In a sensor network localization (SNL) problem, we attempt to determine the two- or three-dimensional layout of a network of sensors from some of their pairwise distances. We present an efficient projected gradient method to approximately solve the SNL problem if a good initial guess of the sensor locations is available. When the sensors are not static, our method is an efficient way to update the estimate of their positions and so provides a way of tracking the sensors as they move. Along the way, we present an analysis of the projected gradient method for arbitrary feasible sets onto which we can project exactly, which is of independent interest. Numerical results demonstrate the practical efficacy and robustness of our method.