Maximum likelihood array calibration using particle swarm optimisation

Calibration of array shape error is a key issue for most existing source localisation algorithms. In this study, the far-field self-calibration and near-field pilot-calibration are carried out using unconditional maximum likelihood (UML) estimator whose objective function is optimised by particle swarm optimisation (PSO). A new technique, decaying diagonal loading (DDL), is proposed to enhance the performance of PSO at high signal-to-noise ratio (SNR) by dynamically lowering it, based on the counter-intuitive observation that the global optimum of the UML objective function is more prominent at lower SNR. Numerical simulations demonstrate that the UML estimator optimised by PSO with DDL is robust to large shape errors, optimally accurate and free of the initialisation problem. In addition, the DDL technique can be coupled with different global optimisation algorithms for performance enhancement. Mathematical analysis indicates that the DDL is applicable to any array processing problem where the UML estimator is employed.

[1]  Jian Li,et al.  On robust Capon beamforming and diagonal loading , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[2]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[3]  Anthony J. Weiss,et al.  Array shape calibration using eigenstructure methods , 1991, Signal Process..

[4]  James Ting-Ho Lo.  Minimization through convexitization in training neural networks , 2002, Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290).

[5]  Salman Mohagheghi,et al.  Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems , 2008, IEEE Transactions on Evolutionary Computation.

[6]  Anthony J. Weiss,et al.  Array shape calibration using sources in unknown locations-a maximum likelihood approach , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[7]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[8]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[9]  Kristine L. Bell,et al.  Array self calibration with large sensor position errors , 1999 .

[10]  Bernard Mulgrew,et al.  Near-field array shape calibration , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[11]  Michael N. Vrahatis,et al.  On the computation of all global minimizers through particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[12]  Rainer Storn,et al.  Minimizing the real functions of the ICEC'96 contest by differential evolution , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[13]  Pei-Jung Chung,et al.  Array shape self-calibration using particle swarm optimization and decaying diagonal loading , 2010 .

[14]  Yide Wang,et al.  Interpolation-based calibration for near-field source localization , 2009, 2009 17th European Signal Processing Conference.

[15]  Hagit Messer,et al.  Sufficient conditions for array calibration using sources of mixed tapes , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[16]  Pei-Jung Chung,et al.  Array self-calibration using SAGE algorithm , 2008, 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop.

[17]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[18]  G. Thiele,et al.  Antenna theory and design , 1981 .

[19]  Y. Hua,et al.  A weighted linear prediction method for near-field source localization , 2002, IEEE Transactions on Signal Processing.

[20]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[21]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[22]  Yilong Lu,et al.  Maximum likelihood DOA estimation in unknown colored noise fields , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[23]  Peter M. Schultheiss,et al.  Array shape calibration using sources in unknown locations-Part I: Far-field sources , 1987, IEEE Trans. Acoust. Speech Signal Process..

[24]  Shuang Wan.  Parametric array calibration , 2011 .

[25]  Peter M. Schultheiss,et al.  Array shape calibration using sources in unknown locations-Part II: Near-field sources and estimator implementation , 1987, IEEE Trans. Acoust. Speech Signal Process..