Multiple model estimation for linear stochastic hybrid systems with non-homogeneous transition probabilities

Abstract

This thesis investigates the field of stochastic hybrid estimation. A broad introduction to the framework surrounding estimation, filtering, and multiple model based systems is presented. More specifically, the often made assumption of a constant time-invariant mode transition probability matrix is relaxed. Recent work done in the area of non-Markov jump stochastic hybrid systems is explored, including semi- Markov systems, non-homogeneous transition probability matrices, and continuous-state-dependent mode transitions. Algorithms needed to develop linear multiple model based filters with non-homogeneous transition probabilities are detailed. Finally, a case study for the practical implementation of an extended Kalman filter in the application of attitude heading and reference systems is conducted.