Modulated Mathematical Formulation of MSE for Assessment of a Positioning System in Live-status

Abstract

In wireless sensor network (WSN), It is a substantial affair to obtain a convenient assessment metric for evaluating created positioning systems. Mean square error (MSE) is one of very paramount assessment metrics utilized for such problem. The conventional mathematical formula of MSE such as the built in MSE function in matlab is utilized only when the real and measured values of the position are available, which means utilizing the MSE is potential only after building the system not while building it. In this paper, for positioning purpose, we offer a mathematical derivation of an MSE formulation based on least square (LS) approach for three-dimensional positioning system without utilizing the real and measured position. The created MSE uses only the measured distance between anchor nodes and a mobile station, that needs its position to be calculated. The formed MSE has the ability to assess a positioning system online based only on the estimated distances, and then the user can modulate his system until obtaining a system ambidextrous to match the requested positioning accuracy. The derived MSE has accuracy 100 % equals to the conventional mathematical formulation such as the built in matlab MSE function.