Cramer-Rao lower bound on doppler frequency of coherent pulse trains

This paper derives the Cramer-Rao lower bound (CRLB) on estimates of the frequency of a coherent pulse-train passively intercepted at a moving antenna. Such estimates are used to locate the transmitting radar. Although frequency estimation algorithms for pulse trains have been proposed, no results were previously available for the CRLB; thus, it has been impossible to assess the complete potential of location. The derived CRLB is compared to previously published algorithm accuracy results. A general rule of thumb is found that the CRLB depends inversely on pulse on-time, number of pulses, variance of pulse times, and the product of signal-to-noise-ratio and sampling frequency; pulse shape and modulation have negligible impact on the result. When K pulses are equally spaced by the pulse repetition interval (PRI), then the CRLB decreases as 1/PRI² and as 1/K³.