Based on measurements of angle of arrival and time difference of arrival, a method is proposed to improve the accuracy of localization with imperfect sensors. A derivation of the Cramér–Rao lower bound and the root mean square error is presented aimed at demonstrating the significance of taking synchronization errors into consideration. Subsequently, a set of pseudo-linear equations are constructed, based on which the constrained total least squares optimization model has been formulated for target localization and the Newton iteration is applied to obtain the source position and clock bias simultaneously. The theoretical performance of the constrained total least squares localization algorithm subject to sensor position errors and synchronization clock bias is derived, and a framework for the performance analysis is developed. In addition, the first-order error analysis illustrates that the proposed method can achieve the Cramér–Rao lower bound under moderate Gaussian noises by a mathematic derivation. Finally, simulation results are presented that verify the validity of the theoretical derivation and superiority of the new algorithm.
Angle-of-Arrival based Constrained Total Least-Squares Location Algorithm