The ultra-wide band radio technology (UWB) is currently considered the de-facto standard for implementing precise indoor positioning systems. Several positioning algorithms are currently being investigated for finding the best implementation in terms of scalability, refresh rate, and energy requirements. Among all the proposed approaches, the Downlink Time Difference of Arrival (DTDoA) is currently considered one of the most promising techniques capable of tracking any number of assets without decreasing the measurement update rate. This paper proposes a model for the DTDoA and validates the algorithms on UWB data, using a motion capture system as ground truth. Results highlight the validity of the previously proposed model, showing that the proposed UWB indoor positioning system achieves a maximum 30 cm uncertainty with only a simple wireless synchronisation, avoiding wired procedure that limits the usability of the infrastructure.