A cardinality modified product multi-sensor PHD

•The paper presents an improved product multi-sensor PHD (PM-PHD) algorithm, CM-GM-PHD.•The authors prove that the infinite sums in the update formula of PM-PHD can be approximated by the sum of exact intervals.•The authors propose a cardinality modified method to deal with the inaccurate state estimation of PM-PHD.

The iterated-corrector PHD (IC-PHD) filter, which is the most commonly used multi-sensor PHD filter, is affected by the sensor order and the probability of detection. To address this problem, the product multi-sensor PHD (PM-PHD) filter, a modified version of the IC-PHD filter, is proposed. The update formulation of the PM-PHD filter consists of a likelihood function and a modified coefficient. Although the coefficient improves the performance of the PM-PHD filter, it still has some drawbacks. In this paper, two improvements on the coefficient are proposed. (1) The coefficient is the quotient of two infinite sums which are computational intractable. We prove that some terms in the infinite sums can be eliminated, and thus the infinite sums can be approximated by the sum of finite terms. (2) Since the coefficient is a scalar quantity, it mainly focuses on maintaining the magnitudes of the posterior PHD and the number of targets. It may lead to an inaccurate state estimation in some situations. In the Gaussian mixture implementation of the PM-PHD filter, a cardinality modified method is proposed to reassign the weight of Gaussian components and modify the posterior PHD. The advantages of these two methods are verified by simulations and experiments.