Quantifying Phase Lock Loop Robustness Through Interference using the Phase Discriminator Output
Wengxiang Zhao, Stefan Stevanovic, Boris Pervan, Illinois Institute of Technology
In this paper, we implement and experimentally validate a new technique to maintain continuous receiver tracking in GPS receivers that are subject to wideband radio frequency interference (RFI). The method is directly applicable to ground-based reference receivers for differential GPS systems such as the Ground Based and Space Based Augmentation Systems (GBAS and SBAS), as well as other ground-based receivers that require high continuity of service. It is also applicable to moving receivers when Doppler aiding is provided to the phase-lock loop (PLL) to compensate for the additional dynamic stresses.
In order to track through wideband interference events, the PLL pre-detection averaging time must be extended beyond the length of a navigation data bit. This is not a significant issue for our intended application, which is to maintain continuity through interference events, not to acquire new satellites during these periods. The most recently decoded ephemeris, prior to the interference event, will be valid for at least two hours beyond the broadcast of the next updated ephemeris. This means that as long as the interference event is shorter than two hours in length, decoding navigation data is not necessary.
However, in previous work , we showed that existing techniques for extended averaging introduce biases in the discriminator output (DO) distributions, which, if not corrected, always lead to biased estimators of tracking error. These, in turn, cause biases in the reconstructed carrier Doppler, ultimately leading to cycle slips. In this work, we quantify the bias effects caused by the different techniques for extended averaging, and we introduce a new calibration method to transform them into unbiased estimators. Using direct simulation of the PLLs, we then demonstrate the effectiveness of the method to eliminate DO and reconstructed carrier Doppler biases.
A major component of this work is direct experimental measurement of cycle slip resistance by implementing the new de-biasing algorithm in a real-time software receiver. The experiments are performed using an RF signal generator to directly simulate a GPS signal with wideband interference, which is realized as a deteriorated carrier-to-noise ratio. The signal generator also reproduces the effects of satellite motion and ionospheric dynamics. The simulated signal enters into a GPS RF front-end kit, which utilizes an external clock input from a commercially available rubidium clock.
Estimating the mean time to cycle slip (MTCS) is the most straightforward metric used to quantify interference robustness. However, it can be very time-consuming. Since we are interested in interference events shorter than two hours in length, we will instead estimate the probability of successful tracking through a two-hour event for various interference levels and receiver configurations. To estimate the probability of tracking, 100 experimental trials are conducted for each case.
Identifying cycle slips in experimental results is difficult because the true carrier phase is unknown. Receivers typically use a phase-lock detector, which functions similar to a phase discriminator, to determine if the PLL is tracking properly. In  we have shown that for pre-detection averaging times greater than the length of a navigation data bit, a bias may exist on the carrier Doppler error, which cannot be detected by observing the discriminator output. For this reason, in this work, a signal with a 45 dB-Hz carrier-to-noise ratio is generated to represent the true carrier phase. This allows us to determine the carrier phase error, and identify cycle slips in our experimental results. An experimental trial is deemed successful if no cycle slips are observed for the entire two-hour interference event. The results show substantial increases in the probability of tracking when using the de-biasing algorithm.
 Stevanovic, S., and Pervan, B., “Coasting Through Wideband Interference Events using Robust Carrier Phase Tracking.” In Proceedings of the 30th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2017), 2017.