TDoA Geolocation Accuracy as a Function of the Number of Randomly Placed Sensors

This paper addresses the problem of locating a radio frequency (RF) emitter on the ground using a set of ground-based or airborne sensors. Time difference-of-arrival (TDoA) measurements at pairs of sensors are combined to obtain an estimate of the emitter location. The central question is to determine the trend of the relative reductions in statistical metrics for Location Distance Error (LDE), in the presence of sensor position and timing errors, as the number of sensors increases. Analysis is based on Monte Carlo simulations of randomly generated geometries of an emitter and the sensors. It is shown that, even in the error-free case, a minimum of five sensors should be used to avoid significant percentages of bad geometries with intrinsically large LDE. Combining the measurements of all pairs of sensors, rather than subsets of pairs, consistently provides the smallest LDE although at increased computational cost. This paper determines the sensitivity of LDE to sensor altitude as well as position errors and timing errors. Regression models relate LDE statistical metrics to the number of sensors and the specific configurations; the double logarithm of each of the LDE statistical metrics is closely estimated by a linear function of the double log of the number of sensors. The improvement in LDE statistical metrics as the number of sensors increases can be approximated by simpler power law regression models. Rough estimates of LDE improvement are provided as multiples of the reciprocal of the number of sensors. This paper also determines the improvement in LDE achieved by the simple rule of enforcing minimum separation between the sensors.