Random set tracking and entropy based control applied to distributed sensor networks

Abstract

This paper describes an integrated approach to sensor fusion and resource management applicable to sensor networks. The sensor fusion and tracking algorithm is based on the theory of random sets. Tracking is herein considered to be the estimation of parameters in a state space such that for a given target certain components, e.g., position and velocity, are time varying and other components, e.g., identifying features, are stationary. The fusion algorithm provides at each time step the posterior probability density function, known as the global density, on the state space, and the control algorithm identifies the set of sensors that should be used at the next time step in order to minimize, subject to constraints, an approximation of the expected entropy of the global density. The random set approach to target tracking models association ambiguity by statistically weighing all possible hypotheses and associations. Computational complexity is managed by approximating the posterior Global Density using a Gaussian mixture density and using an approach based on the Kulbach-Leibler metric to limit the number of components in the Gaussian mixture representation. A closed form approximation of the expected entropy of the global density, expressed as a Gaussian mixture density, at the next time step for a given set of proposed measurements is developed. Optimal sensor selection involves a search over subsets of sensors, and the computational complexity of this search is managed by employing the Mobius transformation. Field and simulated data from a sensor network comprised of multiple range radars, and acoustic arrays, that measure angle of arrival, are used to demonstrate the approach to sensor fusion and resource management.