New alternative derivations of Cramer–Rao bound for equality‐constrained estimation
Xi Li, Yi Liu, Le Yang · Electronics Letters · 2021
Abstract This paper presents new alternative derivations of the well‐known constrained Cramr–Rao bound for estimating parameters that satisfy a set of deterministic and differentiable equality constraints. Specifically, for unbiased parameter estimation, the equality constraints are treated as pseudo‐measurements corrupted by independent zero‐mean Gaussian noise with infinitely small covariance. In this way, the desired constrained Cramr–Rao bound can be established via utilising the property that the Fisher information matrices for independent measurements are additive. This paper also provides a new simple way for deriving the constrained Cramr–Rao bound when the parameter estimate has a specified bias through exploring that the estimation error lies in the null space of the gradient matrix of the constraints and invoking the Cauchy–Schwarz inequality.