GPS Signal Tracking with Kalman Filter Based on Joint Code Delay and Carrier Phase and Frequency Error Discriminator

Chun Yang

Abstract:	The weakest link in a GPS receiver is its carrier-tracking loop. Yet only one carrier replica at a frequency is maintained by the carrier numerical controlled oscillator (NCO) in the receiver. This works just fine for the normal signal to noise ratio (SNR) and the signal dynamics within the tracking loop bandwidth. However, when a sudden acceleration occurs, the carrier-tracking loop is most likely to break if the resulting frequency error goes beyond the pull-in range. Furthermore, the nonlinearity of the carrier phase or frequency error discriminator, evaluated around the estimated frequency, also limits the region in which the carrier-tracking loop can operate. In this paper, the concept of grid tracking is first introduced based on the delay-Doppler mapping of complex correlations. When viewed in the signal parameters space (i.e., the delay-Doppler plane), the conventional receivers making use of delay-locked loop (DLL) and phase-locked loop (PLL) or frequency-locked loop (FLL) can be portrayed as point tracking. In contrast, the grid tracking mechanism calls for at least three carrier replicas (named faster, in-sync, and slower, respectively) for the carrier loop in addition to at least three early, prompt, and late code replicas for the code loop. The new grid tracking therefore covers a larger area in the signal parameters space and thus has the potential to capture the underlying signals despite of high dynamics and large oscillator drifts. The grid tracking mechanism allows for the development of a joint code delay and carrier phase and frequency error discriminator based on even 1ms worth of GPS signal samples (i.e., after each despreading integration). This establishes the framework in which a Kalman filter can be used to track a GPS signal code and carrier jointly. Within this formulation, the state vector primarily consists of the code phase, carrier phase, carrier frequency, and angular acceleration with their state and observation models to account for the signal dynamics and measurement errors for each satellite in view. The joint tracking filter has been successfully developed and applied to real GPS data. The processing results will be presented in this paper to illustrate the grid tracking concept, the joint error discriminator characteristics, and the joint tracking filter performance. Tracking filters tuning and other practical issues are also discussed.
Published in:	Proceedings of the 60th Annual Meeting of The Institute of Navigation (2004) June 7 - 9, 2004 Dayton Marriott Hotel Dayton, OH
Pages:	631 - 640
Cite this article:	Yang, Chun, "GPS Signal Tracking with Kalman Filter Based on Joint Code Delay and Carrier Phase and Frequency Error Discriminator," Proceedings of the 60th Annual Meeting of The Institute of Navigation (2004), Dayton, OH, June 2004, pp. 631-640.
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