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

Abstract

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 ( ) . 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 twoway ranging link.

High‐Precision Carrier Tracking Algorithm for Extremely Weak and High‐Dynamic Signals

“…Therefore, accurate initial frequency estimation is one of the key points to improve the weak signal tracking ability of PLL. The articles (Hao et al, 2017;Vilnrotter et al, 2014) propose that the typical value of loop noise bandwidth should be set to 100 Hz in deep space exploration, probably because DENG ET AL.…”

“…Therefore, accurate initial frequency estimation is one of the key points to improve the weak signal tracking ability of PLL. The articles (Hao et al., 2017; Vilnrotter et al., 2014) propose that the typical value of loop noise bandwidth should be set to 100 Hz in deep space exploration, probably because the influence of the accuracy of the estimated initial frequency on the weak signal tracking ability is not considered. When the accuracy of the estimated initial frequency is very low, a large loop noise bandwidth should be set to achieve the capture of the signal frequency.…”

“…Currently, third‐order phase‐locked loops (PLLs) are used to monitor the soft landing process of lunar probes. When using a traditional third‐order PLL for proper work, the loop noise bandwidth is often set to 100 Hz, and the weak signal tracking threshold is about 27dB‐Hz (Hao et al., 2017; Vilnrotter et al., 2014). However, the CNR of actual data is often less than 27dB‐Hz, for example, the CNR of data received by small‐aperture antennas is often very low.…”

Direct Instantaneous Frequency Rate Estimation to Improve the Carrier Estimation Performance in Mars Entry, Descent, and Landing Flight

“…This is similar to the processing manner in a digital phase locked loop (DPLL) [24]. In a DPLL, a complex mixing operation is carried out between the incoming raw signal samples and the local predicted signal waveform samples, followed by a summation of the dot multiplied samples, which are used to generate the difference phase estimation between the incoming raw signal and the local predicted signal.…”