Filtering-based scanning radiation source tracking method

Abstract

The invention discloses a scanning radiation source tracking method based on filtering, and the method comprises the steps: firstly, an observation station obtains a received pulse signal of a scanning radiation source, records the sampling time, carries out the beam fitting of the pulse signal through a beam fitting model, and estimates the interception time of a pulse signal peak value; secondly, estimating the scanning rate by using the peak time difference of the pulse signals intercepted by the observation stations for two adjacent times, and calculating the scanning angle difference based on the scanning time difference of different observation stations; and finally, performing extended Kalman tracking positioning by taking the scanning angle difference as an observation variable, and estimating and compensating the scanning angle difference by using a tracking result, thereby realizing joint estimation of the scanning radiation source position and the scanning rate. According to the method, the characteristics of the scanning radiation source and the influence of the relative motion relation between the observation station and the radiation source on the scanning angle difference are fully utilized, the scanning rate is corrected in combination with the EKF algorithm, and the tracking precision of the moving radiation source is improved.

Description

Technical Field

[0001] The invention relates to the technical field of passive positioning and tracking, and in particular to a scanning radiation source tracking method based on filtering. Background Art

[0002] Mechanical scanning radar radiation usually has a fixed scanning rate, with characteristics of narrow beam and high signal-to-noise ratio. For the passive positioning problem of scanning radiation sources, due to its narrow beam characteristics, it is impossible to ensure that multiple observation stations receive signals at the same time, so it is impossible to achieve positioning by measuring the main lobe signal TDOA or FDOA; TOA-based positioning methods are usually only applicable to radiation sources with fixed PRI characteristics; for non-cooperative scanning radiation sources, since the prior information such as the carrier frequency and modulation parameters of the transmitted signal cannot be accurately obtained, the FOA-based positioning method is also difficult to apply to the positioning of scanning radiation sources.

[0003] At present, the most in-depth research on scanning radiation sources is the positioning method based on DOA or main lobe signal intercept time (TOI). H.Hmam et al. solved the problem by using the geometric constraints introduced by the antenna main lobe when scanning multiple independent observation stations. On this basis, they further studied the joint estimation problem of scanning rate and scanning transmitter position and proposed a joint estimator based on nonlinear least squares (NLS). K. A closed pseudo-LS solution method is proposed in the N>3 scenario. The key is to introduce a rotation angle, use the receiving station position and the scanning angle difference to evaluate the rotation angle, and then use the rotation angle to calculate the AOA to achieve positioning solution. He You et al. proposed a maximum likelihood positioning method for the case where the scanning rate of a moving scanning radiation source is unknown. This method projects each time difference measurement into the target state space, and realizes the maximum likelihood estimation of the scanning rate and target state by correcting, iterating and fusing the target state.

[0004] Most existing methods consider that both the receiving station and the radiation source are stationary, ignoring the change in the interception time difference caused by the relative motion between the two, which in turn causes a deviation in the scanning angle difference and affects the tracking accuracy. Therefore, how to compensate for the scanning angle difference and improve the tracking accuracy of the moving scanning radiation source is a technical problem that needs to be solved in this field. Summary of the invention

[0005] The object of the present invention is to provide a scanning radiation source tracking method based on filtering, so as to improve the tracking accuracy of the scanning radiation source in motion.

[0006] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0007] A scanning radiation source tracking method based on filtering, comprising:

[0008] Firstly, the observation station obtains the pulse signal of the received scanning radiation source and records the sampling time, performs beam fitting on the pulse signal through the beam fitting model, and estimates the interception time of the pulse signal peak. Secondly, the scanning rate is estimated by using the time difference between the peak values ​​of the pulse signals intercepted twice adjacently by the observation station, and the scanning angle difference is calculated based on the scanning time difference of different observation stations. Finally, the extended Kalman tracking and positioning is performed with the scanning angle difference as the observation variable, and the scanning angle difference is estimated and compensated by the tracking result, thereby realizing the joint estimation of the scanning radiation source position and the scanning rate.

[0009] Furthermore, by sampling the parabola as the beam fitting model, the least square method is used to solve the parameters in the beam fitting model to obtain the parabola equation corresponding to the pulse signal, thereby determining the interception reception time corresponding to the peak value of the pulse signal.

[0010] Furthermore, the estimating the scanning rate by using the time difference between two adjacent peak values ​​of the pulse signal intercepted by the observation station includes:

[0011] The difference in interception and reception time corresponding to the peak values ​​of the pulse signals generated by two consecutive scans of the scanning radiation source intercepted by the observation station is taken as the estimated value T of the scanning period of the scanning radiation source. p ; That is, for two adjacent intercepted scanning signals, calculate the corresponding interception reception time and calculate the difference; then the scan rate estimate is: The estimated value T of the scanning period is obtained by using the relative motion relationship between the scanning radiation source and the observation station. p To compensate, that is:

[0012]

[0013] Where m is the number of scans of the scanning radiation source, are the estimated peak interception times of the pulse signals received for the mth and m-1th scans, respectively, c is the speed of light, and Δr is the distance change caused by the movement of the scanning radiation source, that is:

[0014]

[0015] where p i =[x,y], i≥2 is the location of observation station i, u i (m) = [x i (m),y i (m)]、u i (m-1)=[x i (m-1),y i(m-1)] are the x and y coordinate positions of the scanning radiation source when it is scanned for the mth and m-1th time by observation station i, respectively; ||·|| represents the Euclidean distance of the solution vector, δt is the error caused by scanning fluctuation and its noise, and Δβ is the angular change caused by the movement of the scanning radiation source.

[0016] Further, the calculating of the scanning angle difference based on the scanning time difference of different observation stations includes:

[0017] Estimated value based on compensated scan period Combined with the peak interception time estimated by the pulse signal received by different observation stations i and j during the mth scanning of the scanning radiation source Get the scanning time difference between different observation stations i and j The scanning angle difference between observation stations i and j is calculated using the following formula:

[0018]

[0019] Among them, tdoa=ΔR / c, ΔR=||p i -u i (m)||-||p j -u j (m)|| is the distance difference between the scanning radiation source and observation stations i and j, tdoa is the time difference caused by the distance difference, u j (m) is the coordinate position of the scanning radiation source when it is scanned by observation station j, p j is the coordinate position of observation station j.

[0020] Furthermore, the extended Kalman tracking and positioning is performed using the scanning angle difference as an observation variable, including:

[0021] The first step is to establish the model and define the state variables as:

[0022] X=[x,y,v,a,θ] T (10)

[0023] Among them, x, y are the position coordinates of the scanning radiation source, v is the velocity component of the scanning radiation source, a is the acceleration component of the scanning radiation source, and θ is the steering angle of the scanning radiation source;

[0024] Combined with the mapping relationship between the motion characteristics of the scanning radiation source and the scanning angle difference, the scanning angle difference is used to is the observed variable, and the observed variable is used as the nonlinear observation function h(x,y) of the radiation source position x,y, that is:

[0025]

[0026] In the above formula, (xi ,y i )、(x j ,y j ) are the position coordinates of observation stations i and j respectively;

[0027] Therefore, the observation model can be written as:

[0028] z k =h(X k )+λ k (12)

[0029] Where k represents the number of Kalman update iterations, z k is the observation model at the kth iteration, X k =[x k ,y k ,v k ,a k ,θ k ] T are the state variables x, y, v, a, θ of the scanning radiation source at the kth iteration; λ k Represents the observation noise error, which satisfies the zero-mean Gaussian distribution;

[0030] For each observation, the Jacobian matrix of the corresponding state variable needs to be calculated, that is:

[0031]

[0032] Further, the estimating and compensating the scanning angle difference by using the tracking result includes:

[0033] The state vector and covariance matrix are updated, and the state transfer equation is:

[0034]

[0035] Among them, X k-1 is the state vector of the scanning radiation source at the k-1th iteration, f(X k-1 ) is the state transfer matrix, that is:

[0036]

[0037] in is the peak interception time at the kth iteration and the peak intercept time at the k-1th iteration The difference, is the acceleration, is the steering speed, which is calculated by updating the result of each iteration;

[0038] is the state variable of the scanning radiation source predicted at the kth iteration, w k-1 is the process noise, which is assumed to be zero-mean Gaussian noise;

[0039] By calculating the Jacobian matrix F of the state vector of the state transfer function f() k To achieve linearization:

[0040]

[0041] According to the linearized Jacobian matrix, the covariance matrix of the state prediction error is predicted:

[0042] P k|k-1 =F k P k-1 F k H +Q k-1 (17)

[0043] Among them, P k|k-1 is the covariance matrix of the state prediction error of the kth iteration, P k-1 is the covariance matrix of the state prediction error of k-1 iterations, Q k-1 is the process noise covariance matrix, which can be expressed as in(·) H Indicates the conjugate transpose operation of the matrix;

[0044] The state estimate is updated using the measured value, namely:

[0045]

[0046] Among them, X k is the state variable of the scanning radiation source at the kth iteration, is the predicted value of the kth iteration

[0047] The state variable of the scanning radiation source, z k is the observation model at the kth iteration, h(X k|k-1 ) is the state variable^

[0048] X k|k-1 The predicted observation value calculated by the nonlinear observation function, K k is the Kalman gain, which is used to balance the weights between the predicted value and the measured value. It is calculated as follows:

[0049]

[0050] Among them, P k|k-1 is the covariance matrix of the state prediction error predicted at the kth iteration, H k is the Jacobian matrix of the state variables, R kis the covariance matrix of the observation noise, that is

[0051] The covariance matrix of the state prediction error is updated as:

[0052] P k =(IK k H k ) k|k-1 (20)

[0053] Here, I is the unit matrix with all diagonal elements being 1 and all other elements being 0.

[0054] Furthermore, the joint estimation of the scanning radiation source position and the scanning rate includes:

[0055] Based on the state variable X of the scanning radiation source at the kth and k-1th iterations k and X k-1 , X k and X k-1 The position coordinates of the scanning radiation source in are respectively taken as u i (m),u i (m-1) is substituted into Equation 7 to calculate the k-th iteration Δr, and then the estimated value of the scan period after compensation is calculated based on Equation 6 use The scanning rate is estimated, and the scanning angle difference is calculated using Equation 9, which is used as the value of the nonlinear observation function of the k+1 iteration to calculate the state variable X of the scanning radiation source of the k+1 iteration. k+1 ; where X k+1 x in k+1 ,y k+1 That is, the position tracking result of the scanning radiation source. The scanning radiation source can be tracked through several consecutive iterations.

[0056] An observation station uses a scanning radiation source tracking method based on filtering to track a scanning radiation source.

[0057] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor is executed by a computer, the filtering-based scanning radiation source tracking method is implemented.

[0058] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the filtering-based scanning radiation source tracking method is implemented.

[0059] Compared with the prior art, the present invention has the following technical features:

[0060] The present invention makes full use of the characteristics of the scanning radiation source and the influence of the relative motion relationship between the observation station and the radiation source on the scanning angle difference, and corrects the scanning rate in combination with the EKF algorithm, thereby improving the tracking accuracy of the moving radiation source. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of the scene of scanning radiation source tracking when three observation stations are used;

[0062] Figure 2 is a method flow chart of an embodiment of the present invention;

[0063] Figure 3 (a) is the tracking effect of the example of the present invention when the scanning radiation source makes a maneuvering motion and its comparison with the least squares algorithm (LS); (b) is the tracking error of the example of the present invention and its LS algorithm when the scanning radiation source makes a maneuvering motion. DETAILED DESCRIPTION

[0064] The existing scanning radiation source tracking and positioning method is only suitable for static targets. For moving scanning radiation sources, there are problems of scanning angle deviation and poor tracking accuracy. Based on this, the present invention provides a scanning radiation source tracking method based on filtering. First, the observation station obtains the received pulse signal of the scanning radiation source and records the sampling time. By fitting the scanning radiation source beam, the interception time of the pulse signal peak is estimated; secondly, the scanning rate is estimated by using the peak time difference of the pulse signal intercepted twice by the observation station, and the scanning angle difference is calculated based on the scanning time difference of different observation stations; finally, the scanning angle difference is used as the observation variable to perform extended Kalman (EKF) tracking and positioning, and the scanning angle difference is estimated and compensated by the tracking result, so as to realize the joint accurate estimation of the scanning radiation source position and scanning rate, and improve the tracking accuracy.

[0065] See attached Figure 1 In this scheme, at least two stationary observation stations are set up. The antenna type of the observation station is an omnidirectional antenna. The scanning radiation source is in motion and performs circular scanning motion, and the scanning beam is a narrowband beam. The observation station intercepts the signal emitted by the scanning radiation source and measures the arrival time difference. It combines the scanning time difference of the two observation stations and the periodic characteristics of the scanning radiation source for analysis, and finally realizes the tracking of the moving scanning radiation source.

[0066] Step 1: The pulse signals generated by the scanning radiation source in motion during the circular scanning are captured by multiple observation stations of our side; for each observation station, it is recorded that the scanning radiation source captures N pulse signals each time the observation station scans, and the corresponding time information of the received pulse signals is t = [t1, t2, ..., t N ], the sampling parabola is used as the beam fitting model, and the expression is:

[0067] y(t)=at 2 +bt+c (1)

[0068] Wherein, y(t) represents the power value of the pulse signal received at time t, and a, b, and c are the coefficients of the beam model to be solved.

[0069] Therefore, for the pulse signals of N scanning radiation sources, the beam fitting solution equation can be expressed as:

[0070]

[0071] The equation can be simplified to:

[0072] Y=KX (3)

[0073] in,

[0074] In the above formula, y(t N ) indicates t N The beam fitting model corresponding to the time.

[0075] The least squares method is used to solve the parameter X = [a, b, c], and the result is:

[0076]

[0077] The superscript T represents the transpose operation. are the estimated values ​​of the parameters a, b, and c of the beam fitting model. Substituting them into equation 1 yields a parabolic equation. Therefore, the interception and reception time corresponding to the peak value of the pulse signal obtained by this scan can be estimated by the beam fitting model as follows:

[0078]

[0079] Step 2: For any observation station, the difference in interception reception time corresponding to the peak value of the pulse signal generated by two consecutive scans of the scanning radiation source intercepted by the observation station is used as the estimated value T of the scanning period of the scanning radiation source. p That is, for two adjacent intercepted scanning signals, the corresponding interception reception time is calculated using the method in step 1 respectively and calculate the difference; then the scan rate estimate is: However, due to the relative position relationship between the moving scanning radiation source and the stationary observation station, the angle covered by the time difference of the two intercepted pulse signals is not necessarily 2π, resulting in a deviation in the estimation of the scanning rate. Therefore, the estimated value of the scanning period T is calculated using the relative motion relationship between the scanning radiation source and the observation station. p To compensate, that is:

[0080]

[0081] Where m is the number of scans of the scanning radiation source, are the estimated peak interception times of the pulse signals received for the mth and m-1th scans, respectively, c is the speed of light, and Δr is the distance change caused by the movement of the scanning radiation source, that is:

[0082] Δr=||p i -u i (m)||-||p i -u i (m-1)|| (7)

[0083] where p i =[x,y], i≥2 is the location of observation station i, u i (m) = [x i (m),y i (m)]、u i (m-1)=[x i (m-1),y i (m-1)] are the x and y coordinate positions of the scanning radiation source when it is scanned by the observation station i for the mth and m-1th time, respectively; the coordinates in this scheme refer to the coordinates in the two-dimensional coordinate system established in the plane where the scanning radiation source is located; ||·|| represents the Euclidean distance of the solution vector, δt is the error caused by the scanning fluctuation and its noise, and Δβ is the angle change caused by the movement of the scanning radiation source, that is:

[0084]

[0085] Step 3, based on the estimated value of the scan period after compensation Combined with the peak interception time estimated by the pulse signal received by different observation stations i and j during the mth scanning of the scanning radiation source (m) Get the scanning time difference between different observation stations i and j The scanning angle difference between observation stations i and j is calculated using the following formula:

[0086]

[0087] Among them, tdoa=ΔR / c, ΔR=||p i -u i (m)||-||p j -u j (m)|| is the distance difference between the scanning radiation source and observation stations i and j, tdoa is the time difference caused by the distance difference, u j (m) is the coordinate position of the scanning radiation source when it is scanned by observation station j, p j is the coordinate position of observation station j.

[0088] Step 4: Change the scanning angle difference As the observed variable, the EKF algorithm is used to predict and update the state variables of the scanning radiation source.

[0089] The first step is to establish the model and define the state variables as:

[0090] X=[x,y,v,a,θ] T (10)

[0091] Among them, x, y are the position coordinates of the scanning radiation source, v is the velocity component of the scanning radiation source, a is the acceleration component of the scanning radiation source, and θ is the steering angle of the scanning radiation source.

[0092] Combined with the mapping relationship between the motion characteristics of the scanning radiation source and the scanning angle difference, the scanning angle difference is used to is the observed variable, and the observed variable is used as the nonlinear observation function h(x,y) of the radiation source position x,y, that is:

[0093]

[0094] In the above formula, (x i ,y i )、(x j ,y j ) are the position coordinates of observation stations i and j respectively.

[0095] Therefore, the observation model can be written as:

[0096] z k =h(X k )+λ k (12)

[0097] Where k represents the number of Kalman update iterations, z k is the observation model at the kth iteration, X k =[x k ,y k ,v k ,a k ,θ k ] T are the state variables x, y, v, a, θ of the scanning radiation source at the kth iteration; λ k represents the observation noise error, which satisfies the zero-mean Gaussian distribution; where the nonlinear observation function h(X k ) is only related to the parameters (x,y), while the values ​​of v,a,θ can be calculated by estimating (x,y) twice in a row.

[0098] In the EKF algorithm, the Jacobian matrix of the observation function needs to be calculated for linearization. For each observation, the Jacobian matrix of the corresponding state variable needs to be calculated, that is:

[0099]

[0100] Step 5: Update the state vector and covariance matrix. The state transfer equation is:

[0101]

[0102] Among them, X k-1 is the state vector of the scanning radiation source at the k-1th iteration, f(X k-1 ) is the state transfer matrix, that is:

[0103]

[0104] in is the peak interception time at the kth iteration and the peak intercept time at the k-1th iteration The difference, is the acceleration, is the steering speed, which is calculated by updating the result of each iteration; is the state variable of the scanning radiation source predicted at the kth iteration, w k-1 is the process noise, which is assumed to be zero-mean Gaussian noise.

[0105] The purpose of covariance prediction is to estimate the covariance matrix of the system state prediction error, reflecting the uncertainty of the predicted state. Since the state transfer equation f() is nonlinear, it needs to be linearized in EKF; linearization is achieved by calculating the Jacobian matrix F of the state vector of the state transfer function f(). k accomplish:

[0106]

[0107] in, It means to take partial derivative of the state transfer equation.

[0108] According to the linearized Jacobian matrix, the covariance matrix of the state prediction error is predicted:

[0109] P k|k-1 =F k P k-1 F k H +Q k-1 (17)

[0110] Among them, P k|k-1is the covariance matrix of the state prediction error of the kth iteration, P k-1 is the covariance matrix of the state prediction error of k-1 iterations, Q k-1 is the process noise covariance matrix, which can be expressed as in(·) H It means to perform conjugate transpose operation on the matrix.

[0111] Step 6: Update the state estimate using the measured value, that is:

[0112]

[0113] Among them, X k is the state variable of the scanning radiation source at the kth iteration, is the state variable of the scanning radiation source predicted at the kth iteration, z k is the observation model at the kth iteration, is a state variable The predicted observation value calculated by the nonlinear observation function, K k is the Kalman gain, which is used to balance the weights between the predicted value and the measured value. It is calculated as follows:

[0114]

[0115] Among them, P k|k-1 is the covariance matrix of the state prediction error predicted at the kth iteration, H k is the Jacobian matrix of the state variables, R k is the covariance matrix of the observation noise, that is

[0116] The covariance matrix of the state prediction error is updated as:

[0117] P k =(IK k H k ) k|k -1 (20)

[0118] Here, I is the unit matrix with all diagonal elements being 1 and all other elements being 0.

[0119] Step 7: Repeat steps 4-6, based on the state variable X of the scanning radiation source at the kth and k-1th iterations. k and X k-1 , X k and X k-1 The position coordinates of the scanning radiation source in are respectively taken as u i (m),u i (m-1) is brought into

[0120] Equation 7 calculates the Δr of the kth iteration, and then the estimated value of the scan period after compensation is calculated based on Equation 6 use The scanning rate is estimated, and the scanning angle difference is calculated using Equation 9, which is used as the value of the nonlinear observation function of the k+1 iteration to calculate the state variable X of the scanning radiation source of the k+1 iteration. k+1 ; where X k+1 x in k+1 ,y k+1 That is, the position tracking result of the scanning radiation source. The scanning radiation source can be tracked through several consecutive iterations.

[0121] Example:

[0122] See attached Figure 1 In one embodiment of the present invention, the positioning scenario of the scanning radiation source is established as follows Figure 1 As shown, the number of observation stations is 3, and the coordinate positions are [6×10 4 ,6×10 4 ], [5.7×10 4 ,5.4×10 4 ], [6.4×10 4 ,6.7×10 4 ], the simulated scanning radiation source trajectory has its starting position as [0, 0], the scanning radiation source performs maneuvering motion, the maximum speed does not exceed 10m / s, the maximum acceleration does not exceed 5m / s, and the maximum steering angular velocity does not exceed 50° / s.

[0123] In addition, the radiation source performs circular scanning motion, the scanning rate is set to 3s, the main lobe beam width is 5°, and the pulse repetition interval is set to 2000ns.

[0124] In a static scenario, the main lobe time that each observation station can receive is 5 / 360*3=0.0417s, and the number of pulses that can be received in a single scan is 20850 pulses. However, since the relative motion direction of the scanning radiation source and the observation station is consistent with the scanning direction, the number of received pulses varies. Assuming that a single scan passes through the observation station, the number of pulses received by the observation station is N.

[0125] The results of this example are as follows Figure 3 shown; through Figure 3 It can be seen that the method of the present invention has high tracking accuracy for the trajectory of the scanning radiation source and small tracking error.

[0126] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A scanning radiation source tracking method based on filtering, characterized in that: include: First, the observation station obtains the pulse signal of the received scanning radiation source and records the sampling time. The beam fitting model is used to perform beam fitting on the pulse signal and the interception time of the peak value of the pulse signal is estimated. Secondly, the scanning rate is estimated by using the time difference between the peak values ​​of the pulse signals intercepted twice by the observation station, and the scanning angle difference is calculated based on the scanning time difference of different observation stations; Finally, the extended Kalman tracking and positioning is performed with the scanning angle difference as the observation variable, and the tracking result is used to estimate and compensate the scanning angle difference, thereby realizing the joint estimation of the scanning radiation source position and the scanning rate.

2. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: By taking the sampling parabola as the beam fitting model and solving the parameters in the beam fitting model using the least square method, the parabola equation corresponding to the pulse signal is obtained, thereby determining the interception reception time corresponding to the peak value of the pulse signal.

3. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: The method of estimating the scanning rate by using the time difference between two consecutive peak values ​​of the pulse signal intercepted by the observation station includes: The difference in interception and reception time corresponding to the peak values ​​of the pulse signals generated by two consecutive scans of the scanning radiation source intercepted by the observation station is taken as the estimated value T of the scanning period of the scanning radiation source. p ; That is, for two adjacent intercepted scanning signals, calculate the corresponding interception reception time and calculate the difference; then the estimated scan rate is: The estimated value T of the scanning period is obtained by using the relative motion relationship between the scanning radiation source and the observation station. p To compensate, that is: Where m is the number of scans of the scanning radiation source, are the estimated peak interception times of the pulse signals received for the mth and m-1th scans, respectively, c is the speed of light, and Δr is the distance change caused by the movement of the scanning radiation source, that is: Δr=||p i -her i (m)||-||p i -her i (m-1)|| (7) where p i =[x,y], i≥2 is the location of observation station i, u i (m) = [x i (m),y i (m)]、u i (m-1)=[x i (m-1),y i (m-1)] are the x and y coordinate positions of the scanning radiation source when it is scanned by observation station i for the mth and m-1th times, respectively; ||·|| represents the Euclidean distance of the solution vector, δ t is the error caused by scanning fluctuation and its noise, and Δβ is the angle change caused by the movement of the scanning radiation source.

4. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: The calculating of the scanning angle difference based on the scanning time difference of different observation stations comprises: Estimated value based on compensated scan period Combined with the peak interception time estimated by the pulse signal received by different observation stations i and j during the mth scanning of the scanning radiation source Get the scanning time difference between different observation stations i and j The scanning angle difference between observation stations i and j is calculated using the following formula: Among them, tdoa=ΔR / c, ΔR=||p i -u i (m)||-||p j -u j (m)|| is the distance difference between the scanning radiation source and observation stations i and j, tdoa is the time difference caused by the distance difference, u j (m) is the coordinate position of the scanning radiation source when it is scanned by observation station j, p j is the coordinate position of observation station j.

5. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: The extended Kalman tracking and positioning is performed using the scanning angle difference as an observation variable, including: The first step is to establish the model and define the state variables as: X=[x,y,v,a,θ] T (10) Among them, x, y are the position coordinates of the scanning radiation source, v is the velocity component of the scanning radiation source, a is the acceleration component of the scanning radiation source, and θ is the steering angle of the scanning radiation source; Combined with the mapping relationship between the motion characteristics of the scanning radiation source and the scanning angle difference, the scanning angle difference is used to is the observed variable, and the observed variable is used as the nonlinear observation function h(x,y) of the radiation source position x,y, that is: In the above formula, (x i ,y i )、(x j ,y j ) are the position coordinates of observation stations i and j respectively; Therefore, the observation model can be written as: z k =h(X k )+λ k (12) Where k represents the number of Kalman update iterations, z k is the observation model at the kth iteration, X k =[x k ,y k ,v k ,a k ,θ k ] T are the state variables x, y, v, a, θ of the scanning radiation source at the kth iteration; λ k Represents the observation noise error, which satisfies the zero-mean Gaussian distribution; For each observation, the Jacobian matrix of the corresponding state variable needs to be calculated, that is:

6. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: The method of estimating and compensating the scanning angle difference by using the tracking result includes: The state vector and covariance matrix are updated, and the state transfer equation is: Among them, X k-1 is the state vector of the scanning radiation source at the k-1th iteration, f(X k-1 ) is the state transfer matrix, that is: in is the peak interception time at the kth iteration and the peak intercept time at the k-1th iteration The difference, is the acceleration, is the steering speed, which is calculated by updating the result of each iteration; is the state variable of the scanning radiation source predicted at the kth iteration, w k-1 is the process noise, which is assumed to be zero-mean Gaussian noise; By calculating the Jacobian matrix F of the state vector of the state transfer function f() k To achieve linearization: According to the linearized Jacobian matrix, the covariance matrix of the state prediction error is predicted: P k|k-1 =F k P k-1 F k H +Q k-1 (17) Among them, P k|k-1 is the covariance matrix of the state prediction error of the kth iteration, P k-1 is the covariance matrix of the state prediction error of k-1 iterations, Q k-1 is the process noise covariance matrix, which can be expressed as in(·) H Indicates the conjugate transpose operation of the matrix; The state estimate is updated using the measured value, namely: Among them, X k is the state variable of the scanning radiation source at the kth iteration, is the state variable of the scanning radiation source predicted at the kth iteration, z k is the observation model at the kth iteration, is a state variable The predicted observation value calculated by the nonlinear observation function, K k is the Kalman gain, which is used to balance the weights between the predicted value and the measured value. It is calculated as follows: Among them, P k|k-1 is the covariance matrix of the state prediction error predicted at the kth iteration, H k is the Jacobian matrix of the state variables, R k is the covariance matrix of the observation noise, that is The covariance matrix of the state prediction error is updated as: P k =(I-K k H k )P k|k-1 (20) Here, I is the unit matrix with all diagonal elements being 1 and all other elements being 0.

7. The filtering-based scanning radiation source tracking method according to claim 1, characterized in that: The joint estimation of the scanning radiation source position and the scanning rate comprises: Based on the state variable X of the scanning radiation source at the kth and k-1th iterations k and X k-1 , X k and X k-1 The position coordinates of the scanning radiation source in are respectively taken as u i (m),u i (m-1) is substituted into Equation 7 to calculate the k-th iteration Δr, and then the estimated value of the scan period after compensation is calculated based on Equation 6 use The scanning rate is estimated, and the scanning angle difference is calculated using Equation 9, which is used as the value of the nonlinear observation function of the k+1 iteration to calculate the state variable X of the scanning radiation source of the k+1 iteration. k+1 ; where X k+1 x in k+1 ,y k+1 That is, the position tracking result of the scanning radiation source. The scanning radiation source can be tracked through several consecutive iterations.

8. An observation station, characterized in that: The observation station tracks the scanning radiation source using the filtering-based scanning radiation source tracking method according to any one of claims 1 to 7.

9. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the filtering-based scanning radiation source tracking method according to any one of claims 1-7 is implemented.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the filtering-based scanning radiation source tracking method according to any one of claims 1 to 7 is implemented.

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