| State estimation for nonlinear dynamic systems from noisy, nonlinear observations is the topic of this dissertation. The optimal filter for these systems is well known but is, in general, unrealizable. In its place the sub-optimal extended Kalman filter (EKF) and iterated extended Kalman filter (IKF) are commonly used in practice. In some cases these filters fail to produce accurate estimates. In this dissertation we provide a modified derivation of the EKF and IKF and use it to identify some of the causes of poor performance encountered with the EKF and IKF. In addition, we use the insight provided by this modified derivation to generate a new iterated filter which is less susceptible to these problems. The new iterated filter, based on the Levenberg-Marquardt algorithm and a discrete probability mass function approximation to the standard Gaussian, prevents some types of filter divergence and may even permit an extension of the sampling period beyond the limits encountered with the EKF and IKF. Five target tracking examples are used to compare the performance of the EKF and IKF with the new iterated filter.; The optimal filter for two nonlinear and non-Gaussian system models is also presented in this dissertation. These new results in optimal filtering are derived from a Bayesian interpretation of the Kalman filter paradigm, experience with the sub-optimal filtering problem, and tools from mathematical statistics. The extension of these preliminary results to more general system models is proposed as a topic of future research. |
