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The performance of Global Navigation Satellite Systems (GNSS) is known to be severely affected in multipath scenarios, providing a biased position solution which could jeopardize possible geodetic-grade applications. Indeed, multipath estimation and/or mitigation has attracted the attention of many researchers in the recent years. Nevertheless, few attention has been given to the detection of multipath. That is to say, acknowledging that a given scenario is corrupted by multiple propagation paths, and thus using adequate techniques to combat its effect. This paper proposes a statistical multipath detector based on an antenna array GNSS receiver. Specifically, the detector resorts to the estimated noise covariance matrix to compute a statistic that measures the dispersion of its eigenvalues. The theoretical distribution of such statistic is known. This is used by the proposed method to perform a Kolmogorov-Smirnov one-sample test to assess departures from the theoretical distribution, with the resulting detector being Constant False Alarm Rate. The detector is analyzed in terms of its probability of detection and an analysis is provided regarding its behavior under synchronization errors. Results of the detector under realistic scenarios are also discussed.