Performance Characterization of a GPS Tracking Loop in the Presence of Linear Distortion

Phillip A. Bello

Abstract:	This paper is concerned with the impact of linear distortion on code tracking errors for an arbitrarily specified distortion. A normalized early/late gate power time discriminator is used in the analysis and simulation of the code tracking loop. While the analysis is applicable to any order tracking loop, numerical results are presented only for a discrete second order loop. Three types of tracking errors are evaluated: standard deviation of tracking errors due to noise; steady-state tracking errors due to velocity, acceleration, and jerk; and bias errors. Two methods of evaluating tracking errors due to noise were examined: the high signal-to-noise ratio (SNR) method which involves an expansion of the error variance in powers of 1/SNR and a new method, called the “stochastic” method. The latter method, based upon the open loop statistics of the nonlinear time discriminator, was developed to provide improved estimation of the change in tracking errors due to distortion at low SNR. The stochastic method is shown to yield estimates of root mean square (rms) tracking errors that track simulation results very closely. An interesting and useful byproduct of the stochastic method development is the discovery that the effective time discriminator characteristic decreases and changes shape as the SNR decreases, resulting in a decreasing noise bandwidth with decreasing SNR. Thus, evaluation of stressed dynamic loop responses at low SNR must take this phenomenon into account. Alternatively, an SNRadaptive tracking loop design is outlined that stabilizes the noise bandwidth with decreasing SNR, provided a sufficiently accurate estimate of SNR is available.
Published in:	Proceedings of the 2005 National Technical Meeting of The Institute of Navigation January 24 - 26, 2005 The Catamaran Resort Hotel San Diego, CA
Pages:	282 - 292
Cite this article:	Bello, Phillip A., "Performance Characterization of a GPS Tracking Loop in the Presence of Linear Distortion," Proceedings of the 2005 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2005, pp. 282-292.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In