Localization in unknown environments using low-cost sensors remains a challenge. This paper presents a new localization approach that learns the spatial variation of an observed continuous signal. We model the signal as a piece-wise linear function and estimate its parameters using a simultaneous localization and mapping (SLAM) approach. We apply our framework to a sensor measuring bearing to active beacons where measurements are systematically distorted due to occlusion and signal reflections of walls and other objects present in the environment. Experimental results from running GraphSLAM and EKF-SLAM on manually collected sensor measurements as well as on data recorded on a vacuum-cleaner robot validate our model.