Abstract:
Change-point detection (CPD) aims to identify abrupt changes in the statistical properties of a time series, and has been widely applied across various signal processing domains. The sliding-window Mann–Whitney U statistic (MWUS) , a non-parametric rank-based CPD method, exhibits strong robustness against impulsive noise interference. However, MWUS neglects the temporal correlation introduced by the sliding window and determines thresholds solely based on marginal distributions, leading to uncontrollable false alarm rates. To address this, we propose a low-pass filtering MWUS (LPFMWUS) method. We derive closed-form expressions for the power spectral density of the MWUS sequence under the null hypothesis (no change point) and for the energy spectral density under the ideal scenario (noise-free with only a change point) . This analysis reveals that the noise exhibits band-pass characteristics, while the change point exhibits low-pass characteristic, motivating the application of a low-pass filter. Leveraging the proven ergodic properties of the MWUS sequence and its finite impulse response filtered version under the null hypothesis, we construct a multivariate joint distribution model for the filtered statistics and develop a dynamic threshold setting method. Simulations demonstrate that: (1) the proposed dynamic threshold setting method can precisely control the online false alarm rate; (2) LPFMWUS improves detection performance by enhancing the signal-to-noise ratio, and its localization accuracy outperforms that of representative methods, including the parametric cumulative sum (CUSUM) method and the Non-Parametric UNbounded Changepoint Local (NUNCL) method.