Abstract
CUSUM (cumulative sum) is a well-known method that can be used to detect changes in a signal when the parameters of this signal are known. This paper presents an adaptation of the CUSUM-based change detection algorithms to long-term signal recordings where the various hypotheses contained in the signal are unknown. The starting point of the work was the dynamic cumulative sum (DCS) algorithm, previously developed for application to long-term electromyography (EMG) recordings. DCS has been improved in two ways. The first was a new procedure to estimate the distribution parameters to ensure the respect of the detectability property. The second was the definition of two separate, automatically determined thresholds. One of them (lower threshold) acted to stop the estimation process, the other one (upper threshold) was applied to the detection function. The automatic determination of the thresholds was based on the Kullback-Leibler distance which gives information about the distance between the detected segments (events). Tests on simulated data demonstrated the efficiency of these improvements of the DCS algorithm.
Highlights
Change detection and segmentation are the first steps of many signal processing applications
The first part of this paper provides an overview of the CUSUM algorithm, focusing on the dynamic cumulative sum to describe its main properties and limits
The local approach of change detection allows a local estimation of the distribution parameters before and after the current time t
Summary
Change detection and segmentation are the first steps of many signal processing applications (see, e.g., speech processing [1,2,3,4], video tracking [5], ergonomics [6], biomedical applications [7,8,9], seismic applications [10]). This can be expressed either by a different distribution function before and after the change time, or by a modification of the parameter value of the same distribution For the latter case, when the parameter values are a priori known, an efficient algorithm to solve the detection problem is the CUSUM (cumulative sum) algorithm based on the log-likelihood ratio [10, 13]. The parameters corresponding to the segments to be detected are often unknown and other algorithms have to be applied for change detection Such algorithms can be found in [9, 16], based on the computation of a dynamic cumulative sum (DCS) of the likelihood ratio between two locally estimated distributions. An automatic determination of the thresholds is presented in the third part of the paper
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