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Parameter estimation problems with singular information matrices

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2 Author(s)
Stoica, Petre ; Dept. of Syst. & Control, Uppsala Univ., Sweden ; Marzetta, T.L.

The case of a singular Fisher information matrix (FIM) represents a significant complication for the theory of the Cramer-Rao lower bound (CRB) that is usually handled by resorting to the pseudoinverse of the Fisher matrix. We take a different approach in which the CRB is derived as the solution to an unconstrained quadratic maximization problem, which enables us to handle the singular case in a simple yet rigorous manner. When the Fisher matrix is singular, except under unusual circumstances, any estimator having the specified bias derivatives that figure in the CRB must have infinite variance

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Signal Processing, IEEE Transactions on  (Volume:49 ,  Issue: 1 )