One‐to‐one non‐linear transformation for RSS‐based localization with unknown transmit power

Abstract

For most of the positioning algorithms, based on the received signal strength, the objective function of the estimator is linearized so that the conventional least square algorithm can be executed. This would necessitate using a data model containing many noisy elements which implicitly violates the least squares assumptions. To avoid this violation, an optimized data modelling would have to be set up as shown in this paper. The authors then trivially provide the solution of this new least square problem which is still a primary coarse position estimation because of ignoring the non‐linear relationships existing among parameters of the estimation. To extract quantitative information from these non‐linear relationships, the authors also propose two new signal space points for using Taylor‐series expansion as effectively as possible in accordance of the new data model. The proposed algorithms work without any knowledge about the transmit power. The performance evaluation of the proposed idea indicates that the new suggested estimators perform significantly better than the other existing linear position estimators for a large range of noise variance and path‐loss exponent values.