Space-based adaptive filtering method for near space flying target

Abstract

The invention provides a space-based adaptive filtering method for a near space flying target, and the method comprises the steps: carrying out the state detection and tracking of a near space target through a satellite networking system composed of a plurality of space-based satellites, carrying out the filtering of measurement data through Kalman filtering, and obtaining the estimation of the state of the target; in the Kalman filtering process, the maneuvering frequency of a process noise covariance matrix in the one-step prediction link is corrected according to maneuvering frequency estimation; determining a first error factor of the satellite networking system for target positioning according to the networking geometric configuration of the satellite networking system, and determining a second error factor of a satellite networking system measurement model according to the information; and determining a correction factor according to the first error factor and the second error factor, and correcting the measurement noise covariance matrix in the Kalman filtering time updating link. According to the invention, the tracking precision of the space-based satellite on the target can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace science and technology, and in particular relates to a space-based adaptive filtering method for near-space flight targets. Background Art

[0002] In long-range interception missions against near-space high-speed gliding vehicles, since the target can fly long distances in near-space at speeds exceeding Mach 5, traditional ground-based radar detection methods are difficult to achieve effective networking and deployment for continuous detection of the target due to factors such as geographical constraints and complex electromagnetic interference on the battlefield. As countries continue to strengthen their space delivery capabilities, medium and low-orbit satellite constellations have provided a new way for long-distance continuous tracking.

[0003] Numerous filtering methods are currently used for target tracking, including the Kalman filter (KF) for linear systems, the extended Kalman filter (EKF), the uncented Kalman filter (UKF), and the cubature Kalman filter (CKF) for nonlinear systems. Existing filtering methods for near-space gliding target tracking are mostly improvements upon these methods, focusing primarily on building tracking models and modifying prediction models.

[0004] Some researchers have investigated the impact of sensor measurements on estimation accuracy. For example, Yang Yueshuang et al. addressed the issue of time-varying sensor measurement error characteristics. Based on the Sage-Husa filter, they utilized the local dynamic statistics of new information to improve the measurement noise estimator. This improved the accuracy and stability of the noise estimate and the target tracking performance when the statistical characteristics of the measurement noise are unknown. However, existing research on reducing the impact of measurement error still focuses on optimizing and modifying prediction models, while 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. address the problems of prediction model mismatch caused by unknown maneuvers of near-space gliding targets, as well as unstable detection performance due to interference or obstruction 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, they selectively adjust the process and measurement models, improving the robustness of the filter.

[0006] Existing research on filtering tracking of high-speed targets in near-space using space-based infrared satellites has largely ignored the impact of the satellite's poor detection accuracy on target tracking. While radar tracking accuracy for near-space targets is typically in the hundreds of meters, space-based infrared satellites offer tracking accuracy in the thousands, making them inadequate for sustained and effective tracking of high-speed targets in near-space. 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 to adaptively track space-based satellites that are high-speed gliding targets in near-space, thereby improving the tracking accuracy of space-based satellites on targets.

[0008] In order to solve the above technical problems, the present invention is implemented as follows.

[0009] A space-based adaptive filtering method for near-space flight targets, comprising:

[0010] The satellite network system composed of multiple space-based satellites is used to detect and track nearby space targets, and the Kalman filter is used to filter the measurement data to obtain the target state estimation;

[0011] The maneuvering frequency of the process noise covariance matrix in the one-step prediction link of the Kalman filter is corrected according to the maneuvering frequency estimation;

[0012] 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 satellite networking system measurement model is determined according to the new information; the correction factor is determined according to the first error factor and the second error factor, and the measurement noise covariance matrix in the Kalman filter time update link is corrected.

[0013] Preferably, the maneuvering frequency of the process noise covariance matrix in the one-step prediction link of the Kalman filter is corrected according to the maneuvering frequency estimation as follows:

[0014] Normalize the distance d with the filtered innovation k as a maneuver detection variable;

[0015] If the normalized distance of the filtered innovation d k If the probability of false alarm is greater than the threshold value δd, it is considered that the target is maneuvering and the prediction error increases. Then the maneuvering frequency is estimated and substituted into the process noise covariance matrix Q at the next moment. k In the process, the maneuvering frequency is corrected and then filtered;

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

[0017] Preferably, the estimated maneuvering frequency is:

[0018] Normalize the distance d using filtered innovation k , use the following formula to estimate the maneuvering frequency at time k,

[0019]

[0020] in, and are the estimated values of maneuvering frequency at time k and time k-1 respectively; D, T, and C represent the three dimensions of drag, turning force, and climbing force respectively.

[0021] Preferably, the first error factor for determining the target positioning by the satellite networking system according to the networking geometry of the satellite networking system is:

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

[0023] Preferably, the method uses the binary star line of sight angle α ts Determine the first error factor as:

[0024]

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

[0026] Preferably, the first error factor for determining the target positioning by the satellite networking system according to the networking geometry of the satellite networking system is:

[0027] For n s Satellite networking system with n satellites, s >2, using n s The geometric dilution of precision of the satellite PDOP Determine the first error factor; geometric dilution of precision I PDOP The smaller it is, the higher the satellite network positioning accuracy is and the smaller the first error factor is.

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

[0029]

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

[0031] Preferably, the second error factor of the satellite networking system measurement model determined according to the new information is:

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

[0033] Kalman filtering uses unscented Kalman filtering to construct the measurement noise covariance matrix R k Adaptive matrix for:

[0034]

[0035] Where n is the dimension of the target state space; is the weight coefficient of the Sigma point covariance in the UKF filtering process; is the Sigma point predicted by the measurement model at time k; Predict state values 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] Extract the adaptive matrix Λ k Elements on the diagonal Calculate the second error factor corresponding to each measurement dimension i

[0037]

[0038] Among them, λ max and λ min are respectively the upper and lower limits of the preset second error factor.

[0039] Preferably, the correction factor is determined according to the first error factor and the second error factor, and the measurement noise matrix in the Kalman filter time update link is corrected as follows:

[0040] The measurement noise covariance matrix R k The correction method is:

[0041]

[0042] Where R k is the measurement noise covariance matrix before correction, is the corrected measurement noise covariance matrix; U k is the correction factor matrix; the subscript k represents the kth moment;

[0043] Correction factor matrix is the correction factor for different measurement dimensions i A diagonal matrix composed of i=1,…,2n s ;

[0044] Correction Factor The determination method is: use fuzzy controller to construct the first error factor, the second error factor and the correction factor According to the first error factor and the second error factor of the measurement dimension i, the fuzzy controller is input to obtain the correction factor of the measurement dimension i

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

[0046] Assume that the membership functions of the first error factor and the second error factor are both triangular functions defined in the range [0,1], and the correction factor The membership function of is a triangular function defined within a set range;

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

[0048] The fuzzy controller rules of the fuzzy controller are:

[0049]

[0050]

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

[0052] Beneficial effects:

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

[0054] (2) The satellite configuration weights and the new information orthogonal weights are used to judge the quality of satellite measurement accuracy, and the measurement noise covariance matrix R is adaptively adjusted to dynamically adjust the impact of the measurement value on the estimation result, thereby improving the tracking accuracy of the space-based satellite on the target.

[0055] (3) In a preferred embodiment, the satellite configuration weights and the new information orthogonal weights are converted into correction factors through a fuzzy controller. On the basis of realizing the adaptive correction of the measurement noise covariance matrix, excessive adjustment of the noise matrix by extreme weights is avoided, thereby improving the filtering accuracy and ensuring the smoothness of the filtering process.

[0056] (4) The degree of mismatch between the prediction model and the actual target motion is determined through target maneuver detection, the maneuver frequency of the prediction model is dynamically estimated, and the process noise covariance matrix is adaptively adjusted based on the maneuver frequency, thereby dynamically adjusting the impact of the prediction value on the estimation result and improving the tracking accuracy of the space-based satellite on the target. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0058] Figure 2 Schematic diagram of the angle between the binary star and the target. DETAILED DESCRIPTION

[0059] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0060] Considering that the target tracking model and sensor measurement model in the tracking scenario of the present invention are both nonlinear models, traditional Kalman filtering methods based on linear systems are difficult to apply. The extended Kalman filtering method requires solving the Jacobian matrix of the model, which is computationally intensive. Therefore, this embodiment uses the unscented Kalman filter with higher theoretical accuracy to process the measurement data. At the same time, considering the problems of target maneuvering 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] The present invention's space-based adaptive filtering method for near-space flying targets uses non-cooperative near-space gliding targets as research objects. Multiple space-based satellites are used to detect and track these targets, and an unscented Kalman filter (UKF) is used to filter the measurement data to obtain an estimate of the target state. Taking into account the poor accuracy of satellite measurement, combined with satellite detection characteristics and the orthogonal optimization principle of Kalman filtering innovations, the process noise covariance matrix and the measurement noise covariance matrix are adaptively adjusted during the filtering process to improve the accuracy of the target state estimate. The specific process is shown in the figure below:

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

[0063] 1. Target motion prediction model

[0064] In order to effectively reduce the impact of the earth's curvature on tracking accuracy, the Earth Central Earth Fixed (ECEF) coordinate system is used as the reference coordinate system to construct a near-space flight target motion prediction model:

[0065]

[0066] Where X is the target 9×1 dimensional state vector, that is, 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 are the position and velocity vector of the target in the ECEF coordinate system. g=[g x g y g z ] T and a A =[A x A y A z ] T are the components of the acceleration due to gravity in the three directions of the ECEF coordinate system. u=[u D u T u C ] T They represent the drag parameter, turning force parameter and climbing force parameter of the aircraft in the semi-speed coordinate system respectively. D ,λ T ,λ C are the maneuvering frequencies of the three aerodynamic parameters, ω D 、ω T 、ω C are the noises of the three aerodynamic parameters, all of which obey zero-mean Gaussian distribution. The aerodynamic acceleration of the aircraft can be modeled in the semi-velocity coordinate system (Velocity-Turn-Climb, VTC) as follows:

[0067]

[0068] Where m is the mass of the aircraft; S is the characteristic area of the aircraft; ρ is the atmospheric density at the aircraft's location, which is related to the altitude; is the target speed; C L , CD 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] Convert the aerodynamic acceleration in the upper half velocity coordinate system to the ECEF coordinate system:

[0070]

[0071] Where, is the transformation matrix from the VTC to the ECEF coordinate system, which can be calculated from the target position and velocity vector.

[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 They represent the drag parameter, turning force parameter and climbing force parameter of the aircraft in the semi-speed coordinate system respectively. L , C D 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. The above three parameters correspond to the first-order Markov process in equation (1).

[0075] 2. Satellite sensor measurement model

[0076] Measurements from space-based satellites include azimuth angle θ s and the elevation angle γ s With two field of view angles, it is difficult for a single satellite to describe the exact position of the target, and at least two satellites are needed to track and locate the target. The corresponding measurement model Z s for:

[0077]

[0078] Where n s represents the number of satellite sensors, H s (X) represents n s The measurement equation corresponding to the satellite measurement, V s is a column vector composed of multiple satellite measurement noises. The relationship between the satellite field of view angle and the three-dimensional coordinates in the satellite body coordinate system can be expressed as:

[0079]

[0080] Among them, θ si and γ siare the azimuth and altitude measurements of the i-th satellite, x si 、y si 、z si 、v si,θ 、v si,γ Represents the position and velocity components of the i-th satellite in the body coordinate system.

[0081] Step 2: Use the unscented Kalman filter method to filter the measurement. 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 for UKF filtering, and P is the error covariance matrix for UKF filtering.

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

[0085]

[0086] Where w m and w c Represent the weight coefficients of 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 point and the sigma point, α∈[0,1], κ=3-n; β can be used to adjust the approximate accuracy of the covariance. For Gaussian distribution, β=2 is usually selected. and Represents the weight coefficient of the state mean and covariance of the first Sigma point. and The weight coefficients representing the state mean and covariance of the 2nd to 2n+1th Sigma points. The unscented Kalman filter involves 2n+1 Sigma points.

[0087] 1. One-step prediction

[0088] 1) Calculate the Sigma point based on the state estimate at the previous moment:

[0089]

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

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

[0092]

[0093] Where, and P k|k-1 are the state prediction value and its error covariance matrix, F k-1 (·) represents the state transition function, Q k-1 is the process noise covariance matrix, which is 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 Represents the 2n+1 Sigma points obtained from the state prediction vector.

[0098] 2) Calculate and measure the new information and its covariance based on Sigma points

[0099]

[0100]

[0101] Where, and P zz,k|k-1 Respectively represent the projection of the state prediction value and the state error covariance matrix in the measurement space, H k (·) is the measurement transfer function, R k is the measurement noise covariance matrix, which is used to represent the measurement uncertainty.

[0102] 3) Calculate Kalman gain and current state estimation

[0103]

[0104] Among them, P xz,k|k-1 is the cross-covariance matrix between the target state prediction value and the measured value, K k is the Kalman gain, P k is the error covariance matrix of the state estimate at time k.

[0105] Step 3: Adaptive correction of noise covariance matrix

[0106] On the basis of the above conventional UKF filtering, the measurement noise covariance matrix R k and 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 of the satellite networking system for target positioning based on the networking geometry of the satellite networking system, and determines the second error factor of the satellite networking system measurement model based on the new information; determines the correction factor based on the first error factor and the second error factor, and corrects the measurement noise covariance matrix in the Kalman filter time update link.

[0109] The specific implementation process is as follows:

[0110] The measurement noise covariance matrix R is known k is a diagonal matrix composed of the measurement noise covariance, assuming there are n s Satellites detect the target, and the noise covariance matrix is expressed in the form of

[0111]

[0112] Among them, σ θi and σ γ1 are the standard deviations of the azimuth and elevation angle measurements of the i-th satellite, respectively.

[0113] According to the following weight matrix R k Perform fuzzy adaptive adjustment

[0114] 1) The first error factor - satellite geometry weight c 1,k

[0115] For a multi-satellite network detection system, the detection accuracy of the target is not only affected by the field of view error of the satellite sensor, but also related to the geometric configuration between the satellites. Two cases are discussed:

[0116] The first case: when the number of satellites n s =2, using the binary star line of sight angle α ts Determine the satellite geometry weight; the binary star line of sight angle α ts The closer it is to 90°, the better the network geometry is and the smaller the first error factor is.

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

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

[0119]

[0120] Where, is the position relationship vector between the target and satellite i, is the position vector of the target in the ECEF coordinate system, is the position vector of the i-th satellite in the ECEF coordinate system. Since the true position of the non-cooperative target is unknown, the coarse positioning estimate obtained by the least squares method based on the dual-satellite measurement is used as an approximate substitute.

[0121] Easy to get α ts ∈(0°,180°), according to the satellite detection characteristics, the closer the binary star line of sight angle is to 90°, the better the geometric configuration is and the smaller the positioning error is; conversely, when the angle is closer to 0° or 180°, the error amplification effect is more significant. Construct the weights that describe the binary star geometric configuration, that is,

[0122]

[0123] The second case: For the s Satellite networking system with n satellites, s >2, using n s The geometric dilution of precision of the satellite GDOP Determine the first error factor; geometric dilution of precision I GDOP The smaller it is, the higher the satellite network positioning accuracy is and the smaller the first error factor is.

[0124] Specifically, when the number of satellites is greater than 2, the above weights are not applicable, and the Position Dilution of Precision (PDOP) can be used to describe the geometric configuration of the satellite. Position Dilution of Precision is a very important coefficient for measuring satellite positioning accuracy. According to relevant research on satellite positioning, for multi-satellite networking systems, the PDOP value is generally between 1 and 10. The smaller the PDOP value, the better the geometric distribution of the satellite networking system, and the smaller the impact on the target positioning accuracy. Conversely, the worse the geometric distribution of the satellite networking system, the greater the impact on the target positioning accuracy. The PDOP calculation formula is:

[0125]

[0126] Where tr(·) is the trace operation of the matrix, is the line-of-sight angle matrix of the satellite relative to the target; E i and A i are the altitude angle and azimuth angle of the i-th satellite relative to the target in the ECEF coordinate system. Since the target position is unknown, the result of least square positioning is used to approximate it:

[0127]

[0128] Where, Indicates the relative distance between the satellite and the target.

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

[0130]

[0131] Where, I PDOP The extreme value I min and I max Can be set to 2 and 8 respectively.

[0132] 2) Second error factor - innovation orthogonal weight

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

[0134]

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

[0136]

[0137] Where C k is the theoretical covariance matrix, which is unknown in actual calculation and can be estimated by formula (27)

[0138]

[0139] Where κ is the forgetting factor, which is usually 0.95. ε1 is the filtering innovation vector at the initial moment, ε k is the filtered innovation vector at time k.

[0140] In addition, P zz,k|k-1 is the actual innovation covariance matrix in the UKF filtering process, and its expression is:

[0141]

[0142] Where, is the weight coefficient of the Sigma point covariance in the UKF filtering process, which is calculated by formula (7); n is the dimension of the target state space. From formula (1), it can be seen that n = 9 in this embodiment; is the Sigma point predicted by the measurement model at time k; Predict state values for the target The specific calculation of the projection in the measurement model is shown in formula (12).

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

[0144]

[0145] When the measurement model is inaccurate, the sufficient condition for innovation orthogonality is not completely established. It is considered that the matrix R describing the measurement noise characteristics k Inaccurate, assume that it is multiplied by an adaptive diagonal matrix on the left So that the new information orthogonality condition is established, formula (26) becomes

[0146]

[0147] Convert it as follows

[0148]

[0149]

[0150] Considering the matrix R k Correction means correcting its diagonal elements, so the adaptive diagonal matrix Λ k It can be obtained by the following formula

[0151]

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

[0153] Considering the adaptive matrix Λ obtained by formula (33) k The fluctuation is large due to the influence of the error factor of the new information covariance estimation. If we directly use the R k It is difficult to ensure the stability and non-negative definiteness of the corrected result, so the present invention uses the adaptive matrix Λ k Elements on the diagonal As the influence matrix R k The final correction result is processed by a weight, and the specific method is to extract the adaptive matrix Λ k Elements on the diagonal Calculate the new information orthogonal weight corresponding to each measurement dimension i through the utility function method

[0154]

[0155] Where λ max and λ min are the upper and lower limits of the pre-set innovation orthogonal weights respectively.

[0156] 3) Fuzzy correction factor

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

[0158]

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

[0160] The correction factor The satellite geometry weight c obtained from steps 1) and 2) above 1,k Orthogonal weights to innovation The combination can be obtained by weighting or mapping.

[0161] In this preferred embodiment, a fuzzy controller is used to realize the satellite geometry weight c 1,k Orthogonal weights to innovation The fuzzy correction factor is calculated. Among them, the fuzzy controller is used to construct the satellite geometric configuration weight, the new information orthogonal weight and the correction factor The fuzzy relationship between them; when the satellite geometry weight c is known 1,k Orthogonal weights to innovation Input the fuzzy controller to obtain the correction factor

[0162] The fuzzy controller is set as follows: Set c 1,k and The membership functions of are all triangular functions defined in the range [0,1]. The membership function is defined as [μ min ,μ max ] within the range of triangular functions. The fuzzy set of the fuzzy controller is defined as {VS, S, M, B, VB}, which represent the correction factors 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 it is to 1, the worse the satellite geometry is, and the greater the possibility of deterioration in target detection accuracy. It is necessary to increase the matrix R kTo reduce the Kalman gain, thereby reducing the impact of measurement on the estimation result; similarly, when The closer it is to 1, the larger the error of the measurement dimension is, and the greater the need for correction. On the contrary, when c 1,k and The closer it is to 0, the higher the accuracy of satellite measurement is, and there is no need to adjust the matrix R. k Make corrections.

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

[0167] According to the first-order Markov assumption of the target aerodynamic acceleration related parameters in step 1, the expression of the process noise covariance matrix is:

[0168]

[0169] Where,

[0170]

[0171] In the formula, the subscripts D, T, and C represent the three aerodynamic acceleration directions of drag acceleration, turning force acceleration, and climbing force acceleration respectively. D,k-1 ,q T,k-1 ,q C,k-1 The noise covariance matrix Q in the three aerodynamic acceleration directions is represented by k-1 The diagonal elements in , is the variance of the three aerodynamic acceleration related parameters, λ D,k-1 ,λ T,k-1 ,λ C,k-1 is the maneuvering frequency in the three directions of D, T, and C, and k-1 represents the target state from the k-1 moment to the target state in the filtering process at the k-1 moment. Prediction at the kth moment In the process of , the process noise covariance matrix at the k-1th moment is used, as shown in formula (10).

[0172] Normalize the distance d with the filtered innovation k As a maneuver detection variable, d k The expression is

[0173]

[0174] Since the new information follows a Gaussian distribution, the detection variable follows a degree of freedom of 2n s χ 2 distribution, i.e. d k ~χ 2 (2n s ), 2n sis the dimension of the measurement vector. Define the probability of false alarm as p0, and the corresponding threshold value as δd, then

[0175] P{d k >δd}=p0 (39)

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

[0177]

[0178] in, and are the estimated values of maneuvering frequency at time k and time k-1 respectively. In order to avoid repeated filtering at the current moment and thus save computing power, considering that the maneuvering characteristics of the target will not change significantly in the short term during the movement, the estimated maneuvering frequency Substitute the process noise covariance matrix Q at the next moment k It is corrected in , and then filtered. That is, formula (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, making the filter more trustworthy in the measurement and reducing the impact of the model mismatch error on the estimation result. k When it is less than δd, it is considered that the target does not maneuver, and the matrix Q k No correction is made and conventional filtering is performed.

[0181] The target motion model in the above step 1 can be replaced by the Singer model or the current statistical model in addition to the dynamic model specially established for near-space gliding targets.

[0182] The filtering method in the above step 2 can be replaced by EKF or CKF filtering methods in addition to UKF.

[0183] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A space-based adaptive filtering method for near-space flight targets, characterized in that: include: The satellite network system composed of multiple space-based satellites is used to detect and track nearby space targets, and the Kalman filter is used to filter the measurement data to obtain the target state estimation; The maneuvering frequency of the process noise covariance matrix in the one-step prediction link of the Kalman filter is corrected according to the maneuvering frequency estimation; Determine a first error factor of the satellite networking system for target positioning according to the network geometry of the satellite networking system, and determine a second error factor of the satellite networking system measurement model according to the new information; A correction factor is determined according to the first error factor and the second error factor, and the measurement noise covariance matrix in the Kalman filter time update link is corrected.

2. The method according to claim 1, wherein The maneuvering frequency of the process noise covariance matrix in the one-step prediction link of the Kalman filter is corrected according to the maneuvering frequency estimation as follows: Normalize the distance d with the filtered innovation k as a maneuver detection variable; If the normalized distance of the filtered innovation d k If the probability of false alarm is greater than the threshold value δd, it is considered that the target is maneuvering and the prediction error increases. Then the maneuvering frequency is estimated and substituted into the process noise covariance matrix Q at the next moment. k In the process, the maneuvering frequency is corrected and then filtered; If the normalized distance of the filtered innovation d k If it is not greater than, then the process noise covariance matrix Q is not correct. k Make corrections.

3. The method according to claim 2, wherein The estimated maneuvering frequency is: Normalize the distance d using filtered innovation k , use the following formula to estimate the maneuvering frequency at time k, in, and are the estimated values of maneuvering frequency at time k and time k-1 respectively; D, T, and C represent the three dimensions of drag, turning force, and climbing force respectively.

4. The method according to claim 1, wherein The first error factor for determining the target positioning by the satellite networking system according to the networking geometry of the satellite networking system is: For a satellite networking system consisting of two satellites, the line-of-sight angle α between the two satellites is used. ts Determine the first error factor; the binary star line-of-sight angle α ts The closer it is to 90°, the better the network geometry is and the smaller the first error factor is.

5. The method according to claim 4, wherein The method uses the binary star line of sight angle α ts Determine the first error factor as: Among them, c 1,k is the first error factor at time k.

6. The method according to claim 1, wherein The first error factor for determining the target positioning by the satellite networking system according to the networking geometry of the satellite networking system is: For n s Satellite networking system with n satellites, s >2, using n s The geometric dilution of precision of the satellite PDOP Determine the first error factor; geometric dilution of precision I PDOP The smaller it is, the higher the satellite network positioning accuracy is and the smaller the first error factor is.

7. The method according to claim 6, wherein The geometric dilution of precision I of m satellites is used PDOP Determine the first error factor as: Among them, c 1,k is the first error factor at time k; I min and I max For I PDOP The set extreme value.

8. The method according to claim 1, wherein The second error factor of the satellite networking system measurement model determined according to the new information is: Determine the theoretical covariance matrix estimate of the innovation Kalman filtering uses unscented Kalman filtering to construct the measurement noise covariance matrix R k Adaptive matrix for: Where n is the dimension of the target state space; is the weight coefficient of the Sigma point covariance in the UKF filtering process; is the Sigma point predicted by the measurement model at time k; Predict state values 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; Extract the adaptive matrix Λ k Elements on the diagonal Calculate the second error factor corresponding to each measurement dimension i Among them, λ max and λ min are respectively the upper and lower limits of the preset second error factor.

9. The method according to claim 1, wherein The correction factor is determined based on the first error factor and the second error factor, and the measurement noise matrix in the Kalman filter time update link is corrected as follows: The measurement noise covariance matrix R k The correction method is: Where R k is the measurement noise covariance matrix before correction, is the corrected measurement noise covariance matrix; U k is the correction factor matrix; The subscript k indicates the kth moment; Correction factor matrix is the correction factor for different measurement dimensions i A diagonal matrix composed of i=1,…,2n s ; Correction Factor The determination method is: use fuzzy controller to construct the first error factor, the second error factor and the correction factor The ambiguous relationship between According to the first error factor and the second error factor of measurement dimension i, the fuzzy controller is input to obtain the correction factor of measurement dimension i 10. The method according to claim 9, wherein The fuzzy controller is set up as follows: Assume that the membership functions of the first error factor and the second error factor are both triangular functions defined in the range [0,1], and the correction factor The membership function of is a triangular function defined within a set range; The fuzzy sets of the fuzzy controller are {VS, S, M, B, VB}, which represent very small, small, medium, large, and very large respectively; The fuzzy controller rules of the fuzzy controller are: Among them, c 1,k represents the first error factor at time k, Represents the second error factor of the measurement dimension i at time k.

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