Nonlinear filtering for stochastic hybrid and nonlinear systems with applications to target tracking

This dissertation addresses estimation and filtering problems that can be modeled or analyzed in a switching systems context. Switching systems are systems that experience abrupt random changes in their structure or parameters at unknown time instants. Examples of such systems include rapidly fading communications channels, unexpected jamming in radar and communications systems, any system with unreliable sensors, and maneuvering airborne targets. In Chapter 3, we present a new technique, based on information theoretic measures, for the analysis of the observability level of stochastic switching systems. Unlike other procedures, this formulation does not assume that the jump sequence is perfectly observed on-line. Chapter 4 develops an extension of the standard filtering and estimation techniques for hybrid systems from their application to switching systems to their application to a broad class of nonlinear systems. This work provides a systematic design technique for developing sub-optimal filters for many nonlinear stochastic systems. Several examples are provided which validate the efficacy of the filter for a number of different nonlinear system and measurement functions. In Chapter 5 we provide a background to the radar tracking problem, and apply switched-Markov filtering techniques to the problem of tracking a maneuvering airborne target. It is shown that targets travelling along straight-and-level trajectories induce false accelerations in the polar (measurement) coordinate system that are nonlinear functions of the system state. New contributions in this chapter include the development of two new target models. The first target model models target maneuvers as unknown control inputs. The system matrix is formulated to allow the consistency update stage of the new filter to be applied in the filter aggregation stage. Using this model, a new tracking algorithm was developed to perform 3-dimensional target tracking of maneuvering targets. In the second model, a polar coordinate system is assumed, and target acceleration is formulated as a nonlinear function of the system state. A new tracking filter is developed which exploits this nonlinear relationship. Several examples are provided and the new filter performance is compared to that of an extended Kalman filter.