On the Cramér-Rao Bound Under a Linear Transformation of the Parameter

Hai Victor Habi, Hagit Messer, Shay Sagiv, Joseph Tabrikian

Abstract: This paper deals with the case where the Crarnér-Rao bound (CRB) on the estimation error of a deterministic parameter vector is given, and it is desired to evaluate a bound on a linear transformation of it. The literature suggests two versions of the bound on the estimation error of the reparameterized vector, denoted by $B_{1}$ and $B_{2}$. We first identify the conditions under which either of these bounds exist, focusing on the case where they co-exist, Under such scenario, we find the relations between $B_{1}, B_{2}$, and $CRB$. The results are demonstrated on two practical applications of multi-sensor signal processing.