Spherical interpolation method of emitter localisation using weighted least squares

In this study, a new noise model is presented to address the issue of finding an emitting target using time difference of arrival measurements, based on the range between the emitter and a known sensor. To improve the performance of the estimator under the proposed noise model, a weighted version of the spherical interpolation method is proposed and then two weighting matrices required in the method are derived in two different conditions. A detailed theoretical error analysis associated with this algorithm is presented and the Cramer–Rao lower bound is also derived. Simulation studies verify the validity of the proposed error analysis. In addition, in a two‐dimensional space and in the case of a minimal number of sensors, the authors analytically determine the sensors layout in which the location solution is not unique. Via simulations, several placements in a covered region are studied to select the appropriate placement in which the root mean square error of the target position estimation is minimised. Furthermore, simulation results show that they can do this work by the derived expression of the error analysis, which leads to the same outcome.