Performance Analysis of the Dispersion of Double Differences Algorithm to Detect Single-Source GNSS Spoofing

Global Navigation Satellite Systems (GNSS) spoofing is a pernicious type of intentional interference where a GNSS receiver is fooled into tracking counterfeit signals, with the purpose of inducing a misleading information into the application it is used for. A possible technique able to identify a GNSS spoofing attack is a dual-antenna method based on the analysis of the dispersion of the double differences (D3) of carrier-phase measurements. Such technique has been recently presented as a relatively simple method to detect situations where even only a subset of counterfeit signals is tracked by the receiver. However, the D3 technique has not been analyzed in a rigorous theoretical way so far and the detection threshold was, for instance, set only empirically. Aiming at filling these gaps, this article intends to revise the main concepts of the aforementioned technique in a clear mathematical way. Thus, the detection threshold will be given according to a target probability of missed detection. Moreover, the article provides a thorough analysis of expected performance in terms of probability of missed detection and probability of false alarm, addressing them first as pairwise probability, then as overall probability. The effect of the signal C/N0 ratio on these detection performances is analyzed. Methods to reduce the occurrence of events of false alarm are also discussed. Eventually, an assessment of performance of the ${{\rm{D}}^3}$ algorithm is evaluated through a set of tests that emulate real working conditions.