Derivation of the error in estimating the time separation between two pulses in the presence of either white, lowpass, or bandpass noise

摘要

Measuring the yield of an underground nuclear detonation using sensor cables has been proposed for verification purposes. These cables not only sense the signals associated with the yield they also capture the sensitive primary and secondary electromagnetic pulses associated with the detonation but have nothing to do with the yield. An anti-intrusiveness device is to be connected to the sensor cable to prevent the electromagnetic pulses from passing through to the verifier. The anti-intrusiveness device both attenuates the electromagnetic pulses and adds noise to the cable over the interval of time that the electromagnetic pulses may be present. This report addresses the problem of determining the optimum noise spectral density for masking the electromagnetic pulses. To this end it derives an expression for the lower bound on the error in the estimation of the time separation between two pulses when the time of arrival of neither is known and they are imbedded in Gaussian noise. The noise spectral shapes considered are white, and lowpass, and bandpass.