Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Approximate bounds on frequency estimates for short cisoids incolored noise
IEEE Transactions on Signal Processing
Approximate maximum likelihood estimators for array processing inmultiplicative noise environments
IEEE Transactions on Signal Processing
Theory and application of covariance matrix tapers for robustadaptive beamforming
IEEE Transactions on Signal Processing
Frequency estimation in the presence of Doppler spread: performanceanalysis
IEEE Transactions on Signal Processing
Parameter estimation problems with singular information matrices
IEEE Transactions on Signal Processing
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We discuss the asymptotic Cramer-Rao bound (CRB) for frequency estimation in the presence of multiplicative noise. To improve numerical stability, covariance matrix tapering is employed when the covariance matrix of the signal is singular at high SNR. It is shown that the periodogram-based CRB is a special case of frequency domain evaluation of the CRB, employing the covariance matrix tapering technique. Using the proposed technique, large sample frequency domain CRB is evaluated for Jake's model. The dependency of the large sample CRB on the Doppler frequency, signal-to-noise ratio, and data length is investigated in the paper. Finally, an asymptotic closed form CRB for frequency estimation in the presence of multiplicative and additive colored noise is derived. Numerical results show that the asymptotic CRB obtained in frequency domain is accurate, although its evaluation is computationally simple.