The Asymptotic Cramér-Rao Bound for 2-D Superimposed Exponential Signals

Authors:
Amit Mitra;Petre Stoica
Affiliations:
Department of Statistical Analysis & Computer Services, Reserve Bank of India, Mumbai-400 051, India;Department of Systems & Control, Uppsala University, P.O. Box 27, SE-751 03 Uppsala, Sweden
Venue:
Multidimensional Systems and Signal Processing
Year:
2002

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Abstract

The problem of estimating the parameters of complex-valued two-dimensional (2-D) exponential signals corrupted by noise occurs in many signal processing applications. In this paper we derive a simple and easily interpretable expression for the asymptotic Cramér-Rao bound (CRB) matrix associated with this problem. The Maximum Likelihood (ML) method attains the performance corresponding to the asymptotic CRB as the dimensions of the observed field increase. Furthermore, the Nonlinear Least Squares (NLS) method, which ignores the possible correlation of the noise, achieves the same performance as the ML method in large samples.