A combined MAP and Bayesian scheme for finite data and/or moving horizon estimation

Finite data and moving horizon estimation schemes are increasingly being used for a range of practical problems. However, both schemes suffer from potential conceptual difficulties. In the case of finite data, most of the methods in common use, excluding Bayesian strategies, depend upon asymptotic results. On the other hand, in the case of moving horizon estimation, there are two associated problems, namely (i) estimation error quantification is typically not available as a part of the solution and (ii) one needs to provide some form of prior state estimate (the so-called arrival cost). The current paper proposes a combined MAP–Bayesian scheme which, inter alia, addresses the finite data and moving horizon problems described above. The scheme combines MAP and Bayesian strategies. The efficacy of the method is illustrated via numerical examples.