General Bernoulli Filter for Arbitrary Clutter and Target Measurement Processes

Abstract

The Bernoulli filters are a class of the optimal single-target Bayesian filter. In the classical Bernoulli filter, the clutter process can be arbitrary but the target must be a point target. However, if the target is an extended target or there are multiple propagation paths between the sensor and the target, the measurement process becomes more complicated and single target may produce multiple detections at one scan. Unlike the classical Bernoulli filter, the extended target Bernoulli filter and the multipath Bernoulli filter can be applied to a scenario in which a single target produces multiple detections. However, the clutter process is assumed to be Poisson in these filters. In this letter, the general Bernoulli filter, in which both the clutter and target measurement processes are allowed to be arbitrary, is proposed. The derivation of the filter is on the basis of the probability generating functional in the finite set statistics. In specific circumstances, the general Bernoulli filter can reduce to the classical Bernoulli filter or the multipath Bernoulli filter. In simulation, the measurement model of over-the-horizon radar is used. Simulation results show that the proposed filter can be applied to more general tracking scenarios.