Multipath Mitigation Using Linear Adaptive Filtering Techniques.

S. Ugazio, L. Lo Presti, E. Falletti

Abstract:	Thanks to the improvements brought to GNSS in the last years, multipath (MP) is now one of the more significant error sources affecting the GNSS solution, and more often than not, the dominant one. MP introduces an asymmetry in the correlation function and this shifts the zero crossing point of the discriminator S-curve. This means that due to MP, an error is introduced in the signal delay estimate which has a direct impact in the pseudorange estimate. Many methods have been proposed in literature to counteract this undesired effect, including improvements on the tracking loops and improved antenna technologies. The approach investigated in this paper is the propagation channel estimation making use of Linear Adaptive Filters (LAFs), whose theory is deeply discussed in [1]. LAFs include Least Square (LS), Least Mean Square (LMS) and Recursive Least Square (RLS) filters, which differ in terms of computational cost and convergence speed. LAFs adapt the coefficients of a FIR (Finite Impulse Response) filter to minimize an error function, represented by the difference between the FIR output and an unknown signal to be estimated, given at the FIR input a proper signal from which an estimate of the unknown signal can be obtained. The unknown signal is represented as a sum of delayed and attenuated (or amplified) copies of a known function. In MP detection applications for GNSS, the LAF input is related to the expected GNSS signal in the absence of MP, and the unknown signal to be estimated depends on the received signal. The LAF finds the optimal coefficients and this corresponds to find an estimate of MP delays and amplitudes. In literature, techniques for MP estimation using LAF have been investigated. For example, in [4] the LMS method is applied to the GPS C/A code. In this case, due to the difficulty to model the input signal, the correlation matrixes needed to solve the LS problem are not known and as a consequence a LMS approach is applied, making use of approximations of the unknown matrixes. The LMS method is the most convenient in terms of complexity, but also the slowest one in terms of convergence time and it implies to choose appropriately the time step, which is not a trivial operation. This is why in literature techniques have been proposed to combine different LAF methods in order to find a trade-off between performance and complexity (e.g. [5]). Another approach is proposed in [6], where a RLS method is applied to the correlation function of a Galileo BOC signal. While in [4] the method is applied pre-correlation, as in [6] we propose to apply the LS and LMS techniques post-correlation. This means that the signal at the FIR input is a function with the shape of the ideal correlation function in the absence of disturbances (a triangle in the case of the GPS C/A code), to be compared with the measured correlation between the noisy input and the local code. In this way, the LS method can be used to compute the optimal coefficients of the FIR filter. One of the main problems of adaptive filtering techniques remains the complexity, due, first of all, to the high number of correlators required. This issue is investigated, with the aim of finding a trade-off between performance and number of correlators. In [4] the LAF technique is applied with the aim to find both the delay introduced by the MP and the delay on the direct path, but no MP-mitigation techniques are described. In this paper we investigate different methods to apply a correction on the pseudorange estimate, by exploiting the LAF results, which allow the estimation of the shift in the S-curve. A possible approach is to compute the delay by means of a standard DLL and then correct the PVT measurements according to the LAF estimated coefficients. A fundamental issue is the identification of the direct path correlation peak. In general in literature it is considered to be corresponding to the maximum of the correlation function. Unfortunately, this is not always the case. It the real world it may happen that the MP rays arrive to the receiver antenna with a higher power than the direct path signal, if the direct signal finds obstacles (such as for example trees) on its way. This kind of obstacles does not block the direct signal, but instead they attenuate it. As a result, the direct path does not correspond to the maximum in the correlation function. In order to remedy to this, the direct path delay has to be evaluated as the first peak in the search space above a proper fixed thresholds. The hypothesis is that the MP may have higher power with respect to the direct path, but in any case the MP has a larger delay. It has to be noted that in particular cases, due to atmospheric effects, it may happen that the MP ray results to be anticipated, but this is a very rare case that is not investigated in this paper. Experiments will be shown obtained with realistic data from a GNSS signal simulator. References [1] S. Haykin. Adaptive Filter Theory. Prentice-Hall, N.J., 2002 [2] L. Garin, F. Van Diggelen, J. M. Rousseau, “Strobe and edge correlator multipath mitigation for code,” Proceedings of ION-GPS conference, Kansas City, MO, September 1996. [3] E. Falletti, B. Motella, M. Troglia Gamba, C. Facchinetti, “Multipath Mitigation in SoL Environments Using a Combination of Squared Correlators", Proceedings of the ION GNSS Conference, Nashville, TN, September 2012. [4] Nelson, Lisa M., Axelrad, Penina, Etter, Delores M., "Adaptive Detection of Code Delay and Multipath in a Simplified GPS Signal Model", Proceedings of the ION GPS Conference, Kansas City, MO, September 1997, pp. 569-581. [5] M.F. Mosleh, “Combination of LMS and RLS Adaptive Equalizer for Selective Fading Channel”, European Journal of Scientific Research Vol.43No.1 (2010), pp.127-137 [6] Y. Yanxin, Y. Dongkai, DingFan, “A Multipath-resistant Precise Tracking Method for BOC Signal”. Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, 2009 3rd IEEE International Symposium.
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:	2007 - 2014
Cite this article:	Ugazio, S., Presti, L. Lo, Falletti, E., "Multipath Mitigation Using Linear Adaptive Filtering Techniques.," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2007-2014.
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