A Constrained-Total-Least-Squares Method for Joint Estimation of Source and Sensor Locations: A General Framework

It is well known that sensor location uncertainties can significantly deteriorate the source positioning accuracy. Therefore, improving the sensor locations is necessary in order to achieve better localization performance. In this paper, a constrained-total-least-squares (CTLS) method for simultaneously locating multiple disjoint sources and refining the erroneous sensor positions is presented. Unlike conventional localization techniques, an important feature of the proposed method is that it establishes a general framework that is suitable for many different location measurements. First, a modified CTLS optimization problem is formulated after some algebraic manipulations and then the corresponding Newton iterative algorithm is derived to give the numerical solution. Subsequently, by using the first-order perturbation analysis, the explicit expression for the covariance matrix of the proposed CTLS estimator is deduced under the Gaussian assumption. Moreover, the estimation accuracy of the CTLS method is shown to achieve the Cramér-Rao bound (CRB) before the thresholding effect occurs by a rigorous proof. Finally, two kinds of numerical examples are given to corroborate the theoretical development in this paper. One uses the TDOAs/GROAs measurements and the other is based on the TOAs/FOAs parameters.