Linear Recursive State Estimators under Uncertain Observations.

摘要

For linear systems with uncertain observations, the existence of recursive least-squares state estimators is investigated. Uncertain observations resulting from a binary switching sequence gamma sub k, which is specified by a conditional probability distribution and which enters the observation equation as z sub k = gamma sub k H sub k x sub k + v sub k is considered. Conditions are established which lead to a recursive filter for x sub k; if they are not met, as for example when gamma sub k is Markovian, no linear recursive structure can be found. On the other hand, if the sequence gamma sub k is independent identically distributed (i.i.d.), then these conditions are satisfied and a linear recursive filter exists.