Detection of Correlation Distortions Through Application of Statistical Methods

M. Pini, B. Motella, M, Troglia Gamba

Abstract:	Global Navigation Satellite System (GNSS) receivers are currently increasing in number and capability and continue to be widely used for navigation and precise positioning in air, sea and land transportation. Unfortunately, the low level of received signal power makes GNSS receivers vulnerable to disturbing signals. Recent works demonstrated the disrupting effect of jamming and spoofing attacks to standalone receivers, raising new concerns for GNSS-based civilian applications. In addition to interfering signals from external Radio Frequency sources, in non-ideal conditions, time-varying environments affect the signals through multipath, fading and signal distortions. In such a challenging environment, the tracking loops used to synchronize the received signal with local replicas are not able to provide an accurate estimate of the signal parameters (i.e.: code delay, carrier phase and frequency) and might lose the lock in case of severe conditions. In fact, signal distortions yield to correlation asymmetries that degrade the performance of the tracking loops. For example, multipath creates an asymmetry in the correlation function between the received signal and the local replica, causing a shift of the zero crossing point of the loop discriminator and resulting in biased pseudoranges. In this paper, we investigate methods that leverage the statistical characteristics of the signals to detect correlation distortion. From a general perspective, detection algorithms proposed in GNSS work in time or frequency domain, but when the data to be processed can be modeled as random processes, like the correlator outputs, the domain of the statistical characteristics is also appropriated for detection operations. The methods belong to non-parametric statistics and are popular in economics and biology, but have been rarely used in GNSS so far. Recently, they started to be investigated for interference detection and have been described with the appropriated theory in [1]. Authors successfully demonstrated that the Chi-square Goodness of Fit (GoF) test on raw signal samples enables the detection of different type of interfering signals with a low probability of missed detection, even when the interfering power is low and not discernible by most detection techniques working in time and frequency domains. In [1], the GoF test performs the comparison of two probability density functions, deciding between two hypotheses: interference present or interference absent. For detection purposes, the raw samples at the output of the front-end are used to build the test statistic and take the decision. In case of interfering signals, the histogram of the raw samples modifies the expected shape, allowing the test to detect the distortion. In this paper, we apply the GoF test at the correlators output, taking sets of Early and Late correlations to build the test statistic, which is used to discriminate two hypothesis: the correlation is distorted or not. In particular: 1) the Early and Late correlations have the same statistics (the correlation is not distorted), 2) the Early and Late correlations have different statistics (the correlation is distorted) . The sets of Early and Late correlations are the measured data, and are instances of a discrete-time Gaussian random process. When no disturbances affect the signals and the correlation shape is not distorted, the distribution of the measured data on the Early and Late slopes of the correlation is similar. In this case, the test statistic assumes small values and the probability that the Early and Late correlators have the same statistical characteristics tends to one. On the contrary, in a more critical scenario where multipath or interference distorts the correlation, the distribution of the Early and Late correlators changes significantly. In this case, the test statistic assumes higher values and can be used to flag the anomaly to the receiver control logic that might exclude the corresponding channel from the navigation solution. In addition to the Chi-square GoF test, the paper analyzes another simpler non parametric test, known as sign test. It takes the difference of the Early and Late measured data sets, counting the number of positive and negative values of the results. If the Early and Late correlators have the same statistics (i.e.: the correlation shape is symmetric), the number of positive and negative values is expected to be similar. In this case, the test statistic is the difference between the number of positive and negative values. It is possible to demonstrate that it is a Gaussian random variable, which is used to derive the probability that the two measured data sets have the same characteristics, from a statistical perspective. Compared to the Chi-square GoF test, the sign test is more suitable to practical implementation, since it is associated to a limited computation burden and does not require long sets of measurements to be effective. In order to assess the performance of the methods under investigation, we implemented the GoF and the sign tests in a GNSS software receiver. We tested the detection of correlation distortions, processing simulated signals as they would appear in a critical scenario characterized by multipath propagation and presence of interference. The methods are not tailored to any signal format and have been simulated with GPS L1 C/A code and BOC modulated signals. Results confirmed the ability of the GoF test to detect low power disturbances, even at the post-correlation stage, and demonstrated that also the sign test is able to detect asymmetries with small probabilities of missed detection. In case of simplistic spoofing attack (i.e.: the counterfeit signal is first aligned to the real one and then delayed to produce the tracking lock carry-off) the benefits of the methods are evident, since they improve the receiver robustness. All the results gathered in the paper will be introduced by an accurate signal model, the review of fundamentals of non-parametric test in statistic and the mathematical analysis of the methods adapted to GNSS receivers. References [1] B. Motella, M. Pini, L. Lo Presti, "GNSS interference detector based on Chi-square Goodness-of-fit test," in the Proceedings of 6th European Workshop on GNSS Signals and Signal Processing (NAVITEC) 2012, The Netherland, 5-7 December 2012.
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:	3279 - 3289
Cite this article:	Pini, M., Motella, B., M,, Gamba, Troglia, "Detection of Correlation Distortions Through Application of Statistical Methods," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 3279-3289.
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