Sequential Monte Carlo filtering with Gaussian mixture models for highly nonlinear systems

This dissertation presents two different Bayesian approaches for highly nonlinear systems with a theoretical study on combining the benefits of the Gaussian sum filter and particle filter; the posterior particles of a particle filter are drawn from a Gaussian mixture model approximation of the posterior distribution. The first approach introduces the methods which change each and every particle of a particle filter into a Gaussian mixture component, either using the properties of Dirac delta function or using kernel density estimation; the former treats each particle of the prior distribution as a Gaussian component with a collapsed zero covariance matrix and the latter estimates the covariance matrix of a Gaussian component using the kernel density estimation algorithm. The Gaussian sum filter is then used to calculate the posterior distribution. The second approach uses clustering algorithms. These clustering algorithms are used to recover Gaussian mixture model representation of the prior probability density function from the propagated particles. The expectation-maximization clustering algorithm and modified fuzzy C-means clustering algorithms are applied to this approach. Under the scenarios considered in this study, it is shown through numerical simulations that the proposed algorithms lead to better performances than the existing algorithms such as Gaussian sum filters and particle filters.