A multi-parameter hybrid Barankin-type bound

We use the term hybrid parameter vector to refer to a vector which consists of both random and non-random parameters. We present a novel Barankin-type lower bound which bounds the estimation error of a hybrid parameter vector. The bound is expressed in a simple matrix form which consists of a non-Bayesian bound on the non-random parameters, a Bayesian bound on the random parameters, and the cross terms. We show that the non-Bayesian Barankin (1949) bound for deterministic parameters estimation and the Bobrovsky-Zakai (1976) Bayesian bound for random parameters estimation are special cases of the new bound. Also, the multi-parameter Cramer-Rao bound, in its Bayesian or non-Bayesian versions, are shown to be special cases of the new bound