We present a novel approach for tracking piecewise linear trajectories using a network of cheap "binary sensors" that can only detect whether an object is in their sensing range. We show that an object traveling on almost all straight lines, with an  unknown speed, can be tracked by generically placed three binary sensors whose sensing ranges need not intersect with each other, but do intersect the trajectory. We present asymptotic results that show that if a trajectory comprises a finite number of straight line segments, then high tracking accuracy can be achieved with arbitrarily low density of sensors. We also present efficient algorithms that simulations and theory verify, achieve good tracking performance, robustness to sensing errors.