Combined stochastic and set-membership information filtering in multisensor systems

In state estimation theory, stochastic and set-membership approaches are generally considered separately from each other. Both concepts have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. In order to better utilize the potentials of both concepts, the core element of this paper is a Kalman filtering scheme that allows for a simultaneous treatment of stochastic and set-membership uncertainties. An uncertain quantity is herein modeled by a set of Gaussian densities. Since many modern applications operate in networked systems that may consist of a multitude of local processing units and sensor nodes, estimates have to be computed in a distributed manner and measurements may arrive at high frequency. An algebraic reformulation of the Kalman filter, the information filter, significantly eases the implementation of such distributed fusion architectures. This paper explicates how stochastic and set-membership uncertainties can simultaneously be treated within this information form and compared to the Kalman filter, it becomes apparent that the quality of some required approximations is enhanced.