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Sensors 2017, 17(7), 1550; https://doi.org/10.3390/s17071550

Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors

1,2,* , 1,2
,
1,2
and
1,2
1
National Digital Switching System Engineering & Technological Research Center, Zhengzhou 450002, China
2
Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China
*
Author to whom correspondence should be addressed.
Received: 8 May 2017 / Revised: 22 June 2017 / Accepted: 29 June 2017 / Published: 2 July 2017
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Abstract

The 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
Keywords: direct position determination (DPD); array signal processing; array model errors; mean square error (MSE); success probability (SP); Cramér-Rao bound (CRB) direct position determination (DPD); array signal processing; array model errors; mean square error (MSE); success probability (SP); Cramér-Rao bound (CRB)
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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.

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