PHD and CPHD Algorithms Based on a Novel Detection Probability Applied in an Active Sonar Tracking System

Underwater multi-targets tracking has always been a difficult problem in active sonar tracking systems. In order to estimate the parameters of time-varying multi-targets moving in underwater environments, based on the Bayesian filtering framework, the Random Finite Set (RFS) is introduced to multi-targets tracking, which not only avoids the problem of data association in multi-targets tracking, but also realizes the estimation of the target number and their states simultaneously. Usually, the conventional Probability Hypothesis Density (PHD) and Cardinalized Probability Hypothesis Density (CPHD) algorithms assume that the detection probability is known as a priori, which is not suitable in many applications. Some methods have been proposed to estimate the detection probability, but most assume that it is constant both in time and surveillance region. In this paper, we model the detection probability through the active sonar equation. When fixed the false detection probability, we can get the analytic expression for the detection probability, which is related to target position. In addition, this novel detection probability is used in PHD and CPHD algorithms and applied to underwater active sonar tracking systems. Also, we use the adaptive ellipse gate strategy to reduce the computational load in PHD and CPHD algorithms. Under the linear Gaussian assumption, the proposed detection probability is illustrated in both Gaussian Mixture Probability Hypothesis Density (GM-PHD) and Gaussian Mixture Cardinalized Probability Hypothesis Density (GM-CPHD), respectively. Simulation results show that the proposed Pd-GM-PHD and Pd-GM-CPHD algorithms are more realistic and accuratein underwater active sonar tracking systems.