Improved MDS-based Localization with Non-line-of-sight RF Links

The performance of indoor localization techniques adopted in robot localization systems that use radio positioning is usually degraded in non-line-of-sight (NLOS) environments. In this paper, we propose a technique for estimating NLOS biases and measurement noise in distances under multidimensional scaling (MDS) based positioning with fixed nodes. An ideal matrix of pairwise distance measurements exhibits a symmetry that allows to compute mobile node positions from those of fixed ones, and then recompute exactly the fixed node positions from the earlier computed mobile node positions. In a NLOS environment, this symmetry is lost; fixed node positions can not be reproduced exactly. This work exploits the error in the recomputation of fixed node positions for the correction of NLOS biases and noise in the pairwise distances. A constrained-optimization problem is formulated to estimate biases for each measured distance and final mobile node positions under the MDS scheme. A supplementary approach is presented for special cases where the number of mobile nodes is less than 3. Experimental results show that position errors can be reduced by up to 28{%} for a set up of 4 fixed and 3 mobile nodes. Simulations are used to further validate the results for larger deployments of nodes.