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Estimation problems in systems with Markovian jumps


E. Cinquemani

Dipartimento di Informatica e Sistemistica, Universita' di Pavia (Italy)

Switching dynamic models are frequently used in modern engineering applications. Yet there are modelling issues and several theoretical properties that are still open for investigation. In this talk, we address estimation problems for linear stochastic state-space models whose parameters jump in time among values in a finite known set. Current parameters are determined by the value of a discrete state, whose evolution follows the laws of a finite Markov chain. First, we consider systems with continuous-time dynamics and sampled measurements. In this model, switches are determined by a continuous-time chain, hence they may occur between measurements. This provides an accurate description of scenarios of interest e.g. in medicine, biology and automated surveillance. Yet it makes state estimation a challenging task. For the basic setting where one jump to an unknown discrete state occurs at an unknown time, we present an algorithm that yields optimal estimates of the switching time and of the system's state at low computational cost. Next, we move to discrete-time switching models and focus on the online estimation of the trajectory followed by the discrete state. We discuss certain fundamental limitations that affect a Bayesian solution of the problem, and outline alternative estimation strategies.


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