The Gaussian Mixture Probability Hypothesis Density Filtering Algorithm Research For Extended-target

Extended-target breaks through the traditional point target supposed having at most one observation in every moment, and it is closely related to many practical applications. The traditional data association algorithm will lead to problems such as “combination explosion”, NP-Hard with the increasing of target number or measurements. Probability hypothesis density(PHD) filtering algorithm based on random finite set(RFS) is not a kind of data association algorithm, it avoids the problem of data association effectively, and it can directly estimate the target states and the number of targets jointly through recursion the first-order statistics of posterior probability density, so this algorithm is very suitable for tracking extended-target. Now the existing algorithms with Gaussian mixture PHD(GM-PHD) filter for extended-target are only applicable to system which is the linear Gaussian, and the extended Kalman implementation on the basis of this algorithm can get satisfied filtering accuracy only under the condition of weak nonlinear system, but it cannot deal with the extended-target tracking in strong nonlinear system. In addition, due to every extended-target has multiple observations in every moment, the high dimensional matrix operation is existed in the measurement update process of extended-target.In view of the problems, this thesis is supported by National Natural Science Foundation project “Some Problems Research of Multiple Targets Tracking Method Based on Random Finite Set Theory”(NO.61201118), it is researched on the filtering method for extended-target on the research progress of Gaussian mixture PHD filtering algorithm, combined with the existing nonlinear filtering algorithm and the advantages of centralized fusion algorithm. The specific work of this thesis includes:(1) The GM-PHD filtering algorithm based on Gaussian-Hermite numerical Integration. The existing GM-PHD filter is just applicable to multi-target tracking under the linear Gaussian system, aiming at this, the new filtering algorithm of Gaussian-Hermite PHD is presented combined Gaussian-Hermite numerical integration with GM-PHD filter in the nonlinear system. The Gaussian-Hermite numerical integration method is used to approximate the integrations in the GM-PHD filter in this algorithm. In the filtering stages of prediction and update, we calculate the corresponding Gaussian-Hermite integral points and weights respectively, employ the method of numerical accumulation sum to approximate the integrations of the GM-PHD filter, and then the corresponding Gaussian items are calculated, thereby the recursions of Gaussian mixture are implemented. The new algorithm can estimate not only the state vectors effectively but also get the number of targets accurately at each time in the multiple targets tracking system which is nonlinear, moreover its time complexity increases in a low level. This part work has made bedding for the algorithm research of the next chapter.(2) Extended-target GM-PHD filtering algorithm based on cubature Kalman(CK) filter. Inspired by the idea of previous section to solve the nonlinear problem, in this section, it is proposed a new filtering algorithm: Extended-target PHD filtering algorithm based on the CK filter to solve the problem of extended-target tracking in the nonlinear system. In one step prediction and measurement update, this algorithm adopts a series of cubature points and the corresponding weights to approximate the integrations in the process of PHD respectively, and it estimates the target number by statistics target states on the basis of estimated target states. In guarantee with the same filtering accuracy in existing extended Kalman GM-PHD for extended-target, the error of new algorithm is slightly smaller. In addition, the new algorithm can solve the tracking problems which Jacobian matrix of nonlinear function does not exist or is difficult to solve, this work provides a new approach for the extended-target tracking under the condition of nonlinear Gaussian.(3) The sequential GM-PHD filtering algorithm for extended-target tracking. The dimension of measurement matrix is proportional to the cardinality of the cells which are obtained in the partition stage of existing extended-target PHD filtering algorithm, and this makes some matrixes’ dimension in the update process become larger. But there is problem that high-dimensional matrix computation in the measurement update step of extended-target, especially the operation of the matrix inversion, this spends a lot of time, thereby the computational burden is increasing. Aiming at this, the idea of sequential filter is used to the tracking process of extended-targets, it can reduce the time complexity of matrix inversion effectively. In measurement update step of new algorithm, it does not need to enlarge the dimension of measurement matrix, firstly, it is used the first measurement of the measurements dividing cell to update the PHD in one step prediction, then it is viewed the updated PHD as new prediction PHD at this moment, combined the second measurement of this cell to update, and so on, target state is obtained by the update value of using the last measurement of this cell. The new algorithm can reduce the time complexity effectively and improve the execution efficiency of the algorithm, it provides a new implementation approach for extended-target tracking, meanwhile it maintains the same filtering accuracy of exist algorithm.