On information measures based on particle mixture for optimal bearings-only tracking

In this work we consider a target tracking scenario where a moving observer with a bearings-only sensor is tracking a target. The tracking performance is highly dependent on the trajectory of the sensor platform, and the problem is to determine how it should maneuver for optimal tracking performance. The problem is considered as a stochastic optimal control problem and two sub-optimal control strategies are presented based on the Information filter and the determinant of the information matrix as the optimization objective. Using the determinant of the information matrix as an objective function in the planning problem is equivalent to using differential entropy of the posterior target density when it is Gaussian. For the non-Gaussian case, an approximation of the differential entropy of a density represented by a particle mixture is proposed. Furthermore, a gradient approximation of the differential entropy is derived and used in a stochastic gradient search algorithm applied to the planning problem.