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Paper Count: 30835
Identification of LTI Autonomous All Pole System Using Eigenvector Algorithm
Authors: Sudipta Majumdar
Abstract:This paper presents a method for identification of a linear time invariant (LTI) autonomous all pole system using singular value decomposition. The novelty of this paper is two fold: First, MUSIC algorithm for estimating complex frequencies from real measurements is proposed. Secondly, using the proposed algorithm, we can identify the coefficients of differential equation that determines the LTI system by switching off our input signal. For this purpose, we need only to switch off the input, apply our complex MUSIC algorithm and determine the coefficients as symmetric polynomials in the complex frequencies. This method can be applied to unstable system and has higher resolution as compared to time series solution when, noisy data are used. The classical performance bound, Cramer Rao bound (CRB), has been used as a basis for performance comparison of the proposed method for multiple poles estimation in noisy exponential signal.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1315424Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 551
 G. Ravi Shankar Reddy and Rameshwar Rao, ”Instantaneous frequency estimation based on time-varying auto regressive model andWAX-Kailath algorithm”, Signal Processing: An International Journal, vol. 8, Issue 4, pp. 43-66, 2014.
 Z. K. Peng, G. Meng, F. L. Chu, Z. Q. Lang, W. M. Zhang and Y. Yang, ”Polynomial Chirplet Transform with application to instantaneous frequency estimation”, IEEE Transactions on Instrumentation and Measurements, vol. 60, n0. 9, pp. 3222-3229, September 2011.
 Biao Huang, Steven X. Ding, and S. Joe Qin, ” Closed-loop subspace identification: an orthogonal projection approach”, Journal of Process Control, 15 ,pp. 53-66,(2005).
 Pedro M. Ramos and A. Cruz Serra, ”Comparision of frequency estimation algorithms for power quality assesment”,Measurement, 42 (2009), pp. 1312-1317.
 Paavo Alku and Jouni Pohjalainan, ”Formant frequency estimation of high pitched vowels using weighted linear prediction”, J. Acoust. Soc. Am., 134(2), pp. 1295-1313, August 2013.
 J. R. Jensen, M.G. Christensen and S. H. Jensen, ”Nonlinear least squares methods for joint DOA and pitch estimation: IEEE Trans on Audio, Speech, Lang. Process, vol. 21, no. 5, pp. 923-933, May 2013.
 Petre Stoica, Randolph L. Moses, Benjamin Friedlander, Torsten, Soderstrom, ” Maximum likelihood estimation of the parameter of multiple sinusoids from noisy measurements”, IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 37, no. 3, pp. 378-392, March, 1989.
 Peter Stoica and Arye Nehorai, ”Music, maximum likelihood and Cramer Rao bound”, IEEE Transactions on Acoustics, Speed and Siganl Processing, vol. 37, no. 5, pp.720-741, May 1989,
 Arye Nehorai and David Starer, ”Adaptive pole estimation”, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 5, pp. 825-838, May 1990.
 S. M. Kay,”Modern Spectrum Estimation: Theory and Applications”, Prentice Hall 1988.
 Monson H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley and Sons, 1996.
 Daeyong Kim, Madihally J. Narashima and Donal C. Cox, ”An improved single frequency estimator”, IEEE Signal Processing Letters, vol. 3, no. 7, July 1996, pp. 212-214.
 Bin Liao and Shing Chow Chan, ”An improved eigendecomposition based algorithms for frequencies estimation of two sinusoids”, IEEE Communication Letters, vol.17, no.3, March 2013, pp. 557-560.
 H. L. Vantrees, Detection, Estimation and Modulaion Theory, New York, Wiley, 1968.
 Yonina C. Edlar, ”Uniformly Improving the Cramer-Rao Bound and Maximum-Likelihood Estimation”, IEEE Transactions on Signal Processing”, vol. 54, no. 8, pp. 2943-2956, August, 2006.