Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.