Cubature Kalman Filtering Theory & Applications

Bayesian filtering refers to the process of sequentially estimating the current state of a complex dynamic system from noisy partial measurements using Bayes’ rule. This thesis considers Bayesian filtering as applied to an important class of state estimation problems, which is describable by a discrete-time nonlinear state-space model with additive Gaussian noise. It is known that the conditional probability density of the state given the measurement history or simply the posterior density contains all information about the state. For nonlinear systems, the posterior density cannot be described by a finite number of sufficient statistics, and an approximation must be made instead. The approximation of the posterior density is a challenging problem that has engaged many researchers for over four decades. Their work has resulted in a variety of approximate Bayesian filters. Unfortunately, the existing filters suffer from possible divergence, or the curse of dimensionality, or both, and it is doubtful that a single filter exists that would be considered effective for applications ranging from low to high dimensions. The challenge ahead of us therefore is to derive an approximate nonlinear Bayesian filter, which is theoretically motivated, reasonably accurate, and easily extendable to a wide range of applications at a minimal computational cost.