TDoA Localization in Wireless Sensor Networks Using Constrained Total Least Squares and Newton’s Methods

Abstract

An important service in the wireless systems for the human daily life is the information of a mobile user location. Wireless sensor network is a structure that can be used to determine the mobile user position. The time-difference-of-arrival (TDoA) technique is often considered for wireless localization due to the low cost of the sensor network. In this work, the error covariance matrices are derived for predicting the error performance of the conventional closed-form constrained total least squares (CTLS) estimator. More importantly, three new Newton’s methods are proposed for computing the CTLS solution in the TDoA localization. In addition, theoretical performance of both new Newton-based approaches is provided in closed forms. Numerical simulation is conducted to compare the derived theoretical prediction with the corresponding actual estimation error. It is illustrated that the two new Newton-based techniques provide better performance, in terms of lower bias and root mean square error, less computational time, and more reliability, than the former Newton-based algorithms. Furthermore, the derived expressions for the theoretical error covariance well coincide with the actual random estimation results.

Keywords

• First-order Taylor’s series expansion
• error covariance
• localization
• time difference of arrival
• Newton’s method