Time of arrival (TOA)-based direct location method

The presented direct location method computes the 3D position of an object using exactly four time-of-arrival (TOA) measurements, i.e. range measurements, to four reference points or stations. This operation is also commonly known as multilateration. Traditionally, this problem can also be solved using three TOA measurements to three reference stations, i.e. trilateration. However, a twofold ambiguity, usually of the vertical component, arises, which cannot be resolved without some prior knowledge about the general location of the object or an extra TOA measurement. The developed algorithm is simpler and faster than conventional ones, thus, complexity in terms of time, power consumption, and chip area is reduced. Therefore, the algorithm is suitable for applications with limited computational and power resources.