This article presents a method for step detection from accelerometer and gyrometer signals recorded with Inertial Measurement Units (IMUs). The principle of our step detection algorithm is to recognize the start and end times of the steps in the signal thanks to a predefined library of templates. The algorithm is tested on a database of 1020 recordings, composed of healthy subjects and patients with various neurological or orthopedic troubles. Simulations on more than 40,000 steps show that the template-based method achieves remarkable results with a 98% recall and a 98% precision. The method adapts well to pathological subjects and can be used in a medical context for robust step estimation and gait characterization.

This article thoroughly describes a data set of 1020 multivariate gait signals collected with two inertial measurement units, from 230 subjects undergoing a fixed protocol: standing still, walking 10 m, turning around, walking back and stopping. In total, 8.5~h of gait time series are distributed. The measured population was composed of healthy subjects as well as patients with neurological or orthopedic disorders. An outstanding feature of this data set is the amount of signal metadata that are provided. In particular, the start and end time stamps of more than 40,000 footsteps are available, as well as a number of contextual information about each trial. This exact data set was used in [Oudre et al., Template-based step detection with inertial measurement units, Sensors 18, 2018] to design and evaluate a step detection procedure.

We consider the problem of detecting abrupt changes in the underlying stochastic structure of multivariate signals. A novel non-parametric and model-free off-line change-point detection method based on a kernel mapping is presented. This approach is sequential and alternates between two steps: a greedy detection to estimate a new breakpoint and a projection to remove its contribution to the signal. The resulting algorithm is able to segment time series for which no accurate model is available: it is computationally more efficient than exact kernel change-point detection and more precise than window-based approximations. The proposed method also offers some theoretical consistency properties. For the special case of a linear kernel, an even faster implementation is provided. The proposed strategy is compared to standard parametric and non-parametric procedures on a real-world data set composed of 262 accelerometer recordings.

Motif Discovery consists of finding repeated patterns and locating their occurrences in a time series without prior knowledge about their shape or location. Most state-of-the-art algorithms rely on three core parameters: the number of motifs to discover, the length of the motifs, and a similarity threshold between motif occurrences. Setting these parameters is difficult in practice and often results from a trial-and-error strategy. In this paper, we propose a new algorithm that discovers motifs of variable length given a single motif length and without requiring a similarity threshold. At its core, the algorithm maps a time series onto a graph, summarizes it with persistent homology - a tool from topological data analysis - and identifies the most relevant motifs from the graph summary. We propose two versions of the algorithm, one requiring the number of motifs to discover and another, adaptive, that infers the number of motifs from the graph summary. Empirical evaluation on 9 labeled datasets, including 6 real-world datasets, shows that both algorithm versions significantly outperform state-of-the-art algorithms.