We focus in this paper in the estimation of a target trajectory defined by whether a time constant parameter in a simple stochastic process or a random walk with binary observations. The binary observation comes from binary derivative sensors, that is, the target is getting closer or moving away. Such a binary observation has a time property that will be used to ensure the quality of a max-likelihood estimation, through single index model or classification for the constant velocity movement. In the second part of this paper we present a new algorithm for target tracking within a binary sensor network when the target trajectory is assumed to be modelled by a random walk. For a given target, this algorithm provides an estimation of its velocity and its position. The greatest improvements are made through a position correction and velocity analysis.