Error analysis of electromagnetic motion tracking systems is of growing interest to many researchers. Under sensor movement, it is logical to presume that the error in position and orientation measurements will increase due to the linearization used in the algorithms, among other reasons. In this article, we analyze theoretically the error, that results from linearization, in position measurement of the Polhemus tracking system for a moving sensor. We derive formulas to estimate this error in terms of the sensor position and speed. Then, we verify these formulas by numerical simulations.

In this work, the Mixed-Integer (MIP) formulation for unit commitment problem (UC) for power systems is discussed. A new formulation for the start-up cost is suggested as well. This new formulation of the start-up cost exploits the transformation of the conditional statements into inequalities that comprise linear combination of binary variables. Solutions of the suggested optimization problem were obtained. A comparison between these solutions and those of a strategy common in literature is held to show that the new strategy gives same results with less number of constraints and tighter capture of the start-up cost.