Joint source localisation and sensor refinement using time differences of arrival and frequency differences of arrival

The accuracy of sources locations and velocities estimate is very sensitive to the accurate knowledge of sensor locations and velocities. In the presence of sensor position and velocity errors, this study considers the problem of simultaneously locating multiple disjoint sources and refining erroneous sensor positions and velocities using time differences of arrival and frequency differences of arrival. The previous work by Sun and Ho to solve this problem provided an efficient estimator for multiple disjoint sources, but it cannot provide optimum accuracy for the sensor positions and sensor velocities. In many practical applications, it is necessary and helpful to refine sensor locations and velocities while localising multiple sources. The proposed method improves the previous method so that both the source and the sensor position and velocity estimates can achieve the Cramér-Rao lower bound accuracy very well over small noise region. The theoretical derivation is corroborated by simulations.