Shanghai Posts & Telecommunications Designing Consulting Institute

Abstract Multidimensional scaling (MDS) is an attractive technique for a moving source localisation from time and frequency difference of arrival (time differences of arrival (TDOA)/frequency differences of arrival (FDOA)) measurements. However, its optimality has not yet been proven theoretically because of the difficult Moore–Penrose pesudo‐inverse operation. In addition to the theoretical incompleteness of the MDS technique, the sensor uncertainties are not considered in the MDS framework for the moving source localisation either. A closed‐form estimator is proposed for the TDOA/FDOA‐based localisation with senor uncertainties by exploiting the MDS technique. Furthermore, based on the fundamental corollaries in the MDS analysis, an elegant and detailed analytical proof is also presented for the optimality of the MDS estimator thoroughly in the presence and absence of sensor uncertainties. The theoretical derivation is corroborated by numerical examples.