A tracking calibration method for nonlinear observation distributed networks

Abstract

The present invention proposes a tracking calibration method for a distributed network of nonlinear observations, which has good performance, environmental adaptability and robustness, and can meet the design requirements in engineering. In view of the problem of nonlinear observation, the present invention uses the EKF method to modify the original distributed fusion algorithm; uses the CI algorithm for data fusion to transmit the posterior information of the local filter; based on the idea of ​​ASKF, the target state enhancement under the distributed network is realized, and the filter state vector of each sensor is expanded to realize the estimation of each deviation. After fusion, the target tracking and the fusion of each sensor can still be accurately realized, which is not affected by the low dimension of its nonlinear observation, and does not require repeated compensation.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a tracking calibration method for a nonlinear observation distributed network. Background Art

[0002] In recent years, with the development of wireless networks, distributed architectures have become ubiquitous. In practical applications, in order to reduce communication costs and improve energy efficiency, the consensus steps in state estimation are minimized in each sampling interval. In existing distributed state estimation research, multiple sensors are generally considered to perform local filtering separately, and then the data is transmitted back to the fusion center for processing, which has the advantages of small computational complexity and high fault tolerance. In sensor tracking, nonlinear measurements perform poorly in tracking effects. For example, the Doppler shift is measured by the target motion speed, and then the target is tracked. The final tracking result is poor. This is because the effect of obtaining multidimensional 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 loss on the tracking effect, and the different deviations of multiple sensors will cause errors in the tracking results during the final fusion.

[0003] For the problem of nonlinear measurement, methods such as EKF and UKF have been widely used and their stability has been verified. For filtering methods in distributed networks, consistent volumetric Kalman filtering and consistent information filters have already appeared. For nonlinear observation problems, the above methods can be used to achieve it. In sensor calibration, the method of establishing pseudo-measurement mainly requires first calculating the sensor deviation through the filtering result, and then compensating the sensor deviation into the filtering result. However, the conditions of different nonlinear observations are different, and the method of establishing pseudo-measurement is not applicable to all situations. The Kalman filter based on state enhancement can be better applied to various scenarios, but there is an increase in dimensions. Summary of the invention

[0004] In view of the above problems, the present invention proposes a tracking calibration method for nonlinear observation distributed networks. Experiments are carried out using nonlinear observation conditions as an example. The method 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] The Doppler frequency shift measurement information is obtained by using sensors (observation stations), and the basic parameters are set as follows: the total number of sampling moments is K; the total number of stationary observation stations is M, and the position of the mth observation station is Where x m and m Represent the horizontal and vertical coordinates respectively, represents matrix transpose, m satisfies 1≤m≤M; the number of targets is 1, and the position information of the target at the kth sampling time is Speed ​​information is In the formula and Represent the horizontal and vertical coordinates respectively, and Respectively represent the speed in the horizontal and vertical coordinate axes, k satisfies 1≤k≤K; the signal wavelength is λ;

[0007] The tracking calibration method includes the following steps:

[0008] S1. Using state-enhanced Kalman filtering, the target state is enhanced to achieve joint estimation of the deviation:

[0009] The traditional tracking process generally implements the filtering process for the purpose of tracking the target state information. Based on the augmented state Kalman filter, the fixed bias of the sensor is used as a joint estimate. Therefore, the motion vector of the target not only contains speed and position information, but also should take the fixed bias into account.

[0010] Using state-enhanced Kalman filtering, the target state is enhanced and the state vector in the augmented state is defined Where x t are the kinematic parameters of the target, expressed as b is the identity parameter of the target, and the state transfer equation under the augmented state is established as:

[0011]

[0012] In the formula, and represents the augmented state of the target at the kth sampling time and the k-1th sampling time relative to the mth observation station, is the state transfer matrix of the mth observation station at the kth sampling time, is the process noise of the mth observation station at the k-1th sampling time, with a mean of 0 and a covariance matrix of Gaussian distribution. Since it is a distributed network, when considering local filtering, each sensor has a different observation equation, which will affect the Jacobian matrix derivation during nonlinear observation. At this point, the state model in the augmented state is established.

[0013] S2. For the established augmented state model, the information transmission process in the distributed network is realized based on the covariance intersection fusion strategy. Considering the distributed network without fusion center, and due to the problem of observation nonlinearity, the CI algorithm based on EKF is as follows:

[0014] S21. The prediction process is as follows:

[0015]

[0016]

[0017]

[0018] in and are the predicted target state of the mth observation station at the kth sampling moment and the posterior estimated state at the k-1th sampling moment; represents the prediction information vector of the mth observation station at the kth sampling time; and They represent the predicted inverse covariance matrix of the mth observation station at the kth sampling time and the posterior inverse covariance matrix at the k-1th sampling time respectively; (·) -1 Inverse operation for the matrix; represents the inverse matrix of the process noise covariance matrix of the mth observation station at the k-1th sampling time;

[0019] S22. The update process is as follows:

[0020] The observation equation under the augmented state is established as:

[0021]

[0022] In the formula, is the observation information obtained by the mth observation station at the kth sampling time; ||·|| is the 2-norm; is the angle measurement error of the mth observation station at the kth sampling time, with a mean of 0 and a variance of Gaussian distribution; the specific update formula is as follows:

[0023]

[0024]

[0025]

[0026]

[0027] in, is the observation function of the mth observation station at the kth sampling time, obtained from the observation equation; It means partial derivative of y with respect to x; is the Jacobian matrix of the observation equation of the mth observation station at the kth sampling time; is the observation residual of the mth observation station at the kth sampling time; represents the posterior information vector of the mth observation station at the kth sampling time, satisfying In the formula is the covariance matrix of the augmented state vector of the mth observation station at the kth sampling time, is the posterior estimated state of the mth observation station at the kth sampling time; represents the posterior inverse covariance matrix of the mth observation station at the kth sampling time, which is numerically equal to the inverse matrix of the covariance matrix; represents the noise information matrix of the mth observation station at the kth sampling time, which is also the inverse of the observation noise variance;

[0028] The information of the mth observation station is fused with the information of all observation stations that have information exchange with it. After l fusion iterations, the fused information obtained is:

[0029]

[0030]

[0031] In the formula, and are the information vector and inverse covariance matrix of the mth observation station at the kth sampling time after l fusion iterations respectively; the number of fusion iterations l satisfies 1≤l≤M-1, and there is is the set of other observation stations that have information exchange with the mth observation station; π m,j represents the mth observation station and The fusion weight of the jth observation station in ; if it is finally fused L times, the final state estimate is In the formula is the posterior estimated state of the mth observation station at the kth sampling moment after L fusion iterations.

[0032] At this point, the nonlinear observation CI algorithm based on EKF has been implemented, and the enhancement of the target state vector has been achieved based on ASKF, and the deviations of each sensor have been estimated simultaneously in a distributed network.

[0033] The present invention has good performance, environmental adaptability and robustness, and can meet the design requirements in engineering. In view of the problem of nonlinear observation, the EKF method is used to modify the original distributed fusion algorithm; the CI algorithm is used for data fusion to transmit the posterior information of the local filter; based on the idea of ​​ASKF, the target state enhancement under the distributed network is realized, and the filter state vector of each sensor is expanded to realize the estimation of each deviation. After fusion, the target tracking and the fusion of each sensor can still be accurately realized, which is not affected by the low dimension of its nonlinear observation, and does not require repeated compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Target trajectory and sensor location.

[0035] Figure 2 Average sensor calibration results Root Mean Square Error.

[0036] Figure 3 Target tracking trajectory.

[0037] Figure 4 Position Root Mean Square Error.

[0038] Figure 5 RMS velocity error.

[0039] Figure 6 Comparison of distributed and centralized calibration effects. DETAILED DESCRIPTION

[0040] The present invention is described in detail below in conjunction with embodiments:

[0041] Example

[0042] This example uses Matlab to verify the above-mentioned joint tracking and deviation compensation algorithm based on the distributed network of Doppler sensors. For the sake of simplicity, the following assumptions are made for the algorithm model:

[0043] The effectiveness of the present invention is illustrated below with reference to simulation examples.

[0044] Simulation conditions and parameters:

[0045] 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.

[0046] The target state vector is

[0047] The actual initial state is x0 = [-105(m),-95(m),200(m / s),200(m / s),15,-15,20,-10,15].

[0048] Before filtering begins, since there is no prior information and the size of the bias is unknown, the initial state is given as:

[0049] x0=[-100(m),-100(m),0(m / s),0(m / s),0,0,0,0,0].

[0050] Assume that the total observation time is 2s. Assume that the target is an ideal uniform linear motion. in,

[0051]

[0052] The sensor networks are interconnected, and their adjacency matrix G is:

[0053]

[0054] The mth row represents the adjacency of the mth sensor, and the jth column is 1, indicating that it is connected to the jth sensor.

[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. Figure 6 By comparing the effects of distributed network and centralized deviation estimation, it can be found that the distributed network is slightly inferior to the centralized one in terms of convergence speed, but after a long period of accumulation, it can achieve the same level of calibration effect.

[0057] By keeping the simulation scene unchanged, it can be found that after an effective accumulation time, the method of the present invention can adapt to target tracking under a nonlinear observation distributed network, and can simultaneously consider the deviation compensation problem of each sensor in a distributed state, thereby improving the tracking accuracy and eliminating the need for repeated compensation, thereby reducing the amount of calculation.

Claims

1. A tracking calibration method for a nonlinear observation distributed network, using sensors to obtain Doppler frequency shift measurement information, defining the total number of sampling moments as K; the total number of stationary observation stations as M, where the position of the mth observation station is Where x m and m Represent the horizontal and vertical coordinates respectively, represents matrix transpose, m satisfies 1≤m≤M; The number of targets is 1, and the position information of the target at the kth sampling time is Speed ​​information is In the formula and Represent the horizontal and vertical coordinates respectively, and Respectively represent the speed in the horizontal and vertical coordinate axes, k satisfies 1≤k≤K; The signal wavelength is λ; characterized in that the tracking calibration method includes: S1. Use state-enhanced Kalman filtering to enhance the target state and define the state vector in the augmented state as Where x t are the kinematic parameters of the target, expressed as b is the identity parameter of the target, and the state transfer equation under the augmented state is established as: In the formula, and represents the augmented state of the target at the kth sampling time and the k-1th sampling time relative to the mth observation station, is the state transfer matrix of the mth observation station at the kth sampling time, is the process noise of the mth observation station at the k-1th sampling time, with a mean of 0 and a covariance matrix of Gaussian distribution of S2. Information transmission in distributed networks is realized based on the covariance cross-fusion strategy. Considering the distributed network without fusion center, due to the problem of observation nonlinearity, the covariance cross-fusion strategy based on extended Kalman filtering is implemented as follows: S21. The prediction process is as follows: in and are the predicted target state of the mth observation station at the kth sampling moment and the posterior estimated state at the k-1th sampling moment; represents the prediction information vector of the mth observation station at the kth sampling time; and They represent the predicted inverse covariance matrix of the mth observation station at the kth sampling time and the posterior inverse covariance matrix at the k-1th sampling time respectively; (·) -1 Inverse operation for the matrix; represents the inverse matrix of the process noise covariance matrix of the mth observation station at the k-1th sampling time; S22. The update process is as follows: The observation equation under the augmented state is established as: In the formula, is the observation information obtained by the mth observation station at the kth sampling time; ||·|| is the 2-norm; is the angle measurement error of the mth observation station at the kth sampling time, with a mean of 0 and a variance of Gaussian distribution; the specific update formula is as follows: in, is the observation function of the mth observation station at the kth sampling time; It means partial derivative of y with respect to x; is the Jacobian matrix of the observation equation of the mth observation station at the kth sampling time; is the observation residual of the mth observation station at the kth sampling time; represents the posterior information vector of the mth observation station at the kth sampling time, satisfying In the formula is the covariance matrix of the augmented state vector of the mth observation station at the kth sampling time, is the posterior estimated state of the mth observation station at the kth sampling time; represents the posterior inverse covariance matrix of the mth observation station at the kth sampling time, which is numerically equal to the inverse matrix of the covariance matrix; represents the noise information matrix of the mth observation station at the kth sampling time, which is also the inverse of the observation noise variance; The information of the mth observation station is fused with the information of all observation stations that have information exchange with it. After l fusion iterations, the fused information obtained is: In the formula, and are the information vector and inverse covariance matrix of the mth observation station at the kth sampling time after l fusion iterations respectively; the number of fusion iterations l satisfies 1≤l≤M-1, and there is is the set of other observation stations that have information exchange with the mth observation station; π m,j represents the mth observation station and The fusion weight of the jth observation station in ; if it is finally fused L times, the final state estimate is In the formula is the posterior estimated state of the mth observation station at the kth sampling moment after L fusion iterations.

Images