Localization using the received signal strength indication (RSSI) of wireless local area networks with a priori knowledge of the coordinates of the routers/access points is addressed in this paper. The proposed algorithm employs a path loss model that allows for the inclusion of the logarithmic measurements of the signal strength directly in the state of the nonlinear system that is designed. The nonlinear system is augmented in such a way that the resulting system structure may be regarded as linear time-varying for observability purposes, from which a Kalman filter follows naturally. Simulation results are included that illustrate the performance of the proposed solution.