A fast Root-MUSIC algorithm based on Nystrom method and spectral factorization is proposed. By using Nystrom method, only two sub-matrices of the sample covariance matrix are calculated, which avoids its complete calculation and has the advantage of low computational complexity. At the same time, the polynomial coefficients of the Root-MUSIC based on the Nystrom method are conjugated, and the order of the polynomial is reduced by half when using iterative operations. Finally, the root algorithm is used to estimate the DOA. The performance of the proposed algorithm is demonstrated by simulation results.
2. Rao, B. D. and K. V. S. Hari, "Performance analysis of root-MUSIC," IEEE Transactions on Acoustics Speech & Signal Processing, Vol. 37, No. 12, 1939-1949, 1989.
3. Qian, C., L. Huang, and H. C. So, "Improved unitary root-MUSIC for DOA estimation based on pseudo-noise resampling," IEEE Signal Processing Letters, Vol. 21, No. 2, 140-144, 2013.
4. Ren, Q. S. and A. J. Willis, "Fast root MUSIC algorithm," Electronics Letters, Vol. 33, No. 6, 450-451, 1997.
5. Ru, B. M. and A. B. Gershman, "Direction-of-arrival estimation for nonuniform sensor arrays: From manifold separation to fourier domain MUSIC methods," IEEE Transactions on Signal Processing, Vol. 57, No. 2, 588-599, 2009.
6. Marcos, S., A. Marsal, and M. Benidir, "The propagator method for source bearing estimation," Signal Processing, Vol. 42, No. 2, 121-138, 1995.
7. Tong, M.-S. and C. C. Weng, "Nyström method with edge condition for electromagnetic scattering by 2D open structures," Progress In Electromagnetics Research, Vol. 62, 49-68, 2006.
8. Drineas, P. and M. W. Mahoney, "On the Nystr¨om method for approximating a gram matrix for improved kernel-based learning ," Journal of Machine Learning Research, Vol. 6, No. 12, 2153-2175, 2005.
9. Williams, C. K. I. and M. Seeger, "Using the Nystr¨om method to speed up kernel machines," International Conference on Neural Information Processing Systems, 661-667, 2000.
10. Fowlkes, C., S. Belongie, F. Chung, and J. Malik, "Spectral grouping using the Nyström method," IEEE Transactions on Pattern Analysis & Machine Intelligence, Vol. 26, No. 2, 214-225, 2004.
11. Qian, C. and L. Huang, "A low-complexity Nystr¨om-based algorithm for array subspace estimation," Second International Conference on Instrumentation, Measurement, Computer, Communication and Control, 112-114, 2012.
12. Qian, C., L. Huang, and H. C. So, "Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nyström method," Signal Processing, Vol. 94, No. 1, 74-80, 2014.
13. Liu, G., H. Chen, X. Sun, and R. C. Qiu, "Modified music algorithm for doa estimation with Nyström approximation," IEEE Sensors Journal, Vol. 16, No. 12, 4673-4674, 2016.
14. Yan, F. G., Y. Shen, and M. Jin, "Fast DOA estimation based on a split subspace decomposition on the array covariance matrix," Signal Processing, Vol. 115, No. 10, 1-8, 2015.
15. Sayed, A. H. and T. Kailath, "A survey of spectral factorization methods," Numerical Linear Algebra with Applications, Vol. 8, No. 8, 467-496, 2001.
16. Yan, F. G., Y. Shen, M. Jin, and X. Qiao, "Computationally efficient direction finding using polynomial rooting with reduced-order and real-valued computations," Journal of Systems Engineering & Electronics, Vol. 27, No. 4, 739-745, 2016.
17. Yan, F. G., L. Shuai, J. Wang, J. Shi, and M. Jin, "Real-valued root-music for doa estimation with reduced-dimension evd/svd computation," Signal Processing, Vol. 152, No. 5, 1-12, 2018.