| The sequential Monte Carlo method, or particle filtering, is an important methodology for sequential signal processing of time varying systems. In recent years, it has attracted significant attention in the signal processing community. The primary reason for its popularity is its power to cope with nonlinear and non-Gaussian problems. In such problems the often sought posterior distribution is usually not analytically available. However, a standard particle filter can provide a distribution that approximates the posterior with a discrete random measure composed of a set of particles (samples) and weights associated with the particles.;Besides the theoretical developments of these methods, we provide experimental results that demonstrate the superior performance of the proposed algorithms on the problem of target tracking.;The satisfactory performance of standard particle filters comes down to a good choice of proposal density. Here, new proposal densities which are optimized in terms of cross-entropy (CE) measures are proposed. The resulting particle filter with new proposal density is called the cross entropy-based particle filter (CEPF). For problems without probability assumptions, a new class of particle filters, known as cost-reference particle filters (CRPFs), is studied. Unlike standard particle filters, CRPFs recursively explore the state space with particles and associate costs to optimize a user-defined cost function. In this work, we propose a new CRPF algorithm, named regularized CRPF, which uses a generalized cost function. Several new proposing mechanisms for generating particles are investigated as well. |
