Dicing algorithm for the degeneracy problem of the sequential importance sampling in the sequential Monte Carlo Methods

Abstract

Many problems in science and engineering require estimation of unknown quantities from a sequence of noisy and partial observations. In most cases, the problems can be easily solved, from a theoretical perspective, within a sequential Bayesian inference framework such that the unknown quantities can be inferred from posterior distributions that are recursively computed by the prior distributions of the unknown quantities and the likelihood functions of the observations. In practice, however, numerical approximate techniques are necessary due to the computational intractability of the theoretical methods. As one of the approximate techniques, Sequential Monte Carlo (SMC) methods are a class of simulation-based methods designed to use random samples to recursively simulate the posterior distributions. Over the last few years, the methods have become extremely popular with their supportability of both nonlinearity and non-Gaussianity allowing the problems to be much more realistically modeled. The basis of SMC methods is a Sequential Importance Sampling (SIS) algorithm that is a sequential version of an Importance Sampling (IS) algorithm in Monte Carlo (MC) methods. Because of the degeneracy problem of the SIS scheme, however, SMC methods only using SIS do not provide good estimation performance. To solve this problem, a Resampling algorithm is generally used. Even though it has some limitations such as the loss of diversity problem, there have been no better alternatives to the resampling scheme with respect to estimation accuracy, computational cost and algorithmic efficiency. As a result, the combination of SIS and resampling has been widely regarded as generic SMC methods in the most of literature and many advanced versions developed from the generic methods have been proposed for some improvements of the generic ones. In this thesis, we propose a novel algorithm, called Dicing, designed to not only solve the degeneracy problem of the SIS but also avoid ...