A target tracking and deviation compensation method in Doppler environment

Abstract

The present invention proposes a target tracking and deviation compensation method in a Doppler environment, which has good performance, adaptability to the environment and robustness, and can meet the design requirements in the project. The invention takes the state enhanced Kalman filter as the starting point, combines multiple sensors to solve the problem of poor tracking performance of Doppler measurement, and uses the extended Kalman filter to solve the problem of nonlinearity of Doppler measurement. Finally, the algorithm is combined to solve the target tracking and sensor deviation compensation in the Doppler sensor environment. Finally, the algorithm will directly compensate the sensor deviation in the tracking result, without the need for a second compensation, with a small amount of calculation and significant effect.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a target tracking and deviation compensation method in a Doppler environment. Background Art

[0002] In sensor tracking, nonlinear measurements have poor tracking effects. For example, if the Doppler shift is measured by the target speed and then the target is tracked, the final tracking result is poor. This is because the effect of obtaining multi-dimensional information such as speed and position through one-dimensional information is poor and it is very dependent on prior information before tracking. The fixed deviation of the sensor itself during measurement has a serious impact on the tracking effect. The different deviations of multiple sensors will cause errors in the tracking results when they are finally fused.

[0003] The traditional sensor calibration method first uses the unchanging characteristics of the real target position to establish a pseudo measurement, thereby extracting the sensor deviation value, but it is difficult to achieve for Doppler frequency shift measurement with a high degree of nonlinearity. There is also a particle filter method to describe the distribution of the variable of interest, but to ensure the coverage of the particles, the amount of calculation is large, so it is rarely used. The state-enhanced Kalman filter achieves good results on the tracking results by expanding the target motion state vector or the remaining observation vectors and increasing the amount of information. Summary of the invention

[0004] In view of the above problems, the present invention proposes a target tracking and deviation compensation method in a Doppler environment, which has good performance, adaptability to the environment and robustness, and can meet the design requirements in engineering.

[0005] The technical solution adopted by the present invention is:

[0006] Assume that the total observation sampling time is K, and M stationary sensors measure one target, and the sensor position is s m =[x m ,y m ] T , m=1,2…M; the position of the target is u=[u x ,u y ] T , the speed is v = [v x ,v y ] T , x and y represent the position and velocity information on the horizontal and vertical coordinates respectively, the signal wavelength is λ, and the measurement information of each sensor That is, the corresponding Doppler frequency shift is expressed as follows

[0007]

[0008] u krepresents the target position at time k, is the measurement error of the mth sensor at time k, which has zero mean and variance Gaussian distribution.

[0009] A target tracking and deviation compensation method in a Doppler environment comprises the following steps:

[0010] S1. Using state enhanced Kalman filtering, single sensor tracking of a single target is extended to multi-sensor tracking of a single target

[0011] Traditional Kalman filtering describes the environment of a single sensor tracking a single target. In order to solve the problem that the Doppler sensor observation data only has one-dimensional information, the observation vector is expanded to M dimensions based on the augmented state Kalman filter, where M represents the total number of sensors. In addition, the fixed bias of the sensor is taken into account, so the target's motion vector does not only contain speed and position information, but also the fixed bias should be taken into account.

[0012] The state vector in the augmented state where x t Refers to the motion characteristics of the target when the sensor bias is not extended. Generally, x t =[u x ,u y ,v x ,v y ], including the position and velocity of the target, and b refers to a fixed deviation of the measured Doppler frequency shift. Therefore, the measurement information has the following new representation:

[0013]

[0014] b m The m in still refers to the mth sensor;

[0015] The state equation of the augmented state is expressed as

[0016] x(k+1)=F(k)x(k)+q(k)

[0017] Where k represents the time, F is the state transfer matrix corresponding to the target, q is the state noise, q t is x t The corresponding state noise, the state noise corresponding to the deviation is 0, and the covariance matrix corresponding to q

[0018] Similarly, when observing data, because we consider multiple sensors at this time, we need to expand the traditional single sensor observation matrix to a multi-sensor observation matrix, as shown below The augmented measurement equation can be expressed as

[0019] z(k)=H(k)x(k)+n(k)

[0020] Where H is

[0021]

[0022] in is the measurement error in the measurement information, and its covariance matrix is ​​represented by R = blkdiag{R1,…,R M}. At this point, the multi-sensor observation model in the augmented state is established.

[0023] S2. For the established augmented state model, we rely on the Kalman filter framework to achieve target tracking. The state augmented Kalman filter (ASKF) can be expressed as:

[0024]

[0025] P * (k+1|k)=F(k)P * (k|k)F(k) T +Q(k)

[0026] K(k+1)=P * (k+1|k)H(k+1) T ×[H(k+1)P * (k+1|k)H(k+1) T +R(k+1)] -1

[0027]

[0028] P * (k+1|k+1)=[IK(k+1)H(k+1)]P * (k+1|k)

[0029] In the above formula, P is the covariance matrix, which is important information for adjusting parameters in Kalman filtering, and I is the identity matrix. “*” is used to represent the estimation and covariance matrix of ASKF.

[0030] S3. ASKF filtering for Doppler measurement through extended Kalman filtering

[0031] Traditional Kalman filter tracking cannot achieve tracking due to the high intensity nonlinear characteristics of Doppler measurement. Therefore, the extended Kalman filter is used to implement tracking, which uses the local linear characteristics of nonlinear functions to locally linearize the nonlinear model. The nonlinearity of Doppler measurement is reflected in the nonlinearity of the observed information. Based on the system state equation, around the filter value Do a first-order Taylor expansion and you get:

[0032]

[0033] h is a nonlinear function of the Doppler measurement with respect to the target motion state.

[0034]

[0035]

[0036] Replacing the original Kalman filter formula with the above formula forms the augmented state filter of the extended Kalman filter.

[0037] The beneficial effects of the present invention are as follows: based on the state enhanced Kalman filter model, the present invention considers the observation model when multiple sensors and sensors have fixed bias, and is extended to the state under the condition of nonlinear measurement of Doppler sensors, and uses the extended Kalman filter to complete the filtering of nonlinear measurement on the basis of the model being an augmented state. Finally, when the target is tracked, the estimated sensor deviation can be directly compensated to the tracking result without the need for a second compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Target trajectory and sensor location.

[0039] Figure 2 Average sensor calibration results Root Mean Square Error.

[0040] Figure 3 Target tracking trajectory.

[0041] Figure 4 Position Root Mean Square Error.

[0042] Figure 5 RMS velocity error. DETAILED DESCRIPTION

[0043] The practicability of the present invention is demonstrated below in conjunction with a simulation example:

[0044] Simulation Example

[0045] This example uses Matlab to verify the above Doppler sensor joint tracking and deviation compensation algorithm. For simplicity, the following assumptions are made for the algorithm model:

[0046] The effectiveness of the present invention is illustrated below with reference to simulation examples.

[0047] Simulation conditions and parameters:

[0048] Simulation environment: For the sake of illustration, consider a representative two-dimensional scenario, assuming that the sensor network has 5 sensors r i They are located at [-200,0], [-200,200], [200,200], [200,0], and [0,-200] (m) respectively.

[0049] The target state vector is

[0050] The actual initial state is x0 = [-105(m),-95(m),200(m / s),200(m / s),15,-15,20,-10,15].

[0051] Before filtering begins, since there is no prior information and the size of the bias is unknown, the initial state is given as:

[0052] x0=[-100(m),-100(m),100(m / s),100(m / s),0,0,0,0,0].

[0053] Assume that the total observation time is 2s. Assume that the target is an ideal uniform linear motion, x k =Fx k-1 ,in,

[0054]

[0055] Among them, △ = 0.01s is the sampling period, and the motion trajectory is as follows Figure 1 shown.

[0056] The transmission signal frequency is 300MHz, and the measurement noise of the five sensors is zero mean and the variance is The Gaussian noise vector, σ w 2 =1Hz, 100 Monte Carlo simulations were used to calculate the mean square error, and the results are as follows Figure 2 The target tracking result after filtering is shown in Figure 3 The root mean square errors of the position and velocity of the filtering results are respectively given by Figure 4 and Figure 5 express.

[0057] By simulating a scene that remains unchanged, it can be found that after an effective accumulation time, the method of the present invention can effectively estimate the bias of the sensor, and the final tracking result can accurately overcome the influence of the sensor deviation on the tracking result.

Claims

1. A target tracking and deviation compensation method in a Doppler environment is defined as measuring a target through M stationary sensors, and the sensor position is s m =[x m ,y m ] T , m=1,2...M; the position of the target is u=[u x ,u y ] T , the speed is v = [v x ,v y ] T , x and y represent the position and velocity information on the horizontal and vertical coordinates respectively, the signal wavelength is λ, and the measurement information of each sensor That is, the corresponding Doppler frequency shift is expressed as: in, u k represents the target position at time k, is the measurement error of the mth sensor at time k, which has zero mean and variance Gaussian distribution; characterized in that the method comprises: S1, using state enhanced Kalman filtering to expand single sensor tracking of a single target to multi-sensor tracking of a single target; Define the state vector in the augmented state where x t Refers to the target motion characteristics when the sensor deviation is not extended, x t =[u x ,u y ,v x ,v y ], including the position and velocity information of the target, b refers to a fixed deviation of the measured Doppler frequency shift, so the measurement information has the following new representation: b m The m in represents the mth sensor; the state equation of the augmented state is expressed as: x(k+1)=F(k)x(k)+q(k) Where k represents the time, F is the state transfer matrix corresponding to the target, q is the state noise, q t is x t The corresponding state noise, the state noise corresponding to the deviation is 0; Similarly, when observing data, it is necessary to expand the traditional single-sensor observation matrix to a multi-sensor observation matrix, that is, The augmented measurement equation is expressed as z(k)=H(k)x(k)+n(k) Where H is in is the measurement error in the measurement information; S2. For the established augmented state model, the Kalman filter framework is used to realize target tracking; the state enhanced Kalman filter ASKF is expressed as: K(k+1)=P * (k+1∣k)H(k+1) T ×[H(k+1)P * (k+1∣k)H(k+1) T +R(k+1)] -1 P * (k+1∣k+1)=[I-K(k+1)H(k+1)]P * (k+1∣k) In the above formula, P is the covariance matrix, I is the identity matrix, and "*" is used to represent the ASKF estimate and covariance matrix; S3, ASKF filtering for Doppler measurement through extended Kalman filtering; The nonlinearity of Doppler measurement is reflected in the nonlinearity of the observed information, which is determined by the system state equation around the filter value Do a first-order Taylor expansion and you get: h is the nonlinear relationship between Doppler measurement and target motion state; Replacing the original Kalman filter formula with the above formula forms the augmented state filter of the extended Kalman filter, and the tracking result directly compensates for the sensor deviation.

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