Ultrasonic sensing, for instance for damage or fouling detection, is commonly carried out using rigid transducer collars, carefully placed for monitoring a well-defined local area of a structure. A distributed sensing network consisting of individually placed transducers offers significant opportunities for monitoring larger areas or more complex geometries. For analyzing the signals of such a distributed system, we inherently require precise information on the sensor locations, the physical characteristics of the sensed medium, and the quality of the transducer coupling. Determining these parameters with sufficient accuracy is time-consuming even in laboratory conditions. More importantly, these parameters often change over time in industrial setups due to maintenance operations, the gradual degradation of the coupling, or a change in material characteristics as a result of deformations or fouling accumulation. We propose an automatic data-driven approach for overcoming this challenge. We infer accurate sensor locations and physical characteristics of the sensed medium by aligning observed signal features with a physical forward simulation, providing an automatic routine for both the initial estimation of the required parameters as well as their later automatic adaptation to compensate for drifts during operations. The method is successfully demonstrated in two separate ultrasonic sensing configurations, without requiring prior knowledge of the structure material or accurate sensor locations.