State and parameter estimation for jump Markov linear systems

Abrupt and unexpected changes in system behaviour can often lead to highly undesirable outcomes. For example, mechanical failure of aircraft flight-control surfaces can have devastating consequences if not detected and compensated for. This particular example of change is caused by a system failure or fault, but more generally there are many other possible causes of abrupt change including environmental influences, modified operating conditions, and reconfiguration of system networks. Mitigating the potential impact of these abrupt changes relies on timely and reliable detection of such events. System models that cater for these abrupt changes are often afforded the epithets of either jump or switched to indicate that the system can rapidly change behaviour. Within this broad class of systems are the particular class of interest, jump Markov linear systems (JMLS). The primary reason for restricting our attention to this subclass of systems is that they are relatively simple, and yet offer enough flexibility to model the types of real-world phenomena mentioned above. Despite its apparent simplicity, estimation problems relating to JMLS are traditionally a computationally heavy problem, with various solutions offering compromises between accuracy and algorithm runtime. In this thesis we consider a new system convention called sampled JMLS. This convention is suitable for practical real world robotic applications, as it allows for estimation to be completed by considering noise correlations from integrated sampling and discretisation. This work targets key estimation problems, providing solutions which remove approximations or assumptions, or reduce algorithm runtime when compared to existing approaches. Namely, the thesis provides state inference and parameter identification methods for sampled JMLS, traditional JMLS and the Gaussian mixture model (GMM) sub-class, offering a deep survey of the surrounding literature before offering improvements or removal of assumptions over existing methods. These improvements include the removal of Gaussian assumptions, a new method for handling the likelihood reduction problem, an improved method for faster convergence to the maximum likelihood solution, and a solution to Bayesian unconstrained parameter estimation of multivariate JMLS systems. Some of these advancements are applied to fault diagnosis applications, demonstrating the practicality of the algorithms. Additional contributions include disproving a previously held conjecture about differential entropy during merging processes, convergence analysis, and numerically robust implementation of all algorithms.