Multiple-model Bernoulli filters—part I: A Gaussian mixture implementation

The Bernoulli filter is an exact Bayesian filter for target tracking under the framework of random finite sets. It has been implemented by using Gaussian mixture (GM) and sequential Monte Carlo (SMC) techniques for joint target detection and tracking. However, a single model is not enough to accommodate a maneuvering target that switches between a set of motion models. In this paper, we extend the Bernoulli filter to switching motion models, and propose a multiple-model (MM) Bernoulli filter for a maneuvering target. Then we give a GM implementation of the MM Bernoulli filter for linear Gaussian models. Finally, a numerical example is presented to verify the effectiveness of the GM-MM Bernoulli filter for a maneuvering target.