Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors
AbstractThe direct position determination approach was recently presented as a promising technique for the localization of a transmitting source with accuracy higher than that of the conventional two-step localization method. In this paper, the theoretical performance of a direct position determination estimator proposed by Weiss is examined for situations in which the array model errors are present. Our study starts from a matrix eigen-perturbation result, which expresses the perturbation of eigenvalues as a function of the disturbance added to the Hermitian matrix. The first-order asymptotic expression of the positioning errors is presented, from which an analytical expression for the mean square error of the direct localization is available. Additionally, explicit formulas for computing the probabilities of a successful localization are deduced. Finally, Cramér–Rao bound expressions for the position estimation are derived for two cases: (1) array model errors are absent and (2) array model errors are present. The obtained Cramér-Rao bounds provide insights into the effects of the array model errors on the localization accuracy. Simulation results support and corroborate the theoretical developments made in this paper. View Full-Text
Share & Cite This Article
Wang, D.; Yu, H.; Wu, Z.; Wang, C. Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors. Sensors 2017, 17, 1550.
Wang D, Yu H, Wu Z, Wang C. Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors. Sensors. 2017; 17(7):1550.Chicago/Turabian Style
Wang, Ding; Yu, Hongyi; Wu, Zhidong; Wang, Cheng. 2017. "Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors." Sensors 17, no. 7: 1550.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.