Stability Criteria for GNSS Receiver Tracking Loops

P.W. Ward, T.D. Fuchser

Abstract:	This paper analyzes the stability criteria for closed-loop tracking in a GNSS receiver. It defines the stable limits of predetection integration time (T) for a given loop filter order and noise bandwidth, Bn. The paper uses this stability criteria to determine the limits of T for a given order and Bn for both data and data-less (pilot) tracking loops. The squaring loss is zero in the pilot channel case, so increasing T is no longer a factor in the reduction of the thermal noise contribution by the tracking loop. But the paper describes other benefits of extending the coherent integration time made possible by the availability of a modernized GNSS pilot channel. Clearly, a pilot (data-less) channel in modern GNSS signals permits much longer T than provided by the original GPS data channels, but the stability criteria methodology presented in this paper must be considered in both cases. Loop stability is assured in the design examples used in this paper by maintaining a closed-loop phase margin of 30 degrees or more. The transfer functions for a popular design of first, second and third order sequential GNSS loop filter designs, along with the transfer functions of the other components in a GNSS receiver tracking loop that are associated with the closed tracking loops. Then, the composite transfer function for a given loop filter order and a representative Bn are used to generate a Bode-plot for all three loop filter orders. Each Bode plot depicts the phase margin in degrees as a function of T. The T corresponding to the 30-degree phase margin is obtained from this analysis and becomes the maximum T limit for assured loop stability for each case. For a given loop order and this defined stability criteria, Bn*T is a constant. This product is determined for each loop order and the results are used to plot the maximum T as a function of Bn. In these plots, all T regions at and below the maximum T curve are assured to be stable because the phase margin is equal to or greater than 30 degrees. Other issues such as gain margin, loop filter damping parameters and computation delay issues are addressed. Typical loop filter design examples, based on this stability criteria, are used to demonstrate the robustness improvement achieved by the pilot channel in comparison with traditional GPS signals that do not contain a pilot channel.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2786 - 2806
Cite this article:	Updated citation: Published in NAVIGATION: Journal of the Institute of Navigation
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