Traditional sequential Monte-Carlo methods suffer from weight degeneracy which is where the number of distinct particles collapse. This is a particularly debilitating problem in many practical applications. A new method, the adaptive path particle filter, based on the generation gap concept from evolutionary computation, is proposed for recursive Bayesian estimation of non-linear non-Gaussian dynamical systems. A generation-based path evaluation step is embedded into the general sequential importance resampling algorithm leveraging the descriptive ability of discarded particles. A simulation example of the stochastic volatility problem is presented. In this simulation, the adaptive path particle filter is greatly superior to the standard particle filter and the Markov chain Monte-Carlo particle filter. We present a detailed analysis of the results, and suggest directions for future research.
Recursive Bayesian estimation using sequential Monte Carlos methods is a powerful numerical technique to understand latent dynamics of nonlinear non-Gaussian dynamical systems. It enables us to reason under uncertainty and addresses shortcomings underlying deterministic systems and control theories which do not provide su±cient means of performing analysis and design. In addition, parametric techniques such as the Kalman¯lter and its extensions, though they are computationally e±cient, do not reliably compute states and cannot be used to learn stochastic problems. We review recursive Bayesian estimation using sequential Monte Carlo methods highlighting open problems. Primary of these is the weight degeneracy and sample impoverishment problem. We proceed to detail synergistic computational intelligence sequential Monte Carlo methods which address this. We¯nd that imbuing sequential Monte Carlos with computational intelligence has many advantages when applied to many application and problem domains.
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