Nonlinear Bayesian filtering based on mixture of orthogonal expansions

This dissertation addresses the problem of parameter and state estimation of nonlinear dynamical systems and its applications for satellites in Low Earth Orbits. The main focus in Bayesian filtering methods is to recursively estimate the state a posteriori probability density function conditioned on available measurements. Exact optimal solution to the nonlinear Bayesian filtering problem is intractable as it requires knowledge of infinite number of parameters. Bayes' probability distribution can be approximated by mixture of orthogonal expansion of probability density function in terms of higher order moments of the distribution. In general, better series approximations to Bayes' distribution can be achieved using higher order moment terms. However, use of such density function increases computational complexity especially for multivariate systems. Mixture of orthogonally expanded probability density functions based on lower order moment terms is suggested to approximate the Bayes' probability density function. The main novelty of this thesis is development of new Bayes' filtering algorithms based on single and mixture series using a Monte Carlo simulation approach. Furthermore, based on an earlier work by Culver [1] for an exact solution to Bayesian filtering based on Taylor series and third order orthogonal expansion of probability density function, a new filtering algorithm utilizing a mixture of orthogonal expansion for such density function is derived. In this new extension, methods to compute parameters of such finite mixture distributions are developed for optimal filtering performance. The results have shown better performances over other filtering methods such as Extended Kalman Filter and Particle Filter under sparse measurement availability. For qualitative and quantitative performance the filters have been simulated for orbit determination of a satellite through radar measurements / Global Positioning System and optical navigation for a lunar orbiter. This provides a new unified view on use of orthogonally expanded probability density functions for nonlinear Bayesian filtering based on Taylor series and Monte Carlo simulations under sparse measurements. Another new contribution of this work is analysis on impact of process noise in mathematical models of nonlinear dynamical systems. Analytical solutions for nonlinear differential equations of motion have a different level of time varying process noise. Analysis of the process noise for Low Earth Orbital models is carried out using the Gauss Legendre Differential Correction method. Furthermore, a new parameter estimation algorithm for Epicyclic orbits by Hashida and Palmer [2], based on linear least squares has been developed. The foremost contribution of this thesis is the concept of nonlinear Bayesian estimation based on mixture of orthogonal expansions to improve estimation accuracy under sparse measurements. •.EThOS - Electronic Theses Online ServiceGBUnited Kingdo