Performance Improvement of the AOA Estimation Algorithm Using the Newton Iteration
Keywords:
AOA, accuracy improvement, conventional beam forming algorithm, Capon beam forming algorithm, MUSIC algorithm, Newton method, UCA, ULAAbstract
In this paper, a simple numerical method based on the Newton iteration for improving the accuracy of the Conventional beam forming algorithm, the Capon beam forming algorithm, and the MUSIC algorithm for AOA (Angle-of-Arrival) estimation is presented. Based on observation, the estimates of the AOA’s for a specific AOA algorithm can be obtained from the extrema of a cost function associated with the specific AOA algorithm employed. We derive explicit expressions of the iterations used for the recursive update of the estimates of the AOA’s for the conventional beam forming algorithm, the Capon beam forming algorithm, and the MUSIC algorithm. The formulation is only for the update of the azimuth angle, while the extension to the update of the elevation angle and the azimuth angle can be implemented by taking into account the dependence of the array manifold on the elevation angle as well as the azimuth angle. Note that, for estimation of the azimuth, both the UCA (uniform circular array) and the ULA (uniform linear array) can be employed, and that, for simultaneous estimation of the elevation and the azimuth angle, the UCA, not the ULA, should be adopted since ULA-based algorithm cannot uniquely estimate both the azimuth and the elevation due to the ambiguity pertinent to the ULA structure. We consider the array structure of the ULA and the UCA, but it is quite straightforward to extend the proposed scheme to an arbitrary array structure by simply modifying the array vector consistently with the specific array structure. Index Terms - AOA, accuracy improvement, conventional beam forming algorithm, Capon beam forming algorithm, MUSIC algorithm, Newton method, UCA, and ULA.
Downloads
References
H. Krim and M. Viberg, “Two decades of array signal processing research – The parametric approach,” IEEE Signal Processing Magazine, vol. 13, pp. 67-94, July 1996.
J. –H. Lee and S. –H. Cho, “On initialization of ML DOA cost function for UCA,” Progress in Electromagnetics Research M, vol. 3, pp. 91-102, 2008.
J. –H. Lee, H. -J. Kwon, and Y. -K. Jin, “Numerically efficient implementation of JADE ML algorithm,” Journal of Electromagnetic Waves and Applications, vol. 22, pp. 1693-1704, 2008.
J. –H. Lee and S. –H. Cho, “Initialization of cost function for ML-based DOA estimation,” The Journal of Korea Information and Communications Society, vol. 33, no. 1, pp. 110-116, Jan. 2008.
M. Rubsamen and A. Gershman, “Direction-ofarrival estimation for non uniform sensor arrays: From manifold separation to Fourier domain MUSIC methods,” IEEE Trans. on Signal Processing, vol. 57, no. 2, pp. 588-599, 2009.
S. A. Vorobyov, A. B. Gershman, and K. M. Wong, “Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays,” IEEE Trans. Signal Processing, vol. 53, pp. 34-43, Jan. 2005.
H. Cao, L. Yang, X. Tan, and S. Yang, “Computationally efficient 2-D DOA estimation using two parallel uniform linear arrays,” ETRI Journal, vol. 31, no. 6, pp. 806-808, Dec. 2009.
J. A. Olague, D. C. Rosales, and J. L. Rivera, “Efficiency evaluation of the unconditional maximum likelihood estimator for near-field DOA estimation,” ETRI Journal, vol. 28, no.6, pp. 761- 769, Dec. 2006.
N. Deblauwe and L. Van Biesen, “An angle of arrival location estimation technique for existing GSM networks,” IEEE International Conference on Signal Processing and Communications, pp. 1527-1530, 2007.
S. Lalchand, A. Ijaz, M. M. Manzoor, I. A. Awan, and A. A. Siddique, “Error estimation in angle of arrival in smart antenna,” International Conference on Information and Communication Technologies, pp. 1-3, 2011.
I. Jami and R. F. Ormondroyd, “Improved method for estimating angle of arrival in multipath conditions using the `MUSIC' algorithm,” IEEEAPS Conference on Antennas and Propagation for Wireless Communications, pp. 99-102, 2000.
I. Amundson, X. Koutsoukos, J. Sallai, and A. Ledeczi, “Mobile sensor navigation using rapid RF-based angle of arrival localization,” 17th IEEE Real-Time and Embedded Technology and Applications Symposium, 2011.
Y. Luo and C. L. Law, “Angle-of-arrival estimation with array in a line-of-sight indoor UWB-IR,” 7th International Conference on Information, Communications and Signal Processing, pp. 1-5, 2009.
J. Friedman, A. Davitian, D. Torres, D. Cabric, and M. Srivastava, “Angle-of-arrival-assisted relative interferometric localization using software defined radios,” IEEE Military Communications Conference, pp. 1-8, 2009.
V. Kezys, E. Vertatschitsch, T. Greenlay, and S. Haykin, “High-resolution techniques for angle-ofarrival estimation,” IEEE Military Communications Conference - Communications-Computers: Teamed for the 90's, pp. 41.3.1-41.3.6, 1986.
N. B. Buchanan and V. Fusco, “Angle of arrival detection using retrodirective radar,” Radar Conference, pp. 133-136, 2010.
T. Chan, Y. Kuga, and S. Roy, “Combined use of various passive radar techniques and angle of arrival using music for the detection of ground moving objects,” IEEE International Symposium on Antennas and Propagation, pp. 2561-2564, 2011.
J. Friedman, T. Schmid, Z. Charbiwala, M. B. Srivastava, and Y. H. Cho, “Multistatic pulse-wave angle-of-arrival-assisted relative interferometric radar,” IEEE Radar Conference, pp. 458- 463, 2011.
Y. Kalkan and B. Baykal, “Target localization and velocity estimation methods for frequency-only mimo radars,” IEEE Radar Conference, pp. 458- 463, 2011.
Y. Norouzi and M. Derakhshani, “Joint time difference of arrival/angle of arrival position finding in passive radar,” Radar, Sonar & Navigation, IET, vol. 3, no.2, pp. 167-176, 2009.
C. Du, J. S. Thompson, and Y. R. Petillot, “Hybrid bistatic radar,” International Radar Conference - Surveillance for a Safer World, International, pp. 1-6, 2009.
J. Capon, “High resolution frequency-wavenumber spectrum analysis,” Proceedings of the IEEE, vol. 57, pp. 1408-1418, Aug. 1969.
J. -H. Lee, Y. S. Jeong, S. -W. Cho, W. Y. Yeo, and K. Pister, “Application of the Newton method to improve the accuracy of TOA estimation with the beam forming algorithm and the MUSIC algorithm,” Progress in Electromagnetics Research, vol. 116, pp. 475-515, 2011.
R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” Proceedings of RADC Spectral Est. Work shop, pp. 243-258, Oct. 1979.
R. Roy, A. Paulraj, and T. Kailath, “ESPRIT – a subspace rotation approach to estimation of parameters of cisoids in noise,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. 34, pp. 1340-1342, Oct. 1986.
I. Ziskind and M. Wax, “Maximum likelihood localization of multiple sources by alternating projection,” IEEE Trans. on Signal Processing, vol. 36, no. 10, pp. 1553-1560, Oct. 1988.
H. W. Press, P. B. Flannery, A. S. Teukolsky, and T. W. Vetterling, Numerical Recipes in C, Cambridge University Press, 1992.
http://en.wikipedia.org/wiki/Newton_method_in_o ptimization, August, 2012.
