Performance analysis of digital tracking loops for telemetry-based ranging applications

In this paper, we analyze mathematical models of digital loops used to track the phase and timing of communications and navigations signals. The limits on the accuracy of phase and timing estimates play a critical role in the accuracy achievable in telemetry-based ranging applications. We describe in detail a practical algorithm to compute the loop parameters for discrete update (DU) and the continuous update (CU) loop formulations, consistent with the development of [3], and we show that a simple power-series approximation to the DU model is valid over a large range of time-bandwidth product (B_LT) . Several numerical examples compare the estimation error variance of the DU and CU models to each other and to Cramér-Rao lower bounds. Finally, the results are applied to the problem of ranging, by evaluating the performance of a phase-locked loop designed to track a typical ambiguity-resolving PN code received and demodulated at the spacecraft, on the uplink part of the two-way ranging link.