Hyperbolic ultrasonic LPS using a Cayley-Menger bideterminant-based algorithm

This paper presents a new algorithm to obtain the position of a mobile with an ultrasonic local positioning system (US-LPS). The system consists of five beacons placed in the ceiling covering a wide working area. The simultaneous emissions of all the beacons are synchronized, and encoded by using a DS-CDMA technique with five different 255-bit Kasami sequences. A receiver is placed on the mobile to be positioned and its position is calculated by hyperbolic trilateration using the differences in times of arrival (DTOA) between the received signals (considering one of them as reference) obtained by correlation. With the DTOAs, the position of the mobile device is computed by using a new Cayley-Menger bideterminant-based algorithm. Compared to traditional methods, as the minimization of non-linear equations by the Newton-Gauss algorithm, the new algorithm is easier to implement (no iterations are needed) and it achieves similar performances. Both, simulated and real results are presented for this new algorithm.