The position determination inside a building where no GPS signal is beingreceived can be ascertained using laser transmitters in industrial situations where there areno people or using triangulation of the signal strength, normally electro-magnetic signals,if the required accuracy is more than a metre. Our solution is aimed at situations wherepeople are present and where the required accuracy is less than 30 cm, such as in shoppingprecincts or supermarkets. To achieve this, a network of ultrasonic transmitters is fittedinto the ceiling which receives a synchronised time signal. Each transmitter has a uniqueidentifier code and emits its code with a delay with respect to the common time signalwhich is proportional to its code number with an ASK modulation over the ultrasonic bandcentred on 40 KHz. The receivers circulating beneath the transmitters receive the codes ofthose within their detection range, translate the time delays into distances and then obtaintheir position by triangulation since the receivers know the position of every transmitter.Since the receivers are not synchronised with the common time signal or the actual speedof the sound, whose value varies appreciably with temperature, relative humidity andatmospheric pressure, a consecutive approximation algorithm has been introduced. This isbased on the fact that the Z coordinator of the receiver is known and constant and thus it is possible, with only three different identifiers received, to deduce the phase of the common time signal and estimate the speed of the sound with a fourth identifie