State Estimation Based on Observations Simultaneously Corrupted by Random Noise with Known Distribution and Uncertainties with Known Bounds

This paper presents a new approach for estimating the state of a linear dynamic system when two different types of uncertainties are present simultaneously. The first type of uncertainty is a stochastic process with given distribution. The second type of uncertainty is only known to be bounded, the exact underlying distribution is unknown. This includes inequality constraints between state variables, geometric tolerances, and bounded noise sources which are possibly correlated. For this generalized uncertainty model, a new recursive estimator has been developed. The new estimator unifies Kalman filtering and set theoretic filtering. It converges to a Kalman filter, when the bounded uncertainty goes to zero, and it converges to a set theoretic filter, when the stochastic noise vanishes. In the case of mixed uncertainties, the new estimator provides solution sets that are uncertain in a statistical sense.