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 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 . 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 and SNR.