Location determination using Time Delay Matrix Pencil method with Grey Relational Analysis

A 3D location determination method using three base stations is proposed depending on a time delay matrix pencil (TDMP) method, grey relational analysis (GRA) and installing a small dipole antenna in each base station (BS). A group of signal symbols in time variant domain is received from the transmitter (on mobile station (MS) 2G/3G/4G), then transferred to the frequency domain using FFT. The matrix pencil method is applied to identify the length of each path. Depending on the geometrical distribution of the three receiving base stations and the position of the new installed small dipole antenna, the direction of arrival (DOA) and the signal travelling distances are determined for each path. Knowing the DOA and the distances between the mobile and the base stations help to find the mobile location for each path. Small dipole antennas are used in the numerical examples to clarify this location determination method in the presence of complex noise for GSM, WCDMA and OFDM systems. For the NLOS (non-line of sight), the GRA is used to compensate the NLOS error in location determination.