A particle algorithm for sequential Bayesian parameter estimation and model selection

We describe a particle algorithm for the sequential Bayesian estimation of unknown static parameters. The algorithm combines sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC) to achieve computational efficiency and stability. In its most general form, the algorithm has three components: i) SIS; ii) a rejuvenation test; and iii) MCMC. Measurements are processed sequentially (with an artificial "time-line" if there is no natural one associated with the measurements) by SIS, which is computationally inexpensive. After each measurement is processed, the rejuvenation test checks whether the resulting SIS particles have to be rejuvenated. When indicated by the test, the particles are completely rejuvenated by MCMC, which removes errors that accumulate from SIS due to the finite number of particles, thus ensuring stability. Whenever possible, the SIS particles can be used to advantage in the MCMC. There is flexibility in the choice of the rejuvenation test as well as the MCMC method, with potential to increase the usefulness of the algorithm. In particular, by using reversible-jump MCNIC with multiple models, the algorithm can perform simultaneous model selection and parameter estimation. In this paper, we use a rejuvenation test based on a Kullback-Leibler distance that is easy to compute, and our choice of MCNIC is independent Metropolis-Hastings with a Gaussian proposal density. With these choices, we illustrate the use of the algorithm in two signal processing applications (passive source localization with angle-of-arrival and simultaneous weak signal detection and parameter estimation) involving both simulated and real data. The results demonstrate the algorithm's stability, its built-in protection against model overfitting, and tolerance to model mismatch.