Perturbation analysis of conjugate MI-ESPRIT for single acoustic vector-sensor-based noncircular signal direction finding

• Published in: Signal processing Vol. 87; no. 7; pp. 1597 - 1612
• Main Authors: Xu, Yougen, Liu, Zhiwen, Cao, Jinliang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2007; Elsevier Science
• Subjects: Acoustic array; Antenna arrays; Applied sciences; Array signal processing; Detection, estimation, filtering, equalization, prediction; Direction-of-arrival estimation; Exact sciences and technology; Information, signal and communications theory; Miscellaneous; Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; Acoustic array; Direction-of-arrival estimation; Array signal processing; Antenna arrays; Performance evaluation; Second order; Parameter estimation; Wireless telecommunication; Signal estimation; Radiolocalisation; Mean square error; Directivity; Perturbation method; Accuracy; Correspondence analysis; Antenna array; Acoustic measurement; Redundancy; Subspace method; Two dimensional model; Invariance; Algorithm; Free space propagation; Simulation; Acoustic sensor; Cumulant
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2006.12.016

The closed-form conjugate multiple-invariance ESPRIT (CMI-ESPRIT) algorithm herein analyzed: (1) makes use of redundancy in the nonvanishing conjugated second- and fourth-order cumulants of noncircular signals; (2) recognizes the real-valued two-dimensional directivity inherently achieved by an acoustic vector-sensor in a free-space. It is provided in this correspondence the perturbation analyses on both the norm-penalized and the subspace-constraint ESPRIT matrices that play the key role in the CMI-ESPRIT. It is shown that the norm-penalized ESPRIT matrix is biased (but bounded) and has a minimal mean-squared-error (MSE) for some finite regularization factor, whereas the subspace-constraint ESPRIT matrix is unbiased and its MSE approaches minimum when the regularization factor becomes infinite. These observations are potentially useful for the determination of the regularization parameters which is significant for the performance of CMI-ESPRIT. The results also contribute to the ultimate study of direction-finding accuracy. Simulation results are presented to validate the given analyses.