State Estimation in Systems with Random Coefficients

State estimation in dynamical systems with randomly switching coefficients is an important problem with a variety of applications. The most commonly met problems that are formulated within the random coefficients state-space approach, are maneuvering target tracking and fault-tolerant filtering. A related class of problems is referred to as data association or data ambiguity.
In this family, the estimation process is further complicated by the fact that the acquired data has uncertain origin. Typical applications include target tracking in clutter and multiple target tracking.  In this talk we aim at deriving a unified framework for state estimation problems under data and model uncertainties. First, we present the problem of tracking a maneuvering target restricted to perform a bounded number of maneuvers and show that, despite the inherent deviation from the standard Markov switching assumption underlying most state-of-the-art algorithms, it may be reformulated and solved using a generalized version of such tools. We proceed with an overview of linear minimum mean-square error (LMMSE) algorithms for state estimation in systems with random coefficients. We show that the novel formulation allows treatment of problems that have not been addressed in the LMMSE sense in the past. These include target tracking in clutter and multiple target tracking. Finally, we present a general framework, accompanied by a variety of applications, which allows a utilization of a single IMM-like algorithm to solve a variety of state estimation problems.  These include maneuvering target tracking, clutter and data association, multiple target tracking, tracking of splitting targets and more. In some cases it will be shown that the resulting unified IMM-like filter reduces to some classical algorithms such as PDA and JPDA.