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After the success of Global Positioning System (GPS) which provides precise positioning in open-sky areas having reliable satellites visibility, significant research is currently focused on providing similar systems for indoors in which satellites are poorly visible or unavailable. This paper introduces a GPS-like indoor positioning system based on Received Signal Strength (RSS) of the popular IEEE 802.11 networks (WiFi). Unlike current RSS-based indoor systems, the proposed system doesn't require time-consuming offline radio survey or prior-knowledge about the area or new hardware. Similar to GPS, the system consists of three segments; network segment (WiFi), control segment, and user segment. RSS observations are exchanged periodically between network segment and control segment. The control segment uses a novel hybrid propagation modeling (PM) technique using logarithmic decay model augmented by a nonlinear Gaussian Process Regression (GPR) that models RSS residuals that cannot be modeled by the traditional logarithmic decay models indoors. PM parameters are periodically estimated and sent to each AP. The user segment receives RSS and PM parameters from APs and performs trilateration weighting each observation by a variance calculated by GPR. Real experiments in indoor area show reliable meter accuracy comparable to those obtained from similar RSS-based indoor methods that uses offline time-consuming training such as fingerprinting.