The modified CUSUM algorithm for slow and drastic change detection in general HMMs with unknown change parameters

We study the change detection problem in a general HMM when the change parameters are unknown and the change can be slow or drastic. Drastic changes can be detected easily using the increase in tracking error or the negative log of observation likelihood (OL). But slow changes usually get missed. We have proposed in past work a statistic called ELL which works for slow change detection. Now single time estimates of any statistic can be noisy. Hence we propose a modification of the cumulative sum (CUSUM) algorithm which can be applied to ELL and OL and thus improves both slow and drastic change detection performance.