Stable recursive estimators for systems with multiple models

In many practical situations, such as target tracking of manoeuvring objects and fault detection, one is faced with the task of estimating the state of the system when the model describing the evolution of the system changes abruptly. In this paper we develop an approach for estimating state for systems where the model at any given time is from a finite set of models, though one does not know which model is applicable at any given time. We provide sufficient conditions that guarantee the stability of the filter and at the same time provide a measure of performance of the filter compared to the case when the model is known. The algorithm is easy to implement and does not suffer from combinatoric complexity of considering all trajectories of models. The algorithm involves a set of parallel Kalman filters (one for each possible model) and a linear matrix inequality (LMI) based "mixing" of estimates at every stage.