Reaching asymptotic efficient performance for squared processing of range and range difference localizations in the presence of sensor position errors

Computationally efficient source location solutions from TOAs or TDOAs require the squaring of the measurements before optimization. The squaring operation changes the characteristics of the measurements and causes degradation in the localization accuracy, unless proper weightings are applied when forming the cost function for minimization. The previously developed weighting values are useful for measurements with accurate sensor positions only. This paper extends the study and derives the weightings when the sensor position uncertainties are present such as in sensor networks. The resultant cost functions for TOA and TDOA positionings are analyzed and the performance accuracy is shown to attain the CRLB asymptotically under Gaussian noise. Simulations validate the performance of the new cost functions and the theoretical investigations.