Figure 2

Example showcasing the steps towards the calculation of the PtM duration. In the first step (a) the subset \(\mathbf{y}_{i,u}\) is presented for the inter-bite interval \([b_{i-1},b_{i}]\). Bite timestamps \(b_{i-1}\) and \(b_{i}\) are represented as blue circles. The green stems marked with u symbolize the upwards moments, while the red stems marked with \(\lnot \)u signify the non-upwards moments. In the following step (b) the set of u-regions \(\mathfrak{R}_{i} = \{r_{i,1},r_{i,2},r_{i,3}\}\) is formed and the distances \(d_{i}(r_{i,3},r_{i,2})\) and \(d_{i}(r_{i,2},r_{i,1})\) are calculated. For this example we will use the \(\times \) symbol to indicate that \(d_{i}(r_{i,2},r_{i,1})\) is greater than the \(\lambda _{d}\) threshold and therefore, that merge is considered unsuccessful. As a result, the number of consecutive successful merges \(J_{i}\) equals to one. The last step (c) presents the temporal positioning of the \(\tau _{i}^{s}\) and \(\tau _{i}^{e}\) moments. Finally, duration \(\text {PtM}_{i}\) is given by \(\tau _{i}^{e} -\tau _{i}^{s} - d_{i}(r_{i,3},r_{i,2})\).