ION GNSS 2012
Session D3: GNSS Algorithms & Methods 1: Signal Processing

Title: A Review and Comparison of Carrier Frequency Discrimination for GNSS Receivers
Author(s): J.T. Curran, University of Calgary, Canada
Room: 204 (NCC)

In order to provide a navigation solution, the minimum requirements, in terms of tracking the received satellite signal, is that of carrier frequency synchronization and code-phase alignment. The carrier frequency requirement is often the most difficult criteria to satisfy when the received signal is subject to severe attenuation and distortion and is, generally, the limiting factor in the availability of satellite observations. As the demand for ubiquitous location information continues to grow, so too does the need to address this limitation. In response, a host of novel frequency tracking schemes have emerged over the last number of years, ranging from novel carrier frequency estimators or discriminators to novel search-based estimation algorithms [1, 2]. Despite serving the same purpose, these schemes are quite diverse and exhibit starkly different characteristics, when employed in different environments. This work aims to explore the performance of these discriminator under a range of different conditions to identify where and when each discriminator should be used.

Traditionally, carrier frequency synchronization has been achieved via the use of discriminators which base their frequency estimate on the difference of two successive phase estimates [2, 3]. A range of such discriminator functions exist, of varying complexity and performance and have some key discerning features (for example, sensitivity or insensitivity to data modulation). Under open-sky, line of sight (LOS) conditions, when coupled with in an appropriate FLL, they can provide excellent tracking performance and are particularly computationally efficient. Weak signal conditions, however, pose a significant threat to these discriminators. As the signal-to-noise-floor of the correlator values decreases, the performance of these discriminators degrades rapidly [2]. Furthermore, increasing the coherent integration period offers little respite from this effect as the range of frequencies over which these discriminators can provide a useful frequency estimate is inversely proportional to the coherent integration period. These techniques, therefore, have limited application.

Another useful style of discriminator, computes its frequency estimate based on the difference in energy of two correlator values. One is produced using a local carrier replica with a slightly increased frequency relative to the current estimate of the received signal frequency, while the other uses a slightly decreased frequency. The difference in energy is indicative of the the current frequency error [1]. Under LOS conditions, this approach performs more poorly than the phase-differencing approach, however its performance does not deteriorate quite so rapidly with reductions in received signal quality. Under very weak signal conditions, therefore, this discriminator may prove quite effective. As the frequency spacing of the two correlators is an independent design choice, the range of frequency errors over which the discriminator can provide a useful error estimate is not tightly related to the coherent integration period. Furthermore, its nature may render it suitable for use in applications where combined data/pilot or multi-frequency frequency tracking is required. These benefits, however, come at the cost of increased computational burden over the phase-differencing discriminators.

More fundamentally, of course, a maximum-likelihood estimate of frequency is formed by maximizing an energy measurement as a function of frequency. A discrete realization of this approach is used in the signal acquisition and re-acquisition processes but has also been successfully employed in a number of specialized tracking applications [4]. In such applications, a reduced search space is centered around the current signal parameter estimates and the resultant correlator values are observed collectively to determine the parameter errors. This approach is by far the most computationally intensive. However, the region over which it can provide useful frequency estimates can be extended arbitrarily, making its host tracking system robust against large frequency transients or large errors in the initial estimate of the Doppler frequency.

This can be useful, for example, under high dynamics, immediately subsequent to signal acquisition when the FLL is first closed, or in a vector-based receiver when the current position and velocity are not well known and the receiver has poor satellite visibility. Also, the large number of observations it produces makes it useful for signal quality monitoring, for example multi-path or interference monitoring.

These three styles of discriminator provide the same basic functionality: that of carrier frequency synchronization. A comparison of these discriminators in terms of tracking jitter, tracking threshold and loss of lock statistics may, therefore, offer some insight into which should be used in a given operating environment. Such a comparison will be achieved in this work by assessing each discriminator in terms of gain, noise power and correlation, and linear region. This will provide an initial set of parameters by which some inferences regarding closed loop performance can be made [2]. Subsequently, via extensive simulation and real signal analysis, the relative performance of these discriminators will be explored under LOS conditions, in sub-urban and urban environments, and under weak-signal conditions, for example, within a typical north-American house. These tests will assess the closed loop tracking performance in both the standard receiver configuration, where each satellite is tracked in isolation, and in the vector-based receiver wherein the frequency of each received signal are tracked collectively. It is postulated that these two receiver architectures may be more or less sensitive to certain discriminator features. Ultimately, the study aims to conduct a computational-cost versus performance-benefit analysis for each discriminator and to provide design guidelines which will specify the appropriate discriminator choice for a particular application.

REFERENCES [1] J. C. Juang and Y. H. Chen, "Phase/frequency tracking in a GNSS software receiver," Selected Topics in Signal Processing, IEEE Journal of, vol. 3, no. 4, pp. 651 -660, August 2009. [2] J. T. Curran, G. Lachapelle, and C. C. Murphy, "Improving the design of frequency lock loops for gnss receivers," To appear in: Aerospace and Electronic Systems, IEEE Transactions on, vol. 48, no. 1, pp. 850-868, Jan 2012. [3] E. D. Kaplan, Ed., Understanding GPS: Principles and Applications. Artech House Inc., 2006, vol. 1, ch. 5, pp. 179-194, ISBN 1-58053-894-0. [4] F. v. G. Sanjeev Gunawardena and A. Soloviev, "Real time block processing engine for software GNSS receivers," National Technical Meeting of The Institute of Navigation, pp. 371-377, Jan 2004.

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