Optimal placement of landmarks for indoor localization using sensors with a limited range

Indoor positioning often requires detecting and recognizing ad-hoc landmarks or anchor points with known coordinates and/or a given orientation within a given reference frame. Typically, the available kind of sensors and their detection area determine the landmark features and position. Of course, an excessive use of landmarks pose serious scalability and cost issues, whereas, on the other hand, a too-low amount of deployed landmarks may create areas where agent's position is hard to track or localization accuracy drops. In addition, often sensors are not omni-directional. In this paper, the optimal placement problem of landmarks detected by sensors with a limited detection area is addressed in the general case of wide-open, ideally unbounded, rooms. First, landmarks placement optimization is performed numerically. Then, a closed-form expression of the optimal distance between landmarks on a regular pattern is determined as a function of both the reading range and the directional properties of the sensor considered. Finally, the performances of the chosen placement strategy in more realistic indoor environments (i.e. consisting of multiple rooms with obstacles therein) are evaluated through simulations assuming, without loss of generality, that a wheeled robot equipped with a front camera adjusts its own position by detecting suitable visual landmarks.