Sensor localization with algebraic confidence

In this paper we introduce the concept of algebraic confidence, defined as the measure of belief provided by an algebraic algorithm without a priori information of ranging statistics. This is obtained by employing the Circular-based Interval SMACOF (CIS) algorithm which outputs an algebraic confidence level on targets´ estimates, without relying on the propagation of location distributions. We illustrate the validity of our confidence by comparing it to the Fisher error ellipses derived from the Cramér-Rao lower bound (CRLB), corroborating the concept. To exploit the proposed confidence measures during the optimization process, we modify the cost function used in the Circular-based Interval SMACOF (CIS) algorithm and describe how to solve the corresponding optimization problem by means of majorization techniques. The resulting CIS+ algorithm is shown to outperform the CIS algorithm both in terms of accuracy as well as in terms of computational complexity.