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Title: Change detection with quaternion random signals Authors:  Antonia Oya - Universidad de Jaen (Spain) [presenting]
Abstract: The problem of change detection in continuous-time random signals using statistical tests has been applied for a number of situations, such as medical condition monitoring, climate change detection, speech and image analysis, stock market, traffic data analysis and so on. A typical statistical formulation of this detection problem can be regarded as discrimination between two probability distributions with different models, i.e., the probability distributions of data before and after a candidate change point. In these approaches, the logarithm of the likelihood ratio between two consecutive intervals in continuous-time signals is monitored for detecting change points. A test statistic for change detection with quaternion random signals based on Reproducing Kernel Hilbert Space (RKHS) formulation is given. Specifically, a change detection problem where the pre-change observation signal is purely noise and the post-change observation signal is a noise corrupted signal is considered. First, we reduce the continuous-time change detection problem to a discrete setting by considering the random coefficients obtained from the RKHS representation of the observation quaternion random signal. Second, we compute the log-likelihood ratio to obtain a feasible expression of the detector that involves RKHS inner product computations.