Algebraic confidence in positioning problems

In this paper we extend the previous work on positioning problems using the Circular Interval-based scaling (CIS) algorithm previously proposed by the authors. In particular it is shown how the radius that the CIS algorithm associates to the targets is related to the average statistic of the set of measurements related to them. Together with a factor computed on the basis of the geometric dilution of precision (GDOP), this parameter is utilized to compute a confidence measure for the targets´s locations which can be utilized to account for a priori information over the position estimates when recomputing the network configuration. The results show that the proposed extended CIS cost function, called CIS;, dramatically improve the estimates over the targets´ locations. Non-line-of-sight (NLOS) range observations are also accounted for by modifying the least-square term in the extended CIS cost function with a term favoring sparsity, resulting in the R-CIS; solution. Under these conditions the R-CIS; solution is shown to compensate eventual NLOS range measurements without need for any bias identification algorithm.