The Cramer-Rao bound for position and amplitude estimation of multiple pulses in Gaussian noise

Estimating the position or amplitude of a pulse is a common problem in radar and seismic signal processing. In this paper an approximation to the Cramer-Rao bound for estimation of positions and amplitudes of multiple pulses is derived. It is shown that a vector can be associated with each parameter and the effect of a parameter on the estimation of another parameter is expressed as the normalized cross correlation of the vectors associated with these two parameters. We give examples to show that this approximation is good. These results provide a simple, geometric explanation for the effect of one pulse on the estimation of another.