Averaging logarithms for detection and estimation (Corresp.)

In a number of applications in signal processing it is desirable to estimate the logarithm of the average of noisy physical measurements by averaging
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independent logarithms of the measurements. Only a modest number of bits are necessary in the logarithmic averaging process, which is used in logarithmic radar receivers to improve the effective dynamic range where post-detection averaging occurs, and in ensemble averaging spectral coefficients prior to the detection decision. A knowledge of the estimation error and of the detectability loss becomes important in these applications. This correspondence extends and generalizes Green's work in detection using averaged logarithms and presents an averaging loss methodology for continuous
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. It gives numerical detectability loss results for a representative detection criterion. It contains further results on estimation accuracy attainable from summed logarithms, including numerical results for estimation error as a function of
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and SNR.