Wireless Sensor Network-Based Localization Method Using TDOA Measurements in MPR

Localization is perhaps one of the most interesting research subjects in signal processing. Traditional localization methods rely on the prior information whether the source is located in the near-field or far-field. Since the prior knowledge is hard to obtain in practice, neither positioning nor bearing may not be able to provide reliable performance for both cases. The modified polar representation (MPR) is proposed to solve this contradictory problem in a uniform framework and eliminate the thresholding effect as the source range increases. The maximum likelihood estimator (MLE) in the state-of-art research realizes excellent performance reaching the Cramér-Rao lower bound (CRLB) but it is computation-complex and time-consuming. Besides, it has the possible divergence problem if the initial value is not close enough to the true value. This paper focuses on the localization problem using time difference of arrival measurements in MPR. Formulating it in a new form, we develop a two-step least squares (LS) estimator for the MPR model. The weighted total LS is applied in the first step and the weighted LS for the final solution, where the second step is based on the natural constraint of the unknowns. The proposed method is closed-form and able to reach CRLB in low noise power situation irrespective of the source range. The covariance is analyzed and proved to provide CRLB accuracy for Gaussian noise theoretically. Simulation supports our theoretical results and verifies the advocated performance that is comparable with MLE but simpler and computationally more efficient. It outperforms the classical closed-form solution.