Fast Track Smoothing Algorithm for Underwater Target Tracking Based on KD Tree

Abstract

A fast-track smoothing algorithm based on the KD Tree is proposed to address the problem of state estimation in underwater multi-target tracking. For multi-target tracking, the multi-Bernoulli filter becomes intractable due to the high-dimensional nature of the posterior. This problem can be overcome by the particle filter (PF), which approximates the posterior by a set of weighted samples (“particles”). The probability distribution of the multi-Bernoulli algorithm based on this algorithm contains a series of particles with weights. Therefore, while smoothing it, the state transfer probability of each particle must be computed, and the state transfer function must be calculated, which is related to the difference in states between the k-1 moment and the k moment, we refer to this difference as the state distance. However, the KD Tree can be used to divide the particle set into different state spaces according to the particle states, and thus calculate the state distances more efficiently. The remarkable feature of this algorithm is that the time complexity is greatly reduced from that O(N2) of the traditional algorithm to O(NlogN). This paper implements the proposed method using particles, the improved algorithm based on KD tree effectively mitigates the disadvantages of previous forward-backward smoothing algorithms, and significantly reduces the computation time while improving the system state estimation precision. Experimental results of simulation analysis and the optimal sub-patten assignment distance is employed as an assessment criterion to validate the algorithm’s performance.