WLS-Based Self-Localization Using Perturbed Anchor Positions and RSSI Measurements

We consider the problem of self-localization by a resource-constrained node within a network given radio signal strength indicator (RSSI) measurements from a set of anchor nodes where the RSSI measurements as well as the anchor position information are subject to perturbation. In order to achieve a computationally efficient estimate for the unknown position, we minimize a weighted sum-square-distance-error cost function in an iterative fashion utilizing the gradient-descent method. We calculate the weights in the cost function by taking into account perturbations in both RSSI measurements and anchor node position information while assuming normal distribution for the perturbations in the anchor node position information and log-normal distribution for the RSSI-induced distance estimates. The latter assumption is due to considering the log-distance path-loss model with normally-distributed perturbations for the RSSI measurements in the logarithmic scale. We also derive the Cramer-Rao lower bound associated with the considered position estimation problem. We evaluate the performance of the proposed algorithm considering various arbitrary network topologies and compare it with an existing algorithm that is based on a similar approach but only accounts for perturbations in the RSSI measurements. The experimental results show that the proposed algorithm yields significant improvement in localization performance over the existing algorithm while maintaining its computational efficiency. This makes the proposed algorithm suitable for real-world applications where the information available about the positions of anchor nodes often suffer from uncertainty due to observational noise or error and the computational and energy resources of mobile nodes are limited, prohibiting the use of more sophisticated techniques such as those based on semidefinite or second-order cone programming.