access icon free Spherical interpolation method of emitter localisation using weighted least squares

© The Institution of Engineering and Technology
Received 07/06/2015, Accepted 22/04/2016, Revised 30/03/2016, Published 26/04/2016

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.

Inspec keywords: sensor placement; matrix algebra; direction-of-arrival estimation; least squares approximations; interpolation; error analysis; time-of-arrival estimation

Other keywords: weighting matrices; sensor; emitter target localisation; spherical interpolation method; weighted least squares; two-dimensional space; Cramer–Rao lower bound; error analysis; time difference of arrival measurements; target position estimation; root mean square error; noise model

Subjects: Error analysis in numerical methods; Interpolation and function approximation (numerical analysis); Signal processing theory; Linear algebra (numerical analysis); Signal processing and detection; Linear algebra (numerical analysis); Error analysis in numerical methods; Interpolation and function approximation (numerical analysis)

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