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Sensors 2018, 18(4), 1088; https://doi.org/10.3390/s18041088

Parameter Estimation of Multiple Frequency-Hopping Signals with Two Sensors

1,2,*
,
1
and
1
1
Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
*
Author to whom correspondence should be addressed.
Received: 9 February 2018 / Revised: 30 March 2018 / Accepted: 2 April 2018 / Published: 4 April 2018
(This article belongs to the Section Sensor Networks)
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Abstract

This paper essentially focuses on parameter estimation of multiple wideband emitting sources with time-varying frequencies, such as two-dimensional (2-D) direction of arrival (DOA) and signal sorting, with a low-cost circular synthetic array (CSA) consisting of only two rotating sensors. Our basic idea is to decompose the received data, which is a superimposition of phase measurements from multiple sources into separated groups and separately estimate the DOA associated with each source. Motivated by joint parameter estimation, we propose to adopt the expectation maximization (EM) algorithm in this paper; our method involves two steps, namely, the expectation-step (E-step) and the maximization (M-step). In the E-step, the correspondence of each signal with its emitting source is found. Then, in the M-step, the maximum-likelihood (ML) estimates of the DOA parameters are obtained. These two steps are iteratively and alternatively executed to jointly determine the DOAs and sort multiple signals. Closed-form DOA estimation formulae are developed by ML estimation based on phase data, which also realize an optimal estimation. Directional ambiguity is also addressed by another ML estimation method based on received complex responses. The Cramer-Rao lower bound is derived for understanding the estimation accuracy and performance comparison. The verification of the proposed method is demonstrated with simulations. View Full-Text
Keywords: DOA estimation; synthetic array; Cramer-Rao lower bound (CRLB); maximum likelihood (ML) estimation; expectation maximization (EM) algorithm DOA estimation; synthetic array; Cramer-Rao lower bound (CRLB); maximum likelihood (ML) estimation; expectation maximization (EM) algorithm
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zuo, L.; Pan, J.; Ma, B. Parameter Estimation of Multiple Frequency-Hopping Signals with Two Sensors. Sensors 2018, 18, 1088.

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