Volume 10, no. 4Pages 92 - 104

Matrix Pencil Method for Estimation of Parameters of Vector Processes

M.P. Henry, O.L. Ibryaeva, D.D. Salov, A.S. Semenov
The paper considers one of the modern parametric methods of signal processing - the matrix pencil method (MPM). The method makes it possible to effectively estimate signal parameters from its samples which is the sum of complex exponentials. The number of exponentials is not assumed to be known in advance and can also be estimated using a singular value decomposition of a matrix constructed from the signal samples. The object of this work is a vector process - a set of signals having the same frequencies and damping factors (i.e., the same poles of the signal), but different complex amplitudes. Such signals occur, for example, when considering a phased array antenna, when it is necessary to evaluate the parameters of a signal generated by the same sources but coming from many antenna elements with their amplitudes and phases. A similar problem arises in the evaluation of signals parameters from two spatially-distributed motion sensors of a Coriolis flowmeter. When processing several signals with classical MPM, we obtain several different sets of poles of these signals, which then, for example, need to be averaged to obtain the desired values of the poles assumed to be the same for all signals. The proposed modification of the MPM works with the entire set of signals at once, giving one set of signal poles, and at the same time it proves to be more effective both in terms of speed and in the accuracy of determining the signal parameters. The algorithms of the classical MPM and its modifications for the vector process are presented, as well as numerical experiments with model and real signals taken from one of the commercially available Coriolis flowmeters Du15. Experiments show that the proposed algorithm yields more accurate results in a shorter (approximately 1,5 times) time than the classical MPM
Full text
matrix pencil method; parametric methods of signal processing; sum of complex exponentials; singular value decomposition; vector processes.
1. Marple S.L. Digital Spectral Analysis: with Applications. Upper Saddle River, Prentice-Hall, 1987.
2. Sergienko, A.B. Tsifrovaya obrabotka signalov [Digital Signal Processing]. Saint Petersburg, Piter, 2002. (in Russian)
3. Rabiner L.R., Gold B. Theory and Application of Digital Signal Processing. Upper Saddle River, Prentice-Hall, 1975.
4. Henry M.P., Bushuev O., Ibryaeva O. Prism Signal Processing for Sensor Condition Monitoring. 2017 IEEE 26th International Symposium on Industrial Electronics ISIE 2017 (Edinburgh, UK, 19-21 June 2017), 2017, pp. 1404-1411. DOI:10.1109/ISIE.2017.8001451
5. Huang N.E., Wu Z. A Review on Hilbert - Huang Transform: Method and Its Applications to Geophysical Studies. Reviews of Geophysics, 2008, vol. 46, no. 2, pp. 1-23. DOI:10.1029/2007RG000228.
6. Prony G. Essai experimental et analytique: sur les lois de la dilatabilite de fluides elastiques et sur celles de la force expansive de la vapeur de l'еau et de la vapeur de l'alkool, a differentes temperatures. Journal de l'Ecole polytechnique floreal et plairia, 1795, vol. 1, no. 22, pp. 24-76. (in French)
7. Kumaresan R., Tufts D.W., Scharf L.L. A Prony Method for Noisy Data: Choosing the Signal Components and Selecting the Order in Exponential Signal Models. Proceedings of the IEEE, 1984, vol. 72, no. 2, pp. 230-233. DOI: 10.1109/PROC.1984.12849
8. Hua Y., Sarkar T.K. Matrix Pencil Method for Estimating Parameters of Exponentially Damped / Undamped Sinusoids in Noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990, vol. 38, no. 5, pp. 814-824. DOI: 10.1109/29.56027
9. Sarrazin F., Sharaiha A., Pouliguen P. Comparison Between Matrix Pencil and Prony Methods Applied on Noisy Antenna Responses. Loughborough Antenna and Propagation Conference, Loughborough, 2011, pp. 1-4.
10. Patton R.J., Frank P.M., Clarke R.N. Fault Diagnosis in Dynamic Systems: Theory and Application. Upper Saddle River, Prentice-Hall, 1989.
11. Voskresenskii D.I Aktivnye fazirovannye antennye reshetki [Active Phased Array Antennas], Мoscow, Radiotehnika, 2004. (in Russian)
12. Enrique J., Rio F., Sarkar T.K. Comparison Between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation. Digital Signal Processing, 1996, vol. 6, pp. 108-125.
13. Biao Lu, Dong Wei, Evans B.L., Bovik A.C. Improved Matrix Pencil Methods. Asilomar Conference on Signals, Systems, and Computers, 1998, vol. 2, pp. 1433-1437. DOI: 10.1109/ACSSC.1998.751563
14. Steffens A., Rebentrost P., Marvian I. An Efficient Quantum Algorithm for Spectral Estimation. New Journal of Physics, 2017, vol. 19, Article ID 033005. DOI: 10.1088/1367-2630/aa5e48
15. Ibryaeva O.L. Recursive Matrix Pencil Method. IEEE Explore, II International Conference on Measurements, Chelyabinsk, 2017.