Aerial target tracking method based on continuous discrete model

Abstract

The invention provides an aerial target tracking method based on a continuous discrete model, which comprises the following steps of: firstly, dividing a sensor sampling interval into a plurality of sub-step lengths, estimating a target state and a covariance by utilizing a volume point approximation method, and predicting the state and the covariance of the next step by utilizing a target state process continuous model; and repeating until the state and covariance prediction at the next moment is obtained, then constructing a measurement irrelevant function, and carrying out irrelevant conversion on measurement. And finally, updating the state and covariance prediction of the target by using measurement and irrelevant conversion measurement so as to realize the estimation of the state and covariance of the target, and repeating the steps until the estimation of the state of the target within the observation time is completed. According to the method, the target state model is closer to reality, the target information carried by measurement is fully utilized, the aerial target tracking performance is improved, and the tracking advantage of the aerial target under strong background noise is particularly obvious.

Description

Technical Field

[0001] The invention relates to the technical field of aerial target tracking, in particular to the field of aerial target tracking based on an uncorrelated conversion continuous discrete model, solves the problem of accurate aerial target tracking, and provides a basis for accurate aerial target tracking. Background Art

[0002] Aerial target tracking has always been one of the important branches in the field of target tracking. Due to flight dynamics, flight control and other reasons, the state of aerial targets will undergo continuous and slight changes during the movement process. In addition, due to factors such as the diversity and high speed of the flight state of aerial targets, the traditional discrete target state model has a low match with the actual situation and fails to make full use of the target measurement information, resulting in low tracking accuracy and even target loss. According to the motion characteristics of aerial targets, building a target state process model that matches the actual situation and deeply mining the target measurement information to achieve accurate tracking of aerial targets has become a hot topic of research.

[0003] Traditional tracking of aerial targets is mainly achieved by predicting discrete states and updating the predictions using measurements, thereby realizing the estimation of the target state. In the objective world, the target motion state changes continuously and dynamically within a specific time period. The traditional assumption of the discrete model of the target state cannot well characterize the actual situation of the target state. In order to solve this problem, the target state process is modeled as a continuous model, and the target state process is described by using stochastic differential equations. The measurement maintains the original discrete model to form a tracking method based on a continuous discrete model. There are mainly two methods for solving stochastic differential equations. The first method uses Runge-Kutta solution, and the second method uses 1.5-order Taylor expansion linearization. Studies have found that the tracking accuracy of the two is similar, but the former has a large calculation and is difficult to meet the real-time requirements of aerial targets. Therefore, the present invention uses 1.5-order Taylor expansion linearization to solve the target state model.

[0004] In order to improve the accuracy of aerial target tracking, it is necessary to make full use of effective measurement information. By performing unrelated transformation on the measurement, the target state and covariance prediction are updated simultaneously using the measurement and the unrelated transformation measurement, thereby realizing the estimation of the target state. Compared with the traditional method, since the measurement after unrelated transformation carries the target information, the effective information of the state estimation is increased when the unrelated measurement is updated, and the target information of the measurement can be fully mined.

[0005] The core of the aerial target tracking method based on the continuous discrete model lies in the construction of the continuous model of the state process and the unrelated conversion of the measurement. In view of the poor matching between the traditional discrete model and the actual state changes of the aerial target and the low utilization rate of the effective information measured, the present invention introduces the continuous model of the target state process and the measurement unrelated conversion technology, and proposes an aerial target tracking method based on the continuous discrete model. The method uses the continuous model of the state process to update the time of the target state, and uses the discrete measurement model and unrelated conversion measurement to measure and update the target state, which effectively improves the accuracy of aerial target tracking. Summary of the invention

[0006] In order to overcome the shortcomings of the prior art, the present invention provides an aerial target tracking method based on a continuous discrete model, which not only constructs a continuous model of the target state process that is closer to the actual one, but also effectively mines the target information carried by the measurement by performing unrelated conversion on the measurement, thereby improving the accuracy of aerial target tracking.

[0007] The technical idea of ​​the present invention is: first, the sensor sampling interval is divided into m sub-steps, the target state and covariance are estimated by using the volume point approximation method, and the state and covariance of the next step are predicted by using the continuous model of the target state process, and the above steps are repeated until the state and covariance prediction of the next step is obtained. Then, a measurement-independent function is constructed, and the measurement is subjected to an irrelevant conversion. Finally, the state and covariance prediction of the target are updated using the measurement and the irrelevant conversion measurement, thereby realizing the estimation of the target state and covariance, and the above steps are repeated until the target state estimation within the observation time is completed.

[0008] The present invention introduces a continuous model of target state process and an uncorrelated conversion technology of measurement in aerial target tracking, and uses uncorrelated measurements to estimate target state and covariance, and proposes an aerial target tracking method based on a continuous discrete model, which overcomes the disadvantage of low aerial target tracking performance of traditional tracking methods under high-density clutter.

[0009] The steps of the technical solution adopted by the present invention to solve its technical problem are:

[0010] Step 1: Initialization

[0011] 1a) Set the initial target state x0 and the initial covariance square root S0 of the target;

[0012] 1b) Set the target state sampling time interval [t k-1 ,t k ] is divided into m steps, m>0, and each step length is τ, then:

[0013]

[0014] Step 2: Calculate the target state volume point at step l at time k-1

[0015] Step 3: Calculate the target state prediction and covariance prediction of the l+1 step at time k-1,

[0016] Step 4: Calculate the k-time measurement prediction value and measurement irrelevant transformation,

[0017] Step 5: Calculate the measurement irrelevant transition at time k,

[0018] Step 6: Calculate the center distance at time k,

[0019] Step 7, calculate the square root of the covariance at time k,

[0020] Step 8, calculate the gain at time k,

[0021] Step 9, calculate the state estimate and covariance square root at time k, and estimate the target state information at all times.

[0022] In step 2, the specific steps are as follows:

[0023]

[0024] Where k is the current moment of calculation, k-1 is the previous moment, i=1,2,…2n, n is the dimension of the target state, and the number of steps l=1…m. is the estimated value of the target state at the previous step l, is the square root of the covariance matrix of the previous step l, when i=1,2,…n, When i=n+1,n+2,…2n, i is the dimension of the volume point.

[0025] The specific implementation of step 3 is as follows:

[0026] 3a) Calculate the volume propagation point of the target state at step l+1 at time k-1

[0027]

[0028] Among them, f(.) is the target motion model, which is related to the target motion style.

[0029] F is the first derivative of f(.), C pj is the partial derivative of the rth row and jth column element of the state noise Q, C rj is the partial derivative of the r-th row and j-th column element of the state noise Q;

[0030] 3b) Calculate the target state prediction at the k-1th time and the l+1th step

[0031]

[0032] 3c) Calculate the target state prediction center distance at the k-1th time and the l+1th step

[0033]

[0034] 3d) Calculate the square root of the target state covariance prediction at step l+1 at time k-1

[0035]

[0036] Among them, qr(.) is the QR decomposition of the matrix, G ej The corresponding Q is the e-th and j-th elements, and Q is the error covariance;

[0037] Through the above calculations, the state and covariance estimate of the lth step at the k-1th time are obtained, and then l is added by 1, and steps 2 to 3 are repeated until l = m, that is, the target state value at the kth time is obtained. and covariance predicted values

[0038] The specific implementation of step 4 is as follows:

[0039] 4a) Calculate the target state prediction volume point X at time k i,kk-1 for;

[0040]

[0041] 4b) Calculate the measured predicted volume point Z at time k i,k|k-1 ;

[0042] Z i,k|k-1 =h(X i,k|k-1 )+v k (9)

[0043] Among them, h(.) is the measurement model, v k To measure noise;

[0044] 4c) Calculate the measurement prediction at time k

[0045]

[0046] The specific implementation of step 5 is as follows:

[0047] 5a) Calculate the measurement-independent transformation yk ;

[0048]

[0049] 5b) Calculate the volume point Y of the uncorrelated conversion measurement i,kk-1 ;

[0050]

[0051] Among them, α is determined according to the actual scenario;

[0052] 5c) computing predictions of unrelated conversion measures;

[0053]

[0054] The specific implementation of step 6 is as follows:

[0055]

[0056]

[0057] Among them, χ kk-1 is the center distance of the target state, Z kk-1 is the measured center distance, γ kk-1 is the center distance of the measured unrelated transformations.

[0058] The specific implementation of step 7 is as follows:

[0059]

[0060] Among them, Tria(.) is the triangulation of the matrix, is the measurement noise covariance R k The square root of W 11 ∈R d ×(d+1) , W 12 ∈R 1×(d+1) , W 13 ∈R (d+1)×n , W 32 ∈R n×n It is a triangular array.

[0061] The specific implementation of step 8 is as follows:

[0062] 8a) Calculate the measurement gain K at time k k ;

[0063] K k =W 13 W 11 (18)

[0064] 8b) Calculate the measurement-independent conversion gain G at time kk ;

[0065] G k =W 13 T W 12 T (19).

[0066] The specific implementation of step 9 is as follows:

[0067] 9a) Calculate the state estimate at time k

[0068]

[0069] 9b) Calculate the square root estimate of the covariance at time k

[0070]

[0071] Among them, SVD(.) is the singular value decomposition of the matrix;

[0072] The target state at time k is estimated through step 9. Square root of covariance Then, k is increased by 1, and steps 2 to 9 are repeated until k=N, and the target state information at all times is estimated.

[0073] The beneficial effect of the present invention is that in order to solve the problem that the traditional tracking method has low tracking accuracy for aerial targets, especially the tracking performance drops rapidly under strong background noise, a method for tracking aerial targets based on a continuous discrete model is proposed. The present invention will introduce a continuous model of the target state process and an unrelated conversion technology of the measurement, which not only makes the target state model closer to reality, but also makes full use of the target information carried by the measurement, thereby improving the tracking performance of aerial targets. The tracking advantage of aerial targets under strong background noise is particularly obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a flow chart of the implementation of the method of aerial target tracking based on continuous discrete model (UC-CD-CKFsr);

[0075] Figure 2 It is the performance verification scenario of the UC-CD-CKFsr method;

[0076] Figure 3 is the target running state tracking error when the measurement noise covariance is [100, 0.01, 0.01], Figure 3 (a) is the target position error diagram for tracking. Figure 3 (b) is the target velocity error diagram for tracking;

[0077] Figure 4 is the target running state tracking error when the measurement noise covariance is [900, 0.09, 0.09]; Figure 4 (a) is the tracking error diagram of the target tracking position error, Figure 4 (b) is the tracking error diagram of velocity;

[0078] Figure 5 is the target running state tracking error when the measurement noise covariance is [2500, 0.25, 0.25]; Figure 5 (a) is the tracking error diagram of the target tracking position error, Figure 5 (b) is the velocity tracking error diagram. DETAILED DESCRIPTION

[0079] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0080] In order to verify the performance of the proposed method, a scenario close to the actual scenario of ground sensors tracking aerial targets needs to be set up. The specific scenario is as follows:

[0081] An aircraft is maneuvering at a nearly constant speed and turning rate on a horizontal plane 200m above the ground. A sensor on the ground nearby is continuously tracking the aircraft. A Cartesian coordinate system is established with the ground as the xy plane, the east direction as the x-axis, the north direction as the y-axis, and the vertical direction as the z-axis. The sensor position s = (1500, 10, 0), and the target measurement obtained by the sensor is r is the distance of the target relative to the sensor, is the azimuth of the target relative to the sensor, θ is the pitch of the target relative to the sensor, the state dimension of the target is n = 7, and the actual trajectory of the target flight is shown in the appendix of the manual. Figure 2 .

[0082] The present invention is further described in detail in combination with scenario assumptions.

[0083] Reference Figure 1 , the implementation steps of the present invention are as follows:

[0084] Step 1, Initialization

[0085] 1a) Set the initial state of the aerial target x0 = [1000, 0, 2650, 150, 200, 0, 6°] T , the square root of the state covariance is S o =diag([0.01,0.01,0.01,0.01,0.01,0.01,0.01]), the diffusion matrix is ​​Q=diag([0,10,0,10,0,10,4.9×10 -5 °]).

[0086] 1b) Set the sampling interval of the target state [t k-1 ,t k ] is divided into m=10 steps, each step length is τ, and the sampling period is T.

[0087]

[0088] Step 2: Calculate the target state volume point of step 1 at time k-1

[0089]

[0090] in, is the target state of step 1, is the square root of the covariance matrix of step 1, n=7, k is the current moment of calculation, k-1 is the previous moment, n is the dimension of the target state, when i=1,2,…n,

[0091] When i=n+1,n+2,…2n,

[0092] Step 3: Calculate the target state prediction and covariance prediction of step 1 at time k-1. The specific implementation of this step is as follows:

[0093] 3a) Calculate the volume propagation point of the target state of step 2 at time k-1

[0094]

[0095] in, is the target motion model, e, j, p, r = 1, ..., n, F is The first derivative of pj is the partial derivative of the rth row and jth column element of the state noise Q, C rj is the partial derivative of the r-th row and j-th column element of the state noise Q.

[0096] 3b) Calculate the target state prediction for step 1 at time k-1

[0097]

[0098] 3c) Calculate the target state prediction center distance of step 2 at the k-1th time.

[0099]

[0100] 3d) Calculate the square root of the state covariance prediction for step 1 at time k-1.

[0101]

[0102] Among them, qr(.) is the QR decomposition of the matrix, G ej The corresponding Q is the e-th and j-th elements, and Q is the error covariance.

[0103] Through the above calculations, we can get the state and covariance estimate of the first step at the k-1th time, and then 2+1, loop steps 2 to 3 until l=10, and get the target state value at the kth time and covariance predicted value

[0104] Step 4: Calculate the k-time measurement prediction value and measurement irrelevant conversion. The specific implementation of this step is as follows:

[0105] 4a) Calculate the target state prediction volume point X at time k i,kk-1 .

[0106]

[0107] 4b) Calculate the measured predicted volume point Z at time k i,kk-1 .

[0108] Z i,kk-1 =h(X i,kk-1 )+v k (9)

[0109] in, is the measurement model, v k To measure noise.

[0110] 4c) Calculate the measurement prediction at time k

[0111]

[0112] Step 5: Calculate the measurement-independent transformation at time k. The specific implementation of this step is as follows:

[0113] 5a) Calculate the measurement-independent transformation y at time k k .

[0114]

[0115] 5b) Calculate the volume point Y of the unrelated transformation measurement at time k i,kk-1 .

[0116]

[0117] 5b) Compute the prediction of the uncorrelated transition measure at time k

[0118]

[0119] Step 6: Calculate the center distance at time k. The specific implementation of this step is as follows:

[0120]

[0121] Among them, χ kk-1 is the center distance of the target state, Z kk-1 is the measured center distance, γ kk-1 is the center distance of the measured unrelated transformations.

[0122] Step 7, calculate the square root of the covariance at time k. The specific implementation of this step is as follows:

[0123]

[0124] Among them, Tria(.) is the triangulation of the matrix, is the measurement noise covariance R k The square root of W 11 ∈R d×(d+1) , W 12 ∈R 1×(d+1) , W 13 ∈R (d+1)×n , W 32 ∈R n×n It is a triangular array.

[0125] Step 8: Calculate the gain at time k. The specific implementation of this step is as follows:

[0126] 8a) Calculate the measurement gain K k .

[0127] K k =W 13 W 11 (18)

[0128] 8a) Calculate and measure the uncorrelated conversion gain G k .

[0129] G k =W 13 T W 12 T (19)

[0130] Step 9, calculate the state estimate and covariance square root at time k. The specific implementation of this step is as follows:

[0131] 9a) Calculate the state estimate at time k

[0132]

[0133] 9b) Calculate the square root estimate of the covariance at time k

[0134]

[0135] in, is the singular value decomposition of the matrix.

[0136] The target state at time k is estimated through step 9. Square root covariance estimate Save, then, k+1 loop steps 2 to 9, until k=N (N is the number of measurements), and estimate the target state information at all times.

[0137] This method provides an aerial target tracking method based on a continuous discrete model. This method not only improves the tracking accuracy of aerial targets, but also shows good performance under strong clutter. It can be used for high-precision tracking of aerial targets and for tracking aerial targets under strong clutter.

[0138] from Figure 3 to Figure 5 It can be seen that under different intensities of measurement noise, the three tracking methods CD-CKF, CD-CKFsr, and UC-CD-CKFsr can effectively track the position and velocity of the target, and the target tracking accuracy of UC-CD-CKFsr is better than that of CD-CKF and CD-CKFsr. This is because the UC-CD-CKFsr method performs an uncorrelated conversion on the measurement, and increases the measurement uncorrelated conversion gain when estimating the target state, thereby improving the tracking accuracy. Among them, CD-CKF is a continuous discrete volume Kalman tracking method, CD-CKFsr is a continuous discrete square root volume Kalman tracking method, UC-CD-CKFsr is a continuous discrete uncorrelated square root volume Kalman tracking method, and ARMSE is the cumulative root mean square error.

Claims

1. A method for tracking aerial targets based on a continuous discrete model, characterized in that The steps include: Step 1: Initialization 1a) Set the initial target state x0 and the initial covariance square root S0 of the target; 1b) Set the target state sampling time interval [t k-1 ,t k ] is divided into m steps, m>0, and each step length is τ, then: Step 2: Calculate the target state volume point at step l at time k-1 Step 3: Calculate the target state prediction and covariance prediction of the l+1 step at time k-1, Step 4: Calculate the k-time measurement prediction value and measurement irrelevant transformation, Step 5: Calculate the measurement irrelevant transition at time k, Step 6: Calculate the center distance at time k, Step 7, calculate the square root of the covariance at time k, Step 8, calculate the gain at time k, Step 9, calculate the state estimate and covariance square root at time k, and estimate the target state information at all times.

2. The method for tracking an aerial target based on a continuous discrete model according to claim 1, characterized in that: In step 2, the specific steps are as follows: Where k is the current moment of calculation, k-1 is the previous moment, i=1,2,…2n, n is the dimension of the target state, and the number of steps l=1…m. is the estimated value of the target state at the previous step l, is the square root of the covariance matrix of the previous step l, when i=1,2,…n, When i=n+1,n+2,…2n, i is the dimension of the volume point.

3. The method for tracking an aerial target based on a continuous discrete model according to claim 2, characterized in that: The specific implementation of step 3 is as follows: 3a) Calculate the volume propagation point of the target state at step l+1 at time k-1 Among them, f(.) is the target motion model, which is related to the target motion style. e, j, p, r = 1, ..., n, F is the first-order derivative of f (.), C pj is the partial derivative of the rth row and jth column element of the state noise Q, C rj is the partial derivative of the r-th row and j-th column element of the state noise Q; 3b) Calculate the target state prediction at the k-1th time and the l+1th step 3c) Calculate the target state prediction center distance at the k-1th time and the l+1th step 3d) Calculate the square root of the target state covariance prediction at step l+1 at time k-1 Among them, qr(.) is the QR decomposition of the matrix, e, j = 1, ..., n, G ej The corresponding Q is the e-th and j-th elements, and Q is the error covariance; Through the above calculations, the state and covariance estimate of the lth step at the k-1th time are obtained, and then l is added by 1, and steps 2 to 3 are repeated until l = m, that is, the target state value at the kth time is obtained. and covariance predicted values 4. The method for tracking an aerial target based on a continuous discrete model according to claim 3, characterized in that: The specific implementation of step 4 is as follows: 4a) Calculate the target state prediction volume point X at time k i,kk-1 for; 4b) Calculate the measured predicted volume point Z at time k i,kk-1 ; Z i,kk-1 =h(X i,kk-1 )+v k (9) Among them, h(.) is the measurement model, v k To measure noise; 4c) Calculate the measurement prediction at time k 5. The method for tracking an aerial target based on a continuous discrete model according to claim 4, characterized in that: The specific implementation of step 5 is as follows: 5a) Calculate the measurement-independent transformation y k ; 5b) Calculate the volume point Y of the uncorrelated conversion measurement i,kk-1 ; Among them, α is determined according to the actual scenario; 5c) computing predictions of unrelated conversion measures; 6. The method for tracking an aerial target based on a continuous discrete model according to claim 5, characterized in that: The specific implementation of step 6 is as follows: Among them, χ kk-1 is the center distance of the target state, Z kk-1 is the measured center distance, γ kk-1 is the center distance of the measured unrelated transformations.

7. The method for tracking an aerial target based on a continuous discrete model according to claim 6, characterized in that: The specific implementation of step 7 is as follows: Among them, Tria(.) is the triangulation of the matrix, is the measurement noise covariance R k The square root of W 11 ∈R d ×(d+1) , W 12 ∈R 1×(d+1) , W 13 ∈R (d+1)×n , W 32 ∈R n×n It is a triangular array.

8. The method for tracking an aerial target based on a continuous discrete model according to claim 7, characterized in that: The specific implementation of step 8 is as follows: 8a) Calculate the measurement gain K at time k k ; K k =W 13 W 11 (18) 8b) Calculate the measurement-independent conversion gain G at time k k ; G k =W 13 T W 12 T (19)。 9. The method for tracking an aerial target based on a continuous discrete model according to claim 8, characterized in that: The specific implementation of step 9 is as follows: 9a) Calculate the state estimate at time k 9b) Calculate the square root estimate of the covariance at time k Among them, SVD(.) is the singular value decomposition of the matrix; The target state at time k is estimated through step 9. Square root of covariance Then, k is increased by 1, and steps 2 to 9 are repeated until k=N, and the target state information at all times is estimated.

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