C/A Code Cross Correlation Error with Carrier Smoothing - the Choice of Time Constant: 30 s vs. 100 s

Z. Zhu, F. van Graas

Abstract: The Gold sequences used in the GPS C/A code family are not completely orthogonal to each other. The C/A code cross correlation can be as high as 23.9 dB below the auto correlation. It has been shown that cross correlation can introduce errors in range and Carrier-to-Noise Ratio (C/N0) estimates. The errors can be significant when the received signal power is substantially different between the two satellites. Safety-critical systems that rely on pseudorange measurements are especially sensitive to cross correlation errors. For instance, cross correlation has to be taken into consideration in the monitoring of low signal power, which is an important component of the Ground-Based Augmentation System (GBAS). Cross correlation can potentially impact the accuracy, integrity and continuity of GBAS. It has been suggested that pseudorange error induced by cross correlation can be modeled using an approach similar to that of multipath errors. In addition, cross correlation was also found to be a function of range, Doppler, Doppler rate of change, data bit alignment, code chip alignment, received power level and tracking loop parameters. The Doppler frequency shift between the two signals results in an oscillatory error pattern, which resembles the fading of multipath errors. Cross correlation can be mitigated by a low-pass filter or carrier smoothing. A time constant that is substantially greater than the period of oscillation is very effective in reducing the error magnitude. In fact, for most cases, 100- second carrier smoothing has been found sufficient to bring the pseudorange errors down to an acceptable level. Unfortunately, 100 second carrier smoothing cannot be universally used for all applications. To better deal with other error sources such as ionospheric gradient, it has been proposed that 30 second carrier smoothing should be used in the ground subsystem of GBAS for GBAS Approach Service Type D landing operations. This work investigates the efficacy of carrier smoothing on cross correlation errors, using time constant of 30 seconds and 100 seconds. Depending on the system error budget, cross correlation errors greater than a certain threshold must be detected. Extreme scenarios exist, in which the pseudorange errors are still greater than the threshold after 30 or 100 second carrier smoothing. The maximum residual errors are calculated for both time constants. A detailed analysis of the error model makes it possible to predict or detect the conditions, under which the cross correlation errors may exceed the threshold. The likelihood of experiencing these errors in a practical setup can also be estimated for both time constants, which, in turn, can be used to evaluate the impact of cross correlation on system continuity.
Published in: Proceedings of the 2011 International Technical Meeting of The Institute of Navigation
January 24 - 26, 2011
Catamaran Resort Hotel
San Diego, CA
Pages: 464 - 472
Cite this article: Zhu, Z., van Graas, F., "C/A Code Cross Correlation Error with Carrier Smoothing - the Choice of Time Constant: 30 s vs. 100 s," Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 464-472.
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