A BARANKIN-TYPE LOWER-BOUND ON THE ESTIMATION ERROR OF A HYBRID PARAMETER VECTOR

The Barankin bound is a realizable lower bound on the mean-square erro r (mse) of any unbiased estimator of a (nonrandom) parameter vector. I re this correspondence we present a Barankin-type bound which is usefu l in problems where there is a prior knowledge on some of the paramete rs to be estimated. That is, the parameter vector is a hybrid vector i n the sense that some of its entries are deterministic while other are random variables. We present a simple expression for a positive-defin ite matrix which provides bounds on the covariance of any unbiased est imator of the nonrandom parameters and an estimator of the random para meters, simultaneously. We show that the Barankin bound for determinis tic parameters estimation and the Bobrovsky-Zakai bound for random par ameters estimation are special cases of our proposed bound.