A New Statistical Model for the Behavior of Ranging Errors in TOA-Based Indoor Localization

In time of arrival (TOA)-based indoor geolocation systems ranging error is a function of the bandwidth of the system and the availability of the direct path between the transmitter and the receiver. With a detected direct path (DDP) conditions and ultra wideband (UWB) transmission, precise range estimates are feasible while in undetected direct path (UDP) conditions large ranging errors occur which can not be cured with the increase of the transmission power or bandwidth. UDP conditions are caused by large metallic objects between the transmitter and the receiver or increase in the distance of the transmitter and the receiver so that the direct path fades away but the receiver still receives signal from other paths. For a given location of the transmitter, with respect to the huge metallic objects, the probability of occurrence of the UDP conditions changes. This paper provides an analytical method for calculation of the overall statistics of the ranging error for different location of the transmitter in a typical indoor environment. Results can be used for the analysis of the performance of precise RF localization techniques for sensor networks. Based on this model we show that the IEEE P802.15.3 recommended model is not adequate to represent the behavior of the ranging errors in typical indoor environments.