In pertinence to the application of multidimensional scaling (MDS) methods in ranging-based positioning systems, an analysis is firstly conducted by the classical MDS algorithm. Modified MDS algorithm and subspace method are presented in localization application. We also depicted the unified framework and general solutions of MDS methods. However, the least square solutions under this framework are not optimal. Their performance is still related to selection of coordinate reference points. To address this problem, a minimum residual MDS algorithm based on particle swarm optimization (PSO) is proposed to derive a new solution for indoor robot localization under the unified framework. The result of analysis indicates that the performance of minimum residual MDS method is immune to selection of reference points. Furthermore, the localization accuracy for indoor robot has been enhanced by 41% as compared with the classical MDS algorithm.
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