On Combining Statistical and Set-Theoretic Estimation

We consider state estimation based on observations which are simultaneously corrupted by a deterministic amplitude-bounded unknown bias and a possibly unbounded random process. This problem is solved by developing a combined set-theoretic and Bayesian recursive estimator. The new estimator provides a continuous transition between both concepts in that it converges to a set-theoretic estimator when the stochastic error vanishes and to a Bayesian estimator when the deterministic error vanishes. In the mixed noise case, the new estimator supplies solution sets defined by bounds that are uncertain in a statistical sense.