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WiFi technology has been used pervasively in fine-grained indoor localization, gesture recognition, and adaptive communication. Achieving better performance in these tasks generally boils down to differentiating Line-Of-Sight (LOS) from Non-Line-Of-Sight (NLOS) signal propagation reliably which generally requires expensive/specialized hardware due to the complex nature of indoor environments. Hence, the development of low-cost accurate positioning systems that exploit available infrastructure is not entirely solved. In this paper, we develop a framework for indoor localization and tracking of ubiquitous mobile devices such as smartphones using on-board sensors. We present a novel deep LOS/NLOS classifier which uses the Received Signal Strength Indicator (RSSI), and can classify the input signal with an accuracy of 85\%. The proposed algorithm can globally localize and track a smartphone (or robot) with a priori unknown location, and with a semi-accurate prior map (error within 0.8 m) of the WiFi Access Points (AP). Through simultaneously solving for the trajectory and the map of access points, we recover a trajectory of the device and corrected locations for the access points. Experimental evaluations of the framework show that localization accuracy is increased by using the trained deep network; furthermore, the system becomes robust to any error in the map of APs.