Efficient trilateration algorithm using time differences of arrival

This work presents a novel hyperbolic algorithm to compute the absolute position of a mobile node (tag) in a Local Positioning System (LPS) based on the transmission of encoded signals from a set of beacons and computing the TDOA (Time Differences of Arrival) at the receiver. The new algorithm exploits the properties of Cayley–Menger bideterminants to obtain accurate position location without requiring synchronization among emitters and receivers. Three different resolution approaches for this algorithm are presented here, one of them considering some geometrical constraints. In comparison with traditional methods, such as minimization of non-linear equations by the Gauss–Newton algorithm, this proposal achieves a similar performance with a lower computational load, i.e. is more efficient in this sense. The performance of the algorithm has been validated both by simulation (taking into account the order of complexity for a generic number of beacons) and by real tests in an ultrasonic LPS.