Nonlinear Filtering With Applications To Tracking And Guidance

Kalman filter is the analytical recursive solution for optimal filtering of linear-Gaussian systems. For nonlinear/non-Gaussian cases, such a perfect analytical solution is intractable. Since most practical physical systems are nonlinear, nonlinear filtering is an important research theme in both theory and applications. Under the background of homing missile guidance, this thesis studies the optimal filtering for discrete-time nonlinear systems.First, based on the recursive Bayesian filtering equation, two classes of estimation approach, Gaussian filters and particle filters, for general Markov systems are described. Gaussian filters have the advantages of simple formulation and computational efficiency. However, their precision and consistency are often limited due to the Gaussian assumption to the state distribution. Currently, the most popular and widely used Gaussian-type algorithms are still the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Therefore, some compensation procedures are considered to reduce the errors in the EKF and the UKF. For particle filters, the degeneracy and sample impoverishment problems are investigated from the perspective of Monte Carlo integration. The methods for improving the sampling efficiency are also discussed.Second, the optimal filtering for a class of Markov switching systems (MSS) is investigated. Correspondingly, the recursive Bayesian filtering equation for the systems is derived, from which two deductions are obtained, i.e., interacting multiple model recursive Bayesian filtering equation and static multiple model recursive Bayesian filtering equation. Based on Gaussian assumptions, two classes of multiple model Gaussian filters are then given from the deductions, which extend the classical IMM and MMAE algorithms to a general case. Moreover, by means of Monte Carlo method, two new algorithms, i.e., interacting multiple model particle filter and static multiple model particle filter, are given for system with modes that are highly nonlinear and/or non-Gaussian.In applications, it is of great importance to develop a robust and fast tracking algorithm in bearings-only measurement system because of its inherent disadvantages such as large initial errors and weak observability. In view of this, a novel algorithm, referred to as two-step sigma point filter, is proposed based on least-squares principle. The algorithm improves the traditional two-step estimator by employing unscented transformation and statistical linearization techniques. Moreover, a modified Sage-Husa time-varying measurement noise statistical estimator is integrated with the two-step sigma point filter to produce an adaptive version, which can handle nonlinear filtering in the presence of unknown measurement noise statistics.In infrared homing guidance, the seeker angular measurements are subject to occasional large noise spikes or outliers, which may affect the tracking performance severely. As spiky noise can be modeled as mixture distribution and linear subsection can be separated from the dynamic models, the technique of Rao-blackwellization is adopted to derive a simplified IMM-based marginalized particle filter. A numerical example on bearings-only tracking in spiky environments demonstrates the effectiveness of the proposed algorithm.Finally, the problem of intercepting a randomly maneuvering tactical ballistic missile (TBM) in the terminal phase is considered. In such situation, multiple model approach and unscented transformation technique are utilized to design the tracking filter. Based on the exploitation of the escape strategy characteristics of maneuvering TBM, the traditional multiple model adaptive estimation is further simplified by means of aggregation and pruning, thus leading to a fast effective version for multiple model adaptive estimation.