Recursive algorithms for computing the Cramer-Rao bound

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. For a large class of inverse problems, we show that nonmonotone Gauss-Seidel and preconditioned conjugate gradient algorithms require significantly fewer flops for convergence than monotone "bound preserving" algorithms.