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 e stimator when the deterministic error vanishes. In the mixed noise case, th e new estimator supplies solution sets defined by bounds that are uncertain in a statistical sense. (C) 1999 Elsevier Science Ltd. All rights reserved .