the smoothness of the filtering process.

[0056] (4) By detecting the target maneuver, the degree of mismatch between the prediction model and the actual target motion is judged, the maneuver frequency of the prediction model is dynamically estimated, and the process noise covariance matrix is ​​adaptively adjusted by the maneuver frequency, thereby dynamically adjusting the influence of the prediction value on the estimation result and improving the tracking accuracy of the target by the space-based satellite. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the space-based adaptive filtering method for near-space flying targets according to the present invention.

[0058] Figure 2 This is a schematic diagram showing the angle between the two stars and the target. Detailed Implementation

[0059] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0060] Considering that both the target tracking model and the sensor measurement model in the tracking scenario of this invention are nonlinear models, traditional Kalman filtering methods based on linear systems are difficult to apply. Extended Kalman filtering methods require solving the Jacobian matrix of the model, which involves a large computational load. Therefore, this embodiment uses unscented Kalman filtering, which has higher theoretical accuracy, to process the measurement data. Simultaneously, considering the target's maneuvering motion and the poor measurement accuracy of satellite sensors, a noise adaptive UKF filtering method is designed by adjusting the measurement noise covariance matrix R and the process noise covariance matrix Q to achieve tracking of near-space flying targets.

[0061] This invention presents a space-based adaptive filtering method for near-space flying targets. Taking non-cooperative near-space gliding targets as the research object, it utilizes multiple space-based satellites for detection and tracking. Unscented Kalman Filtering (UKF) is employed to filter the measurement data, yielding an estimate of the target's state. Considering the relatively poor accuracy of satellite measurements, and combining satellite detection characteristics with the orthogonal optimality principle of Kalman filtering innovation, the process noise covariance matrix and measurement noise covariance matrix are adaptively adjusted during the filtering process to improve the accuracy of the target state estimation. The specific flowchart is shown below:

[0062] Step 1: Initialize the target motion prediction model and measurement model.

[0063] 1. Target motion prediction model

[0064] To effectively reduce the impact of Earth's curvature on tracking accuracy, a near-space target motion prediction model is constructed using the Earth-Centered Earth-Fixed (ECEF) coordinate system as the reference coordinate system.

[0065]

[0066] In the formula, X is the 9×1 dimensional state vector of the target, i.e., X=[X,Y,Z,V] x V y V z ,u D ,u T ,u C ] T Where r = [X, Y, Z] T and V = [V X V Y V Z ] T These are the target's position and velocity vectors in the ECEF coordinate system, respectively. g = [g x g y g z ] T and a A =[A x A y A z ] T These represent the components of gravitational acceleration in the three directions of the ECEF coordinate system. u = [u D u T u C ] T λ represents the drag, turning force, and climb force parameters of the aircraft in the half-velocity coordinate system, respectively. D , λ T , λ C The maneuver frequencies of the three aerodynamic parameters, ω D ω T ω C These are the noises for three aerodynamic parameters, all of which follow a zero-mean Gaussian distribution. The aerodynamic acceleration of the aircraft can be modeled in a half-velocity coordinate system (Velocity-Turn-Climb, VTC) as follows:

[0067]

[0068] In the formula, m is the mass of the aircraft; S is the characteristic area of ​​the aircraft; ρ is the atmospheric density at the location of the aircraft, which is related to the altitude. C represents the target speed magnitude. L CD These are the lift coefficient and drag coefficient, respectively, which are related to the aircraft's angle of attack and Mach number; σ is the aircraft's roll angle.

[0069] Transform the aerodynamic acceleration from the above half-velocity coordinate system to the ECEF coordinate system:

[0070]

[0071] In the formula, It is the transformation matrix from the VTC to the ECEF coordinate system, which can be calculated from the target position and velocity vectors.

[0072] Since the mass, characteristic area, and aerodynamic coefficients of the non-cooperative target are unknown, these unknown parameters can be set as:

[0073]

[0074] In the formula, u=[u D u T u C ] T These represent the drag, turning force, and climb force parameters of the aircraft in the half-velocity coordinate system, respectively. C L C D These are the lift coefficient and drag coefficient, respectively, which are related to the aircraft's angle of attack and Mach number; σ is the aircraft's roll angle. These three parameters correspond to the first-order Markov process in equation (1).

[0075] 2. Satellite sensor measurement model

[0076] Space-based satellite measurements include azimuth angle θ s and elevation angle γ s With two fields of view, a single satellite is insufficient to accurately describe the target's position; at least two satellites are needed for target tracking and localization. The corresponding measurement model Z... s for:

[0077]

[0078] In the formula, n s H represents the number of satellite sensors. s (X) represents n s The measurement equation corresponding to each satellite measurement, V s This is a column vector composed of measurement noise from multiple satellites. The relationship between the satellite's field of view and its three-dimensional coordinates in the satellite body coordinate system can be expressed as:

[0079]

[0080] Where, θ si and γ siThe azimuth and elevation angles of the i-th satellite are measured, respectively, x si y si z si v si,θ v si,γ This represents the position and velocity components of the i-th satellite in the body coordinate system.

[0081] Step 2: Apply an unscented Kalman filter to the measurements. The process is as follows:

[0082] 0. Initialize filter parameters

[0083] 1) Confirm the initial value X 0|0 P 0|0 X is the initial state vector used for UKF filtering, and P is the error covariance matrix used for UKF filtering.

[0084] 2) Calculate the weight coefficients of the Sigma point in the unscented Kalman filter.

[0085]

[0086] In the formula, w m and w c These represent the weighting coefficients for the state mean and covariance, respectively. n is the dimension of the state vector; λ = α 2 (n+κ)-n is used to adjust the distance between the mean and Sigma points, α∈[0,1], κ=3-n; β can be used to adjust the approximate accuracy of the covariance. For Gaussian distributions, β=2 is usually chosen. and The weighting coefficients represent the state mean and covariance of the first Sigma point. and These represent the weighting coefficients for the state mean and covariance of the 2nd to 2n+1th Sigma points. Unscented Kalman filtering involves 2n+1 Sigma points.

[0087] 1. One-step prediction

[0088] 1) Calculate the Sigma point based on the state estimate from the previous time step:

[0089]

[0090] In the formula, is the i-th column of the error covariance matrix P after Cholesky decomposition; the subscript k indicates time k. This represents the estimated value of the target state at the previous moment.

[0091] 2) Predicting the target state based on Sigma points

[0092]

[0093] In the formula, and P k|k-1 These are the predicted state values ​​and their error covariance matrix, F. k-1 (·) represents the state transition function, Q k-1 This is the process noise covariance matrix, used to represent the uncertainty of the prediction model.

[0094] 2. Measurement Update

[0095] 1) Generate new Sigma points based on state prediction values

[0096]

[0097] in, and This represents the 2n+1 Sigma points obtained from the state prediction vector.

[0098] 2) Calculate measurement innovation and its covariance based on Sigma points

[0099]

[0100]

[0101] In the formula, and P zz,k|k-1 H represents the projections of the state prediction value and the state error covariance matrix into the measurement space, respectively. k (·) is the measurement transfer function, R k This is the measurement noise covariance matrix, used to represent the uncertainty of the measurement.

[0102] 3) Calculate the Kalman gain and the current state estimate.

[0103]

[0104] Among them, P xz,k|k-1 Let K be the cross-covariance matrix between the predicted and measured values ​​of the target state. k For Kalman gain, P k Let be the error covariance matrix of the state estimate at time k.

[0105] Step 3: Adaptive Correction of Noise Covariance Matrix

[0106] Based on the above conventional UKF filtering, the measurement noise covariance matrix R is analyzed respectively. k The process noise covariance matrix Q k-1 Perform adaptive correction.

[0107] 1. Measurement noise covariance matrix Rk Correction

[0108] This step determines the first error factor for target positioning of the satellite networking system based on the networking geometry of the satellite networking system, and determines the second error factor for the measurement model of the satellite networking system based on the new information; and determines the correction factor based on the first and second error factors to correct the measurement noise covariance matrix in the Kalman filter time update stage.

[0109] The specific implementation process is as follows:

[0110] Given the measurement noise covariance matrix R k Let n be a diagonal matrix composed of measurement noise covariances. s The satellite detects the target, and the noise covariance matrix is ​​given in the following specific form:

[0111]

[0112] Where, σ θi and σ γ1 denoted as , and respectively as the standard deviations of the azimuth and elevation angle measurements of the i-th satellite.

[0113] Based on the following weights, matrix R k Perform fuzzy adaptive adjustment

[0114] 1) First error factor – satellite geometry configuration weight c 1,k

[0115] For multi-satellite network detection systems, the accuracy of target detection is affected not only by the field-of-view error of the satellite sensors but also by the geometric configuration between the satellites. We will discuss two cases:

[0116] First case: When the number of satellites is n s When α = 2, use the angle α between the lines of sight of the two stars. ts Determine satellite geometric configuration weights; line-of-sight angle α between the two satellites. ts The closer to 90°, the better the network geometry and the smaller the first error factor.

[0117] Specifically, let α be the angle between the lines connecting the two satellites and the target. ts ,like Figure 2 As shown.

[0118] The formula for calculating the angle between the lines of sight of two stars is:

[0119]

[0120] In the formula, The vector representing the positional relationship between the target and satellite i. Let be the position vector of the target in the ECEF coordinate system. Let be the position vector of the i-th satellite in the ECEF coordinate system. Since the true position of the non-cooperative target is unknown, a coarse positioning estimate obtained by least squares method based on two-satellite measurements is used as an approximation.

[0121] It is easy to obtain α ts ∈(0°, 180°), according to satellite detection characteristics, the closer the angle between the two satellite lines of sight is to 90°, the better the geometric configuration and the smaller the positioning error; conversely, the closer the angle is to 0° or 180°, the more significant the error amplification effect. We construct weights to represent the geometric configuration of the two satellites, i.e.

[0122]

[0123] The second case: For cases containing n s A satellite constellation system of n satellites s >2, using n s Geometric precision factor I of each satellite GDOP Determine the first error factor; geometric precision factor I GDOP The smaller the value, the higher the positioning accuracy of the satellite network, and the smaller the first error factor.

[0124] Specifically, when the number of satellites is greater than two, the above weightings are not applicable, and the Position Dilution of Precision (PDOP) can be used to describe the satellite's geometric configuration. The PDOP is a crucial coefficient for measuring satellite positioning accuracy. According to satellite positioning research, for multi-satellite network systems, the PDOP value is generally between 1 and 10. A smaller PDOP value indicates a better geometric distribution of the satellite network system and a smaller impact on target positioning accuracy; conversely, a larger PDOP value indicates a worse geometric distribution and a greater impact on target positioning accuracy. The PDOP calculation formula is as follows:

[0125]

[0126] In the formula, tr(·) is the trace operation of the matrix. E is the line-of-sight angle matrix of the satellite relative to the target. i and A i Let be the elevation angle and azimuth angle of the i-th satellite relative to the target in the ECEF coordinate system, respectively. Since the target position is unknown, it is approximated using the results of least squares positioning:

[0127]

[0128] In the formula, This indicates the relative distance between the satellite and the target.

[0129] The weights for constructing the geometric configuration using the utility function method are:

[0130]

[0131] In the formula, I PDOP extreme values ​​I min and I max They can be set to 2 and 8 respectively.

[0132] 2) Second error factor – innovative orthogonal weights

[0133] In Kalman filtering, assuming the system state model is accurate, the innovation reflects the error of the measurement model. The innovation is defined as follows:

[0134]

[0135] For linear filters, optimal filtering performance is related to the orthogonality of the innovation sequences; however, for UKF nonlinear filters, the innovation sequences cannot be perfectly orthogonal, but if the weak autocorrelation condition is met, the filter can be considered to have good performance. The sufficient condition for innovation orthogonality can be simplified to:

[0136]

[0137] In the formula, C k The theoretical covariance matrix is ​​unknown in actual calculations and can be estimated using equation (27).

[0138]

[0139] In the formula, κ is the forgetting factor, typically taken as 0.95. ε1 is the filtered innovation vector at the initial time, ε k Let be the filtered innovation vector at time k.

[0140] In addition, P zz,k|k-1 The actual information covariance matrix in the UKF filtering process is expressed as follows:

[0141]

[0142] In the formula, is the weighting coefficient of the Sigma point covariance in the UKF filtering process, which is calculated by equation (7); n is the dimension of the target state space. As can be seen from equation (1), n ​​= 9 is taken in this embodiment. The Sigma point is predicted by the measurement model at time k. Predict the state value for the target The projection in the measurement model is specifically calculated using formula (12).

[0143] For the sake of brevity, the first term on the right side of equation (28) is denoted as Right now

[0144]

[0145] When the measurement model is inaccurate, the sufficient condition for innovation orthogonality is not fully met, and it is assumed that the matrix R describing the measurement noise characteristics... k Inaccurate, assuming it is multiplied by an adaptive diagonal matrix on its left. For the orthogonality condition of the new information to hold, equation (26) becomes

[0146]

[0147] Perform the following conversion

[0148]

[0149]

[0150] Considering the matrix R k The correction involves modifying its diagonal elements, thus forming an adaptive diagonal matrix Λ. k It can be obtained from the following formula

[0151]

[0152] In the formula, ii in the lower right corner of the matrix represents the diagonal element of the matrix. The superscript (i) represents the measurement dimension.

[0153] Considering the adaptive matrix Λ obtained from equation (33) k The fluctuation is large due to the influence of the error factor in the estimation of the new information covariance. If its value is directly used to estimate R... k Corrections cannot guarantee the stability and non-negativity of the corrected results; therefore, this invention uses an adaptive matrix Λ. k diagonal elements As the influence matrix R k The final corrected result is processed by one of the weights, specifically by extracting the adaptive matrix Λ. k elements on the middle diagonal The novel orthogonal weights corresponding to each measurement dimension i are calculated using the utility function method.

[0154]

[0155] In the formula, λ max and λ min These are the upper and lower limits of the pre-set orthogonal weights of the new information.

[0156] 3) Fuzzy correction factor

[0157] For the measurement noise covariance matrix Rk The correction rules are as follows:

[0158]

[0159] In the formula, R k The measurement noise covariance matrix before correction. This is the corrected measurement noise covariance matrix; U k This is the correction factor matrix. Here, It is a diagonal matrix composed of correction factors for different measurement dimensions, each correction factor The size is limited to the set [μ] min ,μ max Within the range.

[0160] The correction factor The satellite geometric configuration weights c obtained from steps 1) and 2) above 1,k Orthogonal weights of new information It is obtained through combination. The combination method can be weighted or mapped.

[0161] In this preferred embodiment, a fuzzy controller is used to implement the satellite geometry configuration weights c. 1,k Orthogonal weights of new information The fuzzy correction factor is calculated. Specifically, a fuzzy controller is used to construct the satellite geometric configuration weights, novel orthogonal weights, and correction factors. The fuzzy relationship between them; when the satellite's geometric configuration weight c is known. 1,k Orthogonal weights of new information By inputting the fuzzy controller, the correction factor can be obtained.

[0162] The fuzzy controller is set up as follows: Let c 1,k and The membership functions are all trigonometric functions defined in the range [0,1]. The membership function is defined in [μ min ,μ max The triangular function is defined within the range of [ ]. The fuzzy set of the fuzzy controller is defined as {VS,S,M,B,VB}, representing the correction factor as very small, small, medium, large, and very large, respectively. The corresponding fuzzy rules are shown in Table 1.

[0163] Table 1 Fuzzy Controller Rules

[0164]

[0165] When c 1,k The closer the value is to 1, the worse the satellite's geometry, and the greater the likelihood of decreased target detection accuracy. Therefore, it is necessary to increase the matrix R. kTo reduce the Kalman gain, thereby reducing the impact of measurement on the estimation results; similarly, when The closer c is to 1, the larger the error in that measurement dimension, and the greater the need for correction. Conversely, when c... 1,k and The closer the value is to 0, the higher the accuracy of the satellite measurement, and the less need to adjust the matrix R. k Make corrections.

[0166] 2. Process noise matrix Q k-1 Correction

[0167] Based on the first-order Markov assumptions about the target aerodynamic acceleration parameters in step 1, the expression for the process noise covariance matrix is ​​as follows:

[0168]

[0169] In the formula,

[0170]

[0171] In the formula, the subscripts D, T, and C represent the directions of the three aerodynamic accelerations: drag acceleration, turning force acceleration, and climb force acceleration, respectively. D,k-1 ,q T,k-1 ,q C,k-1 The three aerodynamic acceleration directions are represented in the process noise covariance matrix Q. k-1 diagonal elements in Let λ be the variance of the three aerodynamic acceleration-related parameters. D,k-1 , λ T,k-1 , λ C,k-1 Let D, T, and C be the maneuver frequencies, and k-1 represent the frequency of the target state during the filtering process at time k, from the state at time k-1. Predicting at time k During the process, the process noise covariance matrix at time k-1 is used, as shown in equation (10).

[0172] Normalized distance d using filtered information k As a variable for motion detection, d k The expression is

[0173]

[0174] Since the innovation follows a Gaussian distribution, the detection variable follows a distribution with 2n degrees of freedom. s χ 2 Distribution, i.e., d k ~χ 2 (2n s ), 2n sLet p0 be the dimension of the measurement vector. Define the probability of allowing a false alarm as p0, and the corresponding threshold value as δd, then we have...

[0175] P{d k >δd}=p0 (39)

[0176] When d k When the value is greater than δd, the target is considered to have maneuvered, the prediction error of the system model increases, and the process noise covariance matrix Q needs to be corrected. The maneuver frequency is estimated as follows:

[0177]

[0178] in, and These are the estimated maneuver frequencies at time k and time k-1, respectively. To avoid repeated filtering at the current time and thus save computational resources, and considering that the target's maneuver characteristics will not change significantly in the short term during its movement, the estimated maneuver frequencies are... Substitute the process noise covariance matrix Q at the next time step k Then, it is corrected and filtered. That is, equation (37) becomes:

[0179]

[0180] When the target maneuvers, the estimated maneuver frequency increases, the process noise covariance matrix increases, and the uncertainty of the system model increases. This makes the filter more reliant on the measurements, reducing the impact of model mismatch error on the estimation results. When d k When the value is less than δd, the target is considered not to perform any maneuvers, and the matrix Q is... k Perform standard filtering without any modifications.

[0181] The target motion model in step one above, besides the dynamic model specifically designed for near-space gliding targets, can also be replaced by the Singer model or the current statistical model.

[0182] In step two above, the filtering method can be replaced by EKF or CKF filtering methods, in addition to UKF.

[0183] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A space-based adaptive filtering method for near-space flying targets, characterized in that, include: The near-space target is detected and tracked by a satellite network system composed of multiple space-based satellites. Kalman filtering is used to filter the measurement data to obtain the target state estimate. The maneuver frequency of the process noise covariance matrix in the one-step prediction stage of the Kalman filter is corrected based on the maneuver frequency estimation. The first error factor for target positioning by the satellite networking system is determined based on the networking geometry of the satellite networking system, and the second error factor for the measurement model of the satellite networking system is determined based on the new information. The correction factor is determined based on the first error factor and the second error factor, and the measurement noise covariance matrix in the Kalman filter time update stage is corrected. The method for determining the first error factor is as follows: For including A satellite networking system of 100 satellites >2, use Geometric precision factor of a satellite Determine the first error factor; geometric precision factor. The smaller the value, the higher the positioning accuracy of the satellite network, and the smaller the first error factor; the formula is expressed as: in, for k The first error factor at time; and for The set extreme value; The second error factor is determined as follows: Determine the theoretical covariance matrix estimate of the innovation ; Kalman filtering employs unscented Kalman filtering to construct the measurement noise covariance matrix. Adaptive matrix for: in, n denoted as the dimension of the target state space; These are the weighting coefficients of the Sigma point covariance during the UKF filtering process; for k The Sigma point is predicted by the measurement model at a given time. Predict the state value for the target Projection in the measurement model; To represent taking the diagonal elements of a matrix, the superscript ( i () indicates the measurement dimension; Extracting the adaptive matrix elements on the middle diagonal Calculate each measurement dimension i The corresponding second error factor : in, and These are the upper and lower limits of the pre-set second error factor, respectively.

2. The method as described in claim 1, characterized in that, The correction of the maneuver frequency of the process noise covariance matrix in the one-step prediction stage of the Kalman filter based on the maneuver frequency estimation is as follows: Normalized distance with filtered news As a variable for motion detection; If the filtered innovation is normalized to distance The probability of the false alarm being greater than the threshold value is allowed. If the target is assumed to maneuver, increasing the prediction error, then the maneuver frequency is estimated and substituted into the process noise covariance matrix for the next time step. The maneuver frequency is corrected and then filtered. If the filtered innovation is normalized to distance If not greater than, then the process noise covariance matrix is ​​not considered. Make corrections.

3. The method as described in claim 2, characterized in that, The estimated maneuver frequency is: Normalized distance using filtered innovation The following formula is used to estimate k maneuver frequency at any given moment in, and They are respectively k Time and k Estimated maneuver frequency at time -1; These represent the three dimensions: drag, turning force, and climbing force.

4. The method as described in claim 1, characterized in that, The first error factor for target positioning using the satellite networking system, determined based on the networking geometry of the satellite networking system, is: For a satellite constellation system containing two satellites, the line-of-sight angle between the two satellites is utilized. Determine the first error factor; the angle between the lines of sight of the two stars. The closer to 90°, the better the network geometry and the smaller the first error factor.

5. The method as described in claim 4, characterized in that, The use of the angle between two stars The first error factor is determined as: in, for k The first error factor at time.

6. The method as described in claim 1, characterized in that, The step of determining the correction factor based on the first error factor and the second error factor to correct the measurement noise matrix in the Kalman filter time update stage is as follows: For the measurement noise covariance matrix The correction method is as follows: In the formula, The measurement noise covariance matrix before correction. This is the corrected measurement noise covariance matrix; For the correction factor matrix; subscript k express k time; Correction factor matrix For different measurement dimensions i Correction factor The diagonal matrix formed ; Correction factor The determination method is as follows: a fuzzy controller is used to construct the first error factor, the second error factor, and the correction factor. The fuzzy relationship between them; based on the first error factor and the measurement dimension i The second error factor is input into the fuzzy controller to obtain the measurement dimension. i Correction factor .

7. The method as described in claim 6, characterized in that, The fuzzy controller is configured as follows: Suppose that the membership functions of the first error factor and the second error factor are both defined on... Trigonometric functions within the range, correction factor The membership function is a trigonometric function defined within a specified range; The fuzzy set of the fuzzy controller is {VS,S,M,B,VB}, which represent very small, small, medium, large, and very large, respectively. The fuzzy controller rules are as follows: in, express k The first error factor at time, express k Dimensions of time measurement i The second error factor.

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