Exact Angular Accuracy of an Amplitude Comparison Sequential-Lobing Processor

Assume E1 and E2 are the squares of two sequential envelopes from the sequential lobing of an antenna in a given plane. Independent thermal noise is generally present in the envelopes. The statistic e = (E2 ¿ E1)/(E2 + E1) has been used as an estimate of the angle to a target for the significant region of small angles compared to a beamwidth. For a nonfading target, the probability density and characteristic function of e are obtained in closed form. Thence, the exact bias, standard deviation, and rms error in estimating the noise-free value e of e are obtained for all e and signal-to-noise ratios. The same type of statistic as e can be used to estimate time delay in a split range gate tracker.