Multiple‐model Gaussian mixture probability hypothesis density filter based on jump Markov system with state‐dependent probabilities

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Abstract
The Gaussian mixture probability density (GM‐PHD) filter has become a popular approach to solve the multiple‐target tracking (MTT) problem because it can effectively and efficiently estimate the number of targets and target states that change over time from noisy measurements. In the GM‐PHD filter, the target detection and survival probabilities, and the birth rate are assumed to be constant, irrespective of the target state. However, in some applications, for example, when the target follows the planned trajectory, the detection, survival and birth of the target depend on its state. Besides, when the target reaches a waypoint along the planned trajectory, it will take a manoeuvre to go to the next waypoint, but the GM‐PHD filter does not accommodate manoeuvring targets that switch between several motion models. To address this, we propose a multiple‐model GM‐PHD filter with state‐dependent probabilities, which can explicitly consider the mode transition probabilities, the probabilities of detection and survival, and the birth rate as a function of the target state. The performance of the proposed algorithm is demonstrated by illustrative MTT scenarios which include target manoeuvres during occlusion.

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