Applying Modified Cramér-Rao Bound to Random Sensor Deployment

Careful node placement can be a very efficient optimization means for achieving the desired design goals, as well as good performance in the network application. In this paper, we discuss the sensor deployment problem in the context of target location through the Modified Cram´er-RaoBound (MCRB). It provides a minimum variance bound on estimation error giving an idea of the quality in the expected results. Assuming uniformly deployed sensor, Modified Fisher Information Matrix (MFIM) and MCRB expressions have been obtained. They have been derived for different kinds of measurement: Time of Arrival (ToA), Angle of Arrival (AoA)and Received Signal Strength (RSS). In addition we are able to quantify the information increment that the distribution of a new sensor can provide. Finally, all these expressions lead to a methodology, which makes it possible to select the number of deployed sensors and their category. The results point out the behaviour of estimation error when the number of deployed sensors is increased, and which points of the surveillance area are more problematic.