In wireless sensor network (WSN), It is an important matter to have a
convenient evaluation metric for assessing created positioning systems.
Mean square error (MSE) is one of very important evaluation metrics used
for such matter. The typical mathematical formula of MSE such as the
built in MSE function in matlab is used only when the true and estimated
values are available, which means using the MSE is useful only after
creating the system not while creating it. In this paper, we present a
mathematical derivation to derive an MSE formula based on least square
(LS) algorithm for three dimensional positioning system without using
the true and estimated position . The created MSE could evaluate a
positioning system online, and then the user can modify his system until
having the system able to match the requested positioning accuracy. The
created MSE has accuracy 100 % equals to the typical mathematical
formula such as the built in matlab MSE function.