[Filter Tracking] Based on probability hypothesis density combined with extended Kalman filter PHD-EKF to achieve multi-objective state estimation with matlab code…

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Content introduction

In the field of target tracking, multi-target state estimation algorithm is a key technology, which can accurately estimate the status of multiple targets in complex environments. The Extended Kalman Filter (EKF) based on Probabilistic Hypothesis Density (PHD) is a commonly used multi-objective state estimation algorithm. This article will introduce the implementation process of the PHD-EKF algorithm.

First, we need to clarify the background and goals of the problem. In multi-target tracking, our goal is to estimate the state of the target, including position, velocity, acceleration, etc., based on a series of observation data. The goal of the PHD-EKF algorithm is to estimate multiple target states by modeling the probability density of the target.

The process of the PHD-EKF algorithm can be divided into the following steps:

1. Initialization: First, we need to estimate the initial state of the target. This can be initialized by using some prior knowledge or historical data.
2. Prediction: In each time step, we first perform a prediction step, which is to predict the new state of the target based on its dynamic model and previous state estimates. This step can be implemented using extended Kalman filtering.
3. Measurement update: After the prediction step, we need to update the state estimate of the target based on the observation data. This step can be achieved using probabilistic hypothesis density, where we decompose the probability density function of the target into a series of Gaussian distributions.
4. Target extraction: After the measurement update, we need to extract the estimated state of the target from its probability density function. This can be achieved by calculating the expectation and covariance of the Gaussian distribution.
5. Data association: After target extraction, we need to associate the observation data with the estimated state of the target to determine the target corresponding to each observation data.
6. Remove redundant targets: After data association, we may have some redundant target estimates. These redundant targets can be removed through some criteria to improve the accuracy of estimation.
7. Resampling: Finally, we need to resample the probability density of the target to maintain the consistency of the probability density.

Through the above steps, we can achieve accurate estimation of multiple target states. However, it should be noted that the PHD-EKF algorithm may face computational complexity problems when processing a large number of targets. Therefore, in practical applications, we need to choose appropriate algorithms and optimization methods according to specific situations.

To sum up, the multi-target state estimation algorithm (PHD-EKF) based on probability hypothesis density combined with extended Kalman filter is an effective target tracking method. By modeling and updating the target’s probability density, we can achieve accurate estimates of multiple target states. However, in practical applications, it is necessary to pay attention to the computational complexity of the algorithm and select the appropriate algorithm and optimization method according to the specific situation. I hope that readers of this article can understand the implementation process of the PHD-EKF algorithm and play a role in practical applications.

Part of the code

function X= gen_newstate_fn(model,Xd,V)

%nonlinear state space equation (CT model)

if ~isnumeric(V)
    if strcmp(V,'noise')
        V= model.B*randn(size(model.B,2),size(Xd,2));
    elseif strcmp(V,'noiseless')
        V= zeros(size(model.B,1),size(Xd,2));
    end
end

if isempty(Xd)
    X= [];
else %modify below here for user specified transition model
    X= zeros(size(Xd));
    %-- short hand
    L= size(Xd,2);
    T= model.T;
    omega= Xd(5,:);
    tol= 1e-10;
    %-- pre calcs
    sin_omega_T= sin(omega*T);
    cos_omega_T= cos(omega*T);
    a= T*ones(1,L); b= zeros(1,L);
    idx= find( abs(omega) > tol );
    a(idx)= sin_omega_T(idx)./omega(idx);
    b(idx)= (1-cos_omega_T(idx))./omega(idx);
    %-- x/y pos/vel
    X(1,:)= Xd(1,:) + a.*Xd(2,:)- b.*Xd(4,:);
    X(2,:)= cos_omega_T.*Xd(2,:)- sin_omega_T.*Xd(4,:);
    X(3,:)= b.*Xd(2,:) + Xd(3,:) + a.*Xd(4,:);
    X(4,:)= sin_omega_T.*Xd(2,:) + cos_omega_T.*Xd(4,:);
    %-- turn rate
    X(5,:)= Xd(5,:);
    %-- add scaled noise
    X= X + model.B2*V;
end

Running results

References

[1] Qi Bin, Liang Guolong, Zhang Boyu, et al. A multi-target tracking method based on adaptive extended Kalman probability hypothesis density filter: CN202011097165.7[P].CN112328959A[2023-10-30].

[2] Qi Bin, Liang Guolong, Zhang Boyu, et al. A multi-target tracking method based on adaptive extended Kalman probability hypothesis density filter: 202011097165[P][2023-10-30].

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