Biasing of the Covariance-Based Spectral Mean Estimator in the Presence of Band-Limited Noise

Albert J. Plueddemann Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Robert Pinkel Marine Physical Laboratory of the Scripps Institution of Oceanography, La Jolla, California

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Abstract

Estimation of spectral mean frequency (spectral first moment) by the variance technique is considered for a signal process contaminated by band limited, additive noise. It is shown that the covariance-based spectral mean estimator is biased for low signal-to-noise ratios if the noise bandwidth is not large compared to the signal bandwidth. The bias is towards the mean frequency of the noise spectrum, typically equivalent to the center of the frequency band passed by the receiver. This noise-biasing is potentially important in the processing of Doppler data from radars, sodars and sonars operating in a pulse-to-pulse incoherent mode. Biasing of the mean frequency estimator can be easily corrected if measurements of the noise covariance are available. In the absence of noise measurements, correction for biasing can still be accomplished by estimating the signal and noise bandwidths and introducing simple models for the signal and noise covariance functions. This technique allows estimation of noise covariance from measurements of signal-plus-noise covariance at more than one time lag. In addition, the models provide a means or predicting potential biasing problems in a generalized Doppler system.

Abstract

Estimation of spectral mean frequency (spectral first moment) by the variance technique is considered for a signal process contaminated by band limited, additive noise. It is shown that the covariance-based spectral mean estimator is biased for low signal-to-noise ratios if the noise bandwidth is not large compared to the signal bandwidth. The bias is towards the mean frequency of the noise spectrum, typically equivalent to the center of the frequency band passed by the receiver. This noise-biasing is potentially important in the processing of Doppler data from radars, sodars and sonars operating in a pulse-to-pulse incoherent mode. Biasing of the mean frequency estimator can be easily corrected if measurements of the noise covariance are available. In the absence of noise measurements, correction for biasing can still be accomplished by estimating the signal and noise bandwidths and introducing simple models for the signal and noise covariance functions. This technique allows estimation of noise covariance from measurements of signal-plus-noise covariance at more than one time lag. In addition, the models provide a means or predicting potential biasing problems in a generalized Doppler system.

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