Abstract

A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets’ numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets’ intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.

Highlights

  • Analogous to extended Kalman filter (EKF), the linear and Gaussian cardinalized probability hypothesis density (CPHD) recursion is extended to the nonlinear model by linearizing the nonlinear bearing and Doppler measurement function ht,m

  • The greatest merits of passive sonar target tracking are that the passive sonar tracking system is simple and low cost, and can operate covertly due to the use of passive bearing and Doppler measurements

  • The EKF is applied to solve the nonlinearity of bearing and Doppler measurements

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Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In this paper we apply the EKF to deal with the nonlinear bearing and Doppler measurements Another difficulty associated with passive multiple underwater target tracking is the data association uncertainties between targets and measurements [16]. The multiple target tracking problem has been solved by the maximum entropy intuitionistic fuzzy data association algorithm [29], cross entropy [30], maximum-fuzzyentropy-based Gaussian clustering algorithm [31], entropy distribution and game theory based on the random finite set probability hypothesis density (PHD) method [32], maxi-. In this paper we investigate the tracking performance of CPHD recursion in passive underwater multiple target tracking in the two-dimensional state space under a cluttered environment, using bearing and Doppler measurements.

System Model
Measurement Model
RFS Formulation of Multiple Target Filtering
CPHD Recursion
EKF-Based CPHD Recursion
Scans of the average OSPA localization for four targets versus time for the E
Conclusions
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