Detecting steps walking at very low speeds combining outlier detection, transition matrices and autoencoders from acceleration patterns

In this paper, we develop and validate a new algorithm to detect steps while walking at speeds between 30 and 40 steps per minute based on the data sensed from a single tri-axial accelerometer. The algorithm concatenates three consecutive phases. First, an outlier detection is performed on the sensed data based on the Mahalanobis distance to pre-detect candidate points in the acceleration time series that may contain a ground contact segment of data while walking. Second, the acceleration segment around the pre-detected point is used to calculate the transition matrix in order to capture the time dependencies. Finally, autoencoders, trained with data segments containing ground contact transition matrices from acceleration series from labeled steps are used to reconstruct the computed transition matrices at each pre-detected point. A similarity index is used to assess if the pre-selected point contains a true step in the 30-40 steps per minute speed range. Our experimental results, based on a database from three different participants performing similar activities to the target one, are able to achieve a recall = 0.88 with precision = 0.50 improving the results when directly applying the autoencoders to acceleration patterns (recall = 0.77 with precision = 0.50).