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Performance of Maximum Likelihood Estimators of Mean Power and Doppler Velocity with A Priori Knowledge of Spectral Width

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  • 1 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado
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Abstract

The performance of the maximum likelihood (ML) estimates of mean velocity and signal power for Doppler radar and Doppler lidar, assuming known signal spectral width, is presented. The results are compared with the theoretical limit of the Cramer–Rao bound (CRB). The performance of the ML estimator for mean velocity is similar to the performance when the signal power is known ahead of time. For cases of very high signal-to-noise ratio (SNR) and typical values of the spectral width, the performance of the maximum likelihood estimator of signal power, assuming known spectral width, does not approach the CRB for the limit of infinite SNR. The ML estimates of mean power for Doppler radar operated in Doppler lidar mode are more accurate than are traditional estimates.

Corresponding author address: Dr. Rod Frehlich, CIRES Campus Box 216, University of Colorado, Boulder, CO 80309.

Email: rgf@cires.colorado.edu

Abstract

The performance of the maximum likelihood (ML) estimates of mean velocity and signal power for Doppler radar and Doppler lidar, assuming known signal spectral width, is presented. The results are compared with the theoretical limit of the Cramer–Rao bound (CRB). The performance of the ML estimator for mean velocity is similar to the performance when the signal power is known ahead of time. For cases of very high signal-to-noise ratio (SNR) and typical values of the spectral width, the performance of the maximum likelihood estimator of signal power, assuming known spectral width, does not approach the CRB for the limit of infinite SNR. The ML estimates of mean power for Doppler radar operated in Doppler lidar mode are more accurate than are traditional estimates.

Corresponding author address: Dr. Rod Frehlich, CIRES Campus Box 216, University of Colorado, Boulder, CO 80309.

Email: rgf@cires.colorado.edu

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