Fusing information simultaneously corrupted by uncertainties with known bounds and random noise with known distribution

Abstract

A new algorithm is derived for estimating the state of a linear dynamic system by fusing uncertain observations, which suffer from two types of uncertainties simultaneously. The first uncertainty is a stochastic process with given distribution. The second uncertainty is only known to be bounded, the exact underlying distribution is unknown. The new fusion algorithm combines set theoretic and stochastic estimation in a rigorous manner and provides a continuous transition between the two classical information fusion concepts. It converges to a set theoretic estimator, when the stochastic error goes to zero, and to a Kalman filter, when the bounded error vanishes. In the mixed noise case, solution sets are provided that are uncertain in a stochastic sense.