The Local Position Measurement system (LPM) is one of the most precise systems for 3D position estimation. It is able to operate in- and outdoor and updates at a rate up to 1000 measurements per second. Previous scientific publications focused on the time of arrival equation (TOA) provided by the LPM and filtering after the numerical position estimation. This paper investigates the advantages of the TOA over the time difference of arrival equation transformation (TDOA) and the signal smoothing prior to its fitting. The LPM was designed under the general assumption that the position of the base station and position of the reference station are known. The information resulting from this research can prove vital for the systems self-calibration, providing data aiding in locating the relative position of the base station without prior knowledge of the transponder and reference station positions.