Joint Maximum a Posteriori - Maximum Likelihood Estimator for Linear Discrete- Time Systems

This paper is concerned with the joint estimation of a hybrid vector with both random and deterministic parameters when a large set of dependent observations is available. This yields the joint Maximum A Posteriori-Maximum Likelihood estimator (MAP/MLE) for which we derive a recursive estimation scheme by leveraging previous results in the deterministic case. The main novelties are the recursive joint MAP-MLE formulation and the derivation of the recursive hybrid Cramér- Rao bound for a mixture of complex and real parameters vector. The relevance of the general bound expressions and the recursive MAP-MLE estimation performance are illustrated with a practical radar estimation problem.