In this paper, a stride detector algorithm combined with a technique inspired by zero velocity update (ZUPT) is proposed to reconstruct the trajectory of a pedestrian from an ankle-mounted inertial device. This innovative approach is based on sensor alignment and machine learning. It is able to detect 100% of both normal walking strides and more than 97% of atypical strides such as small steps, side steps, and backward walking that existing methods can hardly detect. This approach is also more robust in critical situations, when for example the wearer is sitting and moving the ankle or when the wearer is bicycling (less than two false detected strides per hour on average). As a consequence, the algorithm proposed for trajectory reconstruction achieves much better performances than existing methods for daily life contexts, in particular in narrow areas such as in a house. The computed stride trajectory contains essential information for recognizing the activity (atypical stride, walking, running, and stairs). For this task, we adopt a machine learning approach based on descriptors of these trajectories, which is shown to be robust to a large of variety of gaits. We tested our algorithm on recordings of healthy adults and children, achieving more than 99% success. The algorithm also achieved more than 97% success in challenging situations recorded by children suffering from movement disorders. Compared to most algorithms in the literature, this original method does not use a fixed-size sliding window but infers this last in an adaptive way.