In certain applications, the performance objectives of a Kalman filter (KF) are to compute unbiased, minimum variance estimates of a state mean vector governed by a stochastic system. The KF can be considered as a model based algorithm used to recursively estimate the state mean vector and state covariance matrix. The general objective of this thesis is to investigate the performance limitations of the KF in three state vector estimation applications.

Stochastic observability is a property of a system and refers to the existence of a filter for which the errors of the estimated state mean vector have bounded variance. In the first application, we derive a test to assess the stochastic observability of a KF implemented for discrete linear time-varying systems consisting of known, deterministic parameters. This class of system includes discrete nonlinear systems linearized about the true state vector trajectory. We demonstrate the utility of the stochastic observability test using an aided INS problem.

Attitude determination systems consist of a sensor set, a stochastic system, and a filter to estimate attitude. In the second application, we design an inertially aided (IA) vector matching algorithm (VMA) architecture for estimating a spacecraft's attitude. The sensor set includes rate gyros and a three-axis magnetometer (TAM). The VMA is a filtering algorithm that solves Wahba's problem. The VMA is then extended by incorporating dynamic and sensor models to formulate the IA VMA architecture. We evaluate the performance of the IA VMA architectures by using an extended KF to blend post-processed spaceflight data.

Model predictive control (MPC) algorithms achieve offset-free control by augmenting the nominal system model with a disturbance model. In the third application, we consider an offset-free MPC framework that includes an output integrator disturbance model and a KF to estimate the state and disturbance vectors. Using root locus techniques, we identify sufficient conditions for a class of nominal systems with at least one real pole for which the observer poles can not be arbitrarily selected. We present several examples illustrating the limitations of the observer pole locations.