A Linear Sequential Radar Target Tracking Method Based on an Adaptive Measurement Matrix

Abstract

The present invention belongs to the field of phased array radar target tracking, and particularly relates to a target tracking system and method containing Doppler measurement information. The present invention proposes a linear sequential radar target tracking method based on an adaptive measurement matrix (DH-ALSF). This method constructs a linear measurement matrix containing a controllable parameter λ, estimates the elements in the matrix using the result of position filtering, selects the value of λ based on the idea of maximizing information, and on this basis, simultaneously considers the estimation error introduced by the above use of the estimation result. The introduced estimation error is combined with the original error to form a new error, and the statistical characteristics of the new error are calculated. Then, sequential filtering is performed on the decorrelated pseudo-measurements to obtain the corresponding sequential filtering estimation result. Finally, adaptive information feedback is performed for the corresponding scenario to obtain the final target state estimation result. The present invention can obtain better tracking performance than similar algorithms in different noise scenarios of different sizes.

Description

Technical Field

[0001] The present invention belongs to the field of phased array radar target tracking, and particularly relates to a target tracking system and method containing Doppler measurement information. Background Art

[0002] In the field of radar target tracking, the motion state equation of a target is generally established in a rectangular coordinate system, and its state vector is mainly composed of parameters such as the position, velocity, and acceleration of the target. The measurement information is generally obtained in a polar coordinate system or a spherical coordinate system and is mainly composed of parameters such as slant range, azimuth angle, and elevation angle. In the vast majority of tracking scenarios, the target and the observer are in different coordinate systems. Therefore, the relationship between the target measurement and the motion state is non-linear. Thus, the target tracking problem based on measurement information in the polar coordinate system or the spherical coordinate system is a non-linear estimation problem. To solve such non-linear filtering estimation problems, the simplest method is to use the traditional measurement conversion method (Measurement Conversion) to convert the measurement information obtained from the polar coordinate system or the spherical coordinate system into the Cartesian coordinate system, so that the target state and the measurement are linearly related. However, in the case of a long-distance target and a large measurement angle error, the traditional measurement conversion method will generate a large conversion deviation.

[0003] To eliminate the conversion bias, many scholars have proposed a series of improved measurement conversion methods: Lerro D et al. proposed an additive debiased measurement conversion method (DCM) (D. Lerro and Y. Bar-Shalom, "Tracking with debiased consistent converted measurements versus EKF," in IEEE Transactions on Aerospace and Electronic Systems, vol. 29, no. 3, pp. 1015-1022, July 1993.), which uses the traditional converted measurement value minus the bias mean to remove the conversion error. This method has good debiasing effect and measurement conversion consistency when the angular measurement error is small; Mo L. et al. proposed an unbiased measurement conversion method (UCM) (Mo Longbin, Song Xiaoquan, Zhou Yiyu, Sun Zhong Kang and Y. Bar-Shalom, "Unbiased converted measurements for tracking," in IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 3, pp. 1023-1027, July 1998.). This method uses a multiplicative compensation method to remove the bias, which makes up for the defects of the traditional conversion method to a certain extent, but there are compatibility problems when calculating the mean and covariance of the measurement conversion error; on this basis, the modified unbiased measurement conversion method (MUCM) (Z. Duan, C. Han, and X. R. Li, “Comments on” unbiased converted measurements for tracking, IEEE Trans. On Aerospace and Electronic Systems, vol. 40, no. 4, pp. 1374-1377, Oct. 2004.) solves the compatibility problem of UCM under the condition of ensuring unbiased measurement conversion error, but when deriving the measurement error covariance matrix, MUCM is carried out under the condition that the measurement value is known, which will lead to a certain correlation between the measurement error covariance and the measurement value, resulting in the bias of state estimation.Related scholars who have conducted further research on this have proposed the decorrelated unbiased measurement conversion method (DUCM) (Steven V. Bordonaro, Peter Willett, Yaakov Bar-Shalom, "Tracking with converted position and Doppler measurements," Proc. SPIE 8137, Signal and Data Processing of Small Targets 2011.). By calculating the statistical characteristics of the conversion error based on the predicted values, the problems existing in the above algorithms are solved.

[0004] In the field of target tracking, Doppler radar can not only obtain position measurement information but also provide Doppler measurement information. Theoretical and practical proofs have shown that the introduction of Doppler measurement can more effectively improve the tracking accuracy of targets (Farina A, Studer FA. Radar data processing I-Introduction and Tracking[J]. Memorie Della Societa Astronomica Italiana, 1985, 56.). However, at this time, it is necessary to solve the strong non-linear relationship with the target motion state caused by the introduction of Doppler measurement (Zhansheng Duan, Chongzhao Han and X. Rong Li, Sequential Nonlinear Tracking Filter with Range-rate Measurements in Spherical Coordinates, 7th International Conference on Information Fusion, Stockholm, 2004, 131-138.). The product of the slant range and the Doppler measurement is constructed as a pseudo-measurement, and the pseudo-measurement information is introduced into the measurement conversion Kalman filter algorithm, which is then extended to a sequential filtering tracking algorithm.

[0005] To make full use of Doppler measurement information, several methods have been proposed: The Debiased consistent converted measurements kalman filter with range rate (RCMKF-D) (X.R. Li, Z.S. Duan, and C.Z. Han. Sequential nonlinear tracking filter with range-rate measurements in spherical coordinates. In Proceedings of the 7th International Conference on Information Fusion, (4):599–605, 6 2004.) generalizes the DCM algorithm to handle Doppler measurements, and uses Doppler measurement information to perform sequential filtering on the filtering results based on position measurement information. Among them, the second-order extended Kalman filter is used to obtain the final filtering result. However, the nonlinear error in sequential filtering will accumulate iteratively as the filtering progresses, affecting the filtering effect; The Best Linear Unbiased Estimation with Pseudo Measurement (BLUEPM) applies the best linear unbiased estimation algorithm to the filtering algorithm that processes Doppler pseudo measurements; The Sequential linear filtering with adaptive information feedback (ASLF) (Cheng T, Li L. Sequential linear filtering with non-linear position and Doppler measurements for target tracking IET Radar, Sonar and Navigation, Volume 16, Issue 4, Pages 646-658, April 2022) uses the filtering results of position measurement information to perform linear sequential filtering on Doppler measurement information, and adaptively feeds back information on the state estimation results according to different noise scenarios. However, it is limited by the selection of a lower noise threshold, resulting in poor filtering performance.

[0006] To address the above problems, the present invention proposes a linear sequential radar target tracking method (DH-ALSF) based on an adaptive measurement matrix. This method constructs a linear measurement matrix containing a controllable parameter λ, estimates the elements in the matrix using the results of position filtering, selects the value of λ based on the idea of maximizing information, and on this basis, simultaneously considers the estimation error introduced by the above-mentioned use of the estimation results. This introduced estimation error is combined with the original error to form a new error, and the statistical characteristics of the new error are calculated. Then, sequential filtering is performed on the decorrelated pseudo-measurements to obtain the corresponding sequential filtering estimation results. Finally, adaptive information feedback is performed for the corresponding scenario to obtain the final target state estimation result. Summary of the Invention

[0007] Assume that the target state estimate at time k-1 is The corresponding estimation error covariance is P(k-1). The measurement information obtained by the phased array radar at time k includes the range measurement r m (k), the elevation angle θ m (k), the azimuth angle and the radial velocity measurement where the measurement noise and are zero-mean additive Gaussian white noises, and the standard deviations of the noises are σ r , σ θ , and The correlation coefficient between the range measurement and the radial velocity measurement error is ρ. The filtering steps of a linear sequential radar target tracking method based on an adaptive measurement matrix from time k-1 to time k are as follows:

[0008] Step 1: Construct pseudo-measurements using the radial velocity measurement and the range measurement.

[0009]

[0010] where η m (k) is the constructed pseudo-measurement, is the true value of the pseudo-measurement, is the measurement error of the pseudo-measurement.

[0011] Step 2: Perform unbiased measurement transformation and debiased measurement transformation correspondingly as follows.

[0012]

[0013] where Z uc (k) is the measurement vector after unbiased and debiased measurement transformation, x uc (k), y uc (k), z uc(k) is the position term after unbiased measurement conversion, η dc (k) is the pseudo-measurement term after bias-removed measurement conversion.

[0014] Step 3: Calculate the state prediction of the target at time k according to the following formula.

[0015]

[0016] where, is the predicted value obtained from the state estimation at time k - 1, F(k - 1) is the transition matrix at time k - 1, is the state estimation at time k - 1, G(k - 1) is the noise driving matrix, is the expected value of the process noise, x p (k), y p (k), z p (k) are the predicted positions in the x, y, and z directions respectively, are the predicted velocities in the x, y, and z directions respectively, are the predicted accelerations in the x, y, and z directions respectively.

[0017] The predicted estimation error covariance is expressed as:

[0018] P p (k) = F(k - 1)P(k - 1)F T (k - 1) + G(k - 1)Q(k - 1)G T (k - 1) (4)

[0019] where, (·) T is the transpose operation of the matrix, P p (k) is the predicted error covariance matrix obtained from the error covariance matrix at time k - 1, P(k - 1) is the state estimation error covariance matrix at time k - 1, Q(k - 1) is the process noise covariance matrix.

[0020] Step 4: Linear Kalman filtering based on position measurement information.

[0021]

[0022] K pos (k) = P p (k)[H pos (k)] T [S pos (k)] -1 (6)

[0023]

[0024] P pos (k) = [I - Kpos (k) H pos (k) ]P p (k) (8)

[0025] wherein, is the target state estimation result of position filtering at time k, P pos (k) is the covariance matrix of the target state estimation error of position filtering at time k, S pos (k) is the innovation covariance matrix of position filtering, K pos (k) is the Kalman gain in the process of position filtering, is the position measurement vector after unbiased measurement transformation, is the error covariance matrix of the position measurement vector after decorrelated unbiased measurement transformation, H pos (k) is the linear measurement matrix between the target motion state vector and the position measurement, and the specific expression is as follows:

[0026]

[0027]

[0028]

[0029] where The specific expression forms of the elements in are as shown in the following formulas (12)-(17):

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] where, r p , θ p , are obtained from the predicted values in the Cartesian coordinate system, and for the sake of simplicity in derivation, the time k is omitted in the expression, where the prediction error variance is calculated from the Jacobian transformation matrix and the predicted estimation error covariance matrix P p (k) of the Cartesian coordinate system, and the prediction information therein can be obtained by the following method:

[0037] The predicted value of the distance and its variance:

[0038]

[0039]

[0040] Predicted value of azimuth angle and its variance:

[0041]

[0042]

[0043] Predicted value of pitch angle and its variance:

[0044]

[0045]

[0046] Predicted value of radial velocity and its variance:

[0047]

[0048]

[0049]

[0050] Step 5: Adaptively optimize the controllable parameter λ.

[0051]

[0052] where t h is the threshold for determining the way to select the value of λ. When the standard deviation of the angle measurement error is less than the threshold, the position information estimation result from Step 4 is accurate enough to be directly used in the sequential measurement matrix. When the standard deviation exceeds the threshold, the position information and velocity information estimation results from Step 4 need to be considered simultaneously; f(λ) is shown in the following formula (28):

[0053]

[0054] where each element is shown in the following formulas (29)-(31):

[0055] Position information extraction matrix Λ:

[0056] Λ = [1 0 0 1 0 0 1 0 0] T (29)

[0057] Adaptive measurement matrix considering position filtering estimation error in the linear sequential filtering of the present invention

[0058]

[0059] where L1 (k), L 2 (k), L 3 The specific expression of (k) is shown in Equation (56); is the position term in the position filtering target state estimation result, is the radial velocity term in the position filtering target state estimation result.

[0060] Consider the error covariance of the position estimation error:

[0061]

[0062] Among them, is the new error after considering the position filtering estimation error, is the original error of the pseudo-measurement term after decorrelation processing, e pos (k) is the new error introduced by considering the position filtering estimation error, and its expression is shown in Equation (32); The elements in Equation (31) are shown in the following Equations (33)-(35):

[0063]

[0064]

[0065]

[0066]

[0067] Among them, P in Equation (34) pos (k) each component is shown in Equation (43), and in Equation (33) and are shown in Equations (36) and (37) respectively

[0068]

[0069]

[0070] Among them, the prediction information in Equation (36) can be obtained through Equations (20)-(26).

[0071] Step 6: Linear sequential Kalman filtering based on decorrelation and bias removal pseudo-measurement.

[0072]

[0073]

[0074]

[0075]

[0076] Among them, and are the output results of the linear sequential Kalman filter at the current moment k, and S ε (k) is the innovation of the sequential filter and P pos (k) is the filtering result of the position filter at the current moment k, and their specific expressions are shown in Eqs. (42) and (43) respectively:

[0077]

[0078]

[0079]

[0080]

[0081] Among them is the corresponding measurement error, and its mean expression is shown in Eq. (35), and the specific expression of the statistical characteristics is shown in Eq. (31).

[0082] Step 7: Adaptive information feedback.

[0083]

[0084] Among them, is the feedback output of the target state estimation at moment k, and P(k) is the feedback output of the target state estimation error covariance matrix, which enters the next iteration loop as the filtering input for the next moment.

[0085] Principle of the invention

[0086] In the phased array radar target tracking method based on measurement conversion, after introducing the radial velocity measurement information, in order to reduce the nonlinear degree of joint processing, the radial velocity measurement and position measurement information are processed separately. Here, in order to weaken the strong nonlinear relationship between the radial velocity measurement and the target state, it is necessary to first construct a pseudo-measurement and perform measurement conversion on the corresponding measurement information. According to the conversion relationship between the spherical coordinate system and the Cartesian coordinate system, we can obtain:

[0087]

[0088]

[0089]

[0090]

[0091] Taking the expectation of the above formula, we can get:

[0092]

[0093] where r(k), θ(k), are the true distance, azimuth angle, elevation angle, and radial velocity of the target at time k, and σ r , σ θ , are the measurement errors of the target distance, azimuth angle, elevation angle, and radial velocity. It can be seen from Equation (51) that the original measurement conversion result is biased and needs to be debiased.

[0094] The present invention uses a multiplicative debiasing method for the position measurement vector and performs a subtractive debiasing process on the pseudo-measurement vector constructed for the radial velocity, thereby obtaining the measurement conversion result shown in Equation (2) in Step 2. Based on Equation (2), the following linear measurement equation can be obtained:

[0095] Z (u , d)c (k) = H η (k)X(k) + V (u , d)c (k) (52)

[0096] where V (u,d)c (k) is the corresponding unbiased and debiased measurement conversion error, and H η (k) is the measurement matrix, and its specific expression is as follows:

[0097]

[0098] First, calculate the statistical characteristics of the measurement conversion error. Here, its mean and covariance are calculated based on the target prediction information. The mean of the unbiased measurement conversion error based on the predicted value is:

[0099]

[0100] Calculate the covariance R uc (k) of the unbiased measurement conversion error based on the predicted value as shown in Equation (55) below:

[0101]

[0102] where in R uc (k) and the specific expressions of its elements are as in Equations (12)-(17), and the cross-term has a specific expression as in Equation (36), and the specific expression of the element is as in Equation (37).

[0103] Since the pseudo-measurement is constructed from range and radial velocity measurements, it is clearly cross-correlated with the position measurement. Therefore, there is a correlation between the position measurement transformation error and the pseudo-measurement error, which is shown in of Equation (55). For subsequent sequential filtering, it is necessary to decorrelate the position measurement and the pseudo-measurement as shown in Equation (56):

[0104] Construct

[0105]

[0106]

[0107] Multiply both sides of Equation (52) by B(k) on the left simultaneously to remove the correlation between the position measurement and the pseudo-measurement, and obtain Equation (58):

[0108]

[0109] where and ε ddc (k) are the decorrelated position measurement vector and pseudo-measurement vector respectively, H pos (k) and Hε(k) are the linear measurement matrices between the target state vector and the position measurement vector and the pseudo-measurement vector respectively, and are the decorrelated position measurement error vector and pseudo-measurement error respectively. The following Equation (59) calculates the error covariance after removing the correlation between the position measurement vector and the pseudo-measurement vector.

[0110] The unbiased measurement transformation after removing the correlation between the position and pseudo-measurement vectors is still zero-mean, and its covariance is shown as follows:

[0111]

[0112] where, is the same as in Equation (10), is the same as in Equation (33).

[0113] According to Equation (59), it can be seen that the correlation between the position measurement and the pseudo-measurement has been removed. Therefore, based on the upper part of Equation (58), a measurement equation based on the position measurement is formed, and Kalman filtering based on the position measurement can be performed, as shown in Step 4. Based on the lower part of Equation (58), a linear measurement equation based on the decorrelated pseudo-measurement is formed.

[0114] However, in the measurement matrix H ε (k) of Equation (53), the true values x(k), y(k), z(k) cannot be obtained. Therefore, the position terms and the velocity terms Estimation is carried out, and a parameter λ ∈ [0, 1] is introduced to obtain the measurement matrix As shown in Equation (30), considering the estimation error e pos (k) shown in Equation (32), and calculate the new error formed by this estimation error and the original error Statistical characteristics such as the mean and variance of

[0115]

[0116]

[0117] Among them, the specific expressions of the elements in Equation (61) are as shown in Equations (33)-(35) in Step 5. Then, the above formula is calculated to obtain Equation (31) in Step 5 and Equation (44) in Step 6.

[0118] So far, the debiasing process of the parametric measurement matrix has been completed. In order to make more full use of the position and velocity information, the selection of the parameter λ value is particularly important. The present invention will adopt the method of maximizing the information increment to determine the optimal parameter λ, so as to change the weights of the position information and the radial velocity information in the sequential measurement matrix. Therefore, an optimization problem as shown in Equation (62) is constructed.

[0119]

[0120] Among them, the elements of Equation (62) are as shown in Equations (29)-(31) in Step 5.

[0121] For the convenience of calculation, in Equation (33) is denoted as c 1 , in Equation (35) is denoted as c 2 , E{[e pos (k)] 2} in Equation (34) is denoted as aλ 2 + bλ + c, and at the same time, its position term information can be expressed as the following Equation (63) and denoted as mλ 2 + nλ + c 3 :

[0122]

[0123] Therefore, the objective function f(λ) in Step 5, that is, Equation (28), can be expressed as Equation (64):

[0124]

[0125] To obtain the maximum value of the objective function \(f(\lambda)\) in the interval \(\lambda\in[0,1]\), first solve for the extreme value by setting the first derivative function to zero, and compare it with the two endpoint values \(f(0)\) and \(f(1)\), so as to obtain the value of \(\lambda\) that maximizes \(f(\lambda)\) in the interval \([0,1]\).

[0126] Differentiate \(f(\lambda)\) with respect to the independent variable and set it to 0 to obtain Equation (65):

[0127]

[0128] Solve the equation in Equation (65) to get:

[0129]

[0130] where \(A\) 1 and \(A\) 2 are shown in the following equations (67) and (68) respectively:

[0131]

[0132] \(A\) 2 =(4nmb - 4n 2 a)(c + c 1 - c 2 ) - 4mc 3 b 2 + 4nbc 3 a (68)

[0133] The endpoint values of \(f(\lambda)\) are shown in Equations (69) and (70):

[0134]

[0135]

[0136] By comparing the extreme value \(f(\lambda\) 1，2 ) with the endpoint values \(f(0)\) and \(f(1)\), the optimal \(\lambda\) parameter value is obtained, as shown in the lower part of Equation (27) in Step 5.

[0137] Finally, perform adaptive information feedback on the state estimation result according to different noise scenarios, that is, under small noise measurement errors, the position estimation result is good and can be directly fed back; when the noise increases, sequential filtering improves the position estimation result, so the estimation result of sequential filtering is fed back, and its specific expression is shown in Step 7.

[0138] The present invention performs bias removal on the parametric measurement matrix in the linear sequential filtering process and optimizes the parameters by using the method of maximizing information gain as shown in Step 5, and finally adaptively estimates the state result by Step 7. And P(k) are continuously updated in state as inputs to the iterative loop. Description of the Drawings

[0139] Figure 1 For the RMSE performance comparison of the algorithm positions in Scenario 1;

[0140] Figure 2 For the RMSE performance comparison of the algorithm speeds in Scenario 1;

[0141] Figure 3 For the RMSE performance comparison of the algorithm positions in Scenario 2;

[0142] Figure 4 For the RMSE performance comparison of the algorithm speeds in Scenario 2;

[0143] Figure 5 For the RMSE performance comparison of the algorithm positions in Scenario 3;

[0144] Figure 6 For the RMSE performance comparison of the algorithm speeds in Scenario 3;

[0145] Figure 7 For the RMSE performance comparison of the algorithm positions in Scenario 4;

[0146] Figure 8 For the RMSE performance comparison of the algorithm speeds in Scenario 4. Detailed Implementation Manner

[0147] Consider a target in uniform linear motion in the scenario, with its initial position being (15 km, 15 km, 10 km), initial velocity being (100 m / s, 100 m / s, 0 m / s), the target motion duration being 100 s, the radar sampling period being 1 s, and the measured values of the target including radial distance, elevation angle, azimuth angle, and radial velocity measurement. Among them, the correlation coefficient ρ of the radial distance and radial velocity measurement errors is -0.5, and the threshold t h = 3°. In the present invention, it is assumed that each measurement noise is Gaussian zero-mean white noise, and its noise standard deviation is defined as shown in Table 1. The process noise is assumed to be Gaussian white noise, with its standard deviation being q = 0.01 m / s 2 . The number of Monte Carlo loops for the entire simulation is 500 times.

[0148] Table 1 Simulation Scenario Parameters

[0149]

[0150] The DH-ALSF method proposed by the present invention is used to achieve target tracking. At the same time, in order to illustrate the advantages of the algorithm of the present invention, its performance is compared with the debiased and decorrelated measurement conversion Kalman filter algorithm with radial velocity (RCMKF-D), the target tracking filter algorithm based on the best linear unbiased estimation that can handle Doppler pseudo-measurements (BLUEPM), and the adaptive information feedback linear sequential filter algorithm (ASLF). Among them, the adaptive feedback threshold of the ASLF algorithm is 0.5°. The following compares the tracking performance of the algorithms in terms of the root mean square error (RMSE) of position and velocity estimation.

[0151] Under four simulation scenarios, the position and velocity RMSE performance comparisons of the RCMKF-D algorithm, the BLUEPM algorithm, the ASLF algorithm and the DH-ALSF algorithm (the algorithm of this article) are as Figure 1-8 shown, where the position RMSE performance comparison is as Figure 1 , 3, 5, 7 shown, and the velocity RMSE performance comparison is as Figure 2 , 4, 6, 8 shown: In Scenario 1, through the simulation of the position and velocity RMSE, several algorithms can converge well to similar positions; in Simulation Scenario 2, the position and velocity RMSE performance comparisons of the three comparison algorithms and the DH-ALSF algorithm are as Figure 3 , 4 shown. All four algorithms finally converge, but the DH-ALSF algorithm of the present invention has the smallest RMSE in both the position and velocity terms, that is, the algorithm of the present invention has the best tracking performance in this scenario; in Simulation Scenario 3, the position and velocity RMSE performance comparisons of the three comparison algorithms and the DH-ALSF algorithm are as Figure 5 , 6 shown. The DH-ALSF algorithm of the present invention still has the smallest RMSE compared with the other three comparison algorithms, and the convergence effect and performance are better; in Simulation Scenario 4, the position and velocity RMSE performance comparisons of the three comparison algorithms and the DH-ALSF algorithm are as Figure 7 , 8 shown. In this scenario, both the RCMKF-D algorithm and the BLUEPM algorithm have diverged, and the ASLF algorithm converges to a higher position compared with the algorithm of the present invention. The tracking performance of the DH-ALSF algorithm of the present invention is still better in this scenario. Combining the experimental results with the foregoing, it can be concluded that in various different noise scenarios, the algorithm of the present invention has a smaller RMSE and better tracking performance compared with other algorithms.

Claims

1. A linear sequential radar target tracking method based on an adaptive measurement matrix, and the specific technical solution is as follows: Assume that the target state estimate at time k-1 is The corresponding estimated error covariance is P(k-1); the measurement information obtained by the phased array radar at time k includes the range measurement r m (k), the elevation angle θ m (k), the azimuth angle and the radial velocity measurement Among them, Measurement noise and are zero-mean additive Gaussian white noises, and the standard deviations of the noises are σ r , σ θ , and The correlation coefficient between the range measurement and the radial velocity measurement error is ρ; The filtering steps of a linear sequential radar target tracking method based on an adaptive measurement matrix from time k - 1 to time k are as follows: Step 1: Construct pseudo-measurements using radial velocity measurements and distance measurements; where η m (k) is the constructed pseudo-measurement, is the true value of the pseudo-measurement, is the measurement error of the pseudo-measurement; Step 2: Perform unbiased measurement conversion and debiased measurement conversion correspondingly in the following manner; where Z uc (k) is the measurement vector after unbiased and debiased measurement transformation, x uc (k), y uc (k), z uc (k) are the position terms after unbiased measurement transformation, and η dc (k) is the pseudo-measurement term after debiased measurement transformation; Step 3: Calculate the state prediction of the target at time k according to the following formula; Among them, is the predicted value obtained from the state estimation at time k - 1, F(k - 1) is the transition matrix at time k - 1, is the state estimation at time k - 1, G(k - 1) is the noise driving matrix, is the expected value of the process noise, x p (k), y p (k), z p (k) are the predicted positions in the x, y, and z directions respectively, are the predicted velocities in the x, y, and z directions respectively, are the predicted accelerations in the x, y, and z directions respectively; The predicted estimation error covariance is expressed as: P p P(k) = F(k - 1)P(k - 1)F T (k - 1)+G(k - 1)Q(k - 1)G T (k - 1) (4) where (·) T is the transpose operation of the matrix, and P p (k) is the predicted error covariance matrix obtained from the error covariance matrix at time k - 1, P(k - 1) is the state estimation error covariance matrix at time k - 1, and Q(k - 1) is the process noise covariance matrix; Step 4: Linear Kalman filtering based on position measurement information; K pos ψ(k)=P p ψ(k)[H pos (k)] T [S pos (k)] -1 (6) It should be noted that the symbol "ψ" in the above translation is used to replace the original text which may be an unclear or incorrect symbol in the source text. If there is a specific correct symbol, it should be used for accurate translation. Also, the meaning of this formula may need to be further understood and interpreted in the context of relevant patent content. P pos (k) = [I - K pos (k)H pos (k)]P p (k) (8) Among them, is the target state estimation result of position filtering at time k, and P pos (k) is the covariance matrix of the target state estimation error of position filtering at time k, and S pos (k) is the innovation covariance matrix of position filtering, and K pos (k) is the Kalman gain in the position filtering process. is the position measurement vector after unbiased measurement transformation. is the covariance matrix of the error of the position measurement vector after decorrelated unbiased measurement transformation, and H pos (k) is the linear measurement matrix between the target motion state vector and the position measurement, and the specific expression is as follows: Among them The specific expression forms of the elements are as shown in the following formulas (12)-(17): where r p , θ p , is obtained from the predicted values in the Cartesian coordinate system, and for the sake of simplicity in derivation, the time instant k is omitted in the expression, where the predicted error variance is calculated from the Jacobian transformation matrix and the predicted estimation error covariance matrix P p (k), and the prediction information therein can be obtained by the following method: The predicted value of the distance and its variance: The predicted value of the azimuth angle and its variance: The predicted value of the elevation angle and its variance: The predicted value of the radial velocity and its variance: Step 5: Adaptively optimize the controllable parameter λ; where t h is a threshold for determining the way to select the value of λ. When the standard deviation of the angular measurement error is less than the threshold, the position information estimation result from step 4 is accurate enough to be directly used in the sequential measurement matrix. When the standard deviation exceeds the threshold, the position information and the velocity information estimation results from step 4 need to be considered simultaneously; f(λ) is shown in the following formula (28): Among them, each element is shown in the following formulas (29)-(31): Position information extraction matrix Λ: Λ = [1 0 0 1 0 0 1 0 0] T (29) Adaptive Measurement Matrix Considering the Position Filtering Estimation Error in Linear Sequential Filtering Among them, is the position term in the position filtering target state estimation result, is the radial velocity term in the position filtering target state estimation result; Error covariance considering position estimation error: Among them, is the new error after considering the position filtering estimation error, is the original error of the pseudo-measurement item after decorrelation processing, e pos (k) is the new error introduced by considering the position filtering estimation error, and its expression is shown in Equation (32); the elements in Equation (31) are shown in the following Equations (33)-(35): Among them, P in formula (34) pos (k) each component is as shown in formula (43), in formula (33) and are respectively as shown in formulas (36) and (37) Among them, the predicted information in formula (36) can be obtained through formulas (20)-(26); Step 6: Linear sequential Kalman filtering based on decorrelated and debiased pseudo-measurements; Among them, and P ε (k) is the output result of the linear sequential Kalman filter at the current time k, and S ε (k) is the innovation covariance of the sequential filter, and Kε(k) is the Kalman gain of the sequential filter. and P pos (k) is the filtering result of the position filter at the current time k, and its specific expressions are shown in Eqs. (42) and (43) respectively: wherein is the corresponding measurement error, the mean expression of which is as shown in Equation (35), and the specific expression of the statistical characteristics is as shown in Equation (31); Step 7: Adaptive information feedback; Among them, is the feedback output of the target state estimation at time k, and P(k) is the feedback output of the target state estimation error covariance matrix, which enters the next iteration loop as the filtering input for the next moment.

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