A method for localizing robots and other objects when ranging devices are partially obstructed. The method includes retrieving a digital map of the space and then identifying potential locations for the object in the space. The method involves generating a prediction of expected ranges between the object and surfaces in the space at each of the potential locations. The method includes operating a ranging device to measure ranges to the surfaces in the space and comparing, for each of the predictions, the measured ranges with the expected ranges to identify the most accurate prediction. The comparing includes weighting ranges that are too small neutrally as these are strikes on obstructions, weighting ranges that provide matches positively, and weighting ranges that are too large negatively, and the comparing then involves summing the weighted ranges to identify a most accurate one of the predictions and associated current location for the object.