Detecting trend in randomly switched measurements

We introduce a new trend detection problem inspired by real-time monitoring applications where the origin of the measurements is uncertain: The observed sequence under the alternative hypothesis is the result of a random switching between two sequences, each with a trend. The association between each measurement sample and the two sequences is unknown to the detector. We propose a Generalized Mann-Kendall trend detection algorithm, and show via simulation that it achieves better performance than the Mann-Kendall algorithm for problems with randomly switched measurements. We show that the test statistic can be calculated using an Mixed Integer Linear Programming (MILP) solver. We also show that computing the Generalized Mann-Kendall test statistic can be cast as a Max-Bisection problem, connecting the computation of test statistics to graph optimization.