Vector ARMA estimation: a reliable subspace approach

IEEE Transactions on Signal Processing

Volumn 48, Issue 7, 2000, Pages 2092-2104

  Mari, Jorge ^a   Stoica, Petre ^b   Mc Kelvey, Thomas ^c  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b UPPSALA UNIVERSITY   (Sweden)

^c LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; REGRESSION ANALYSIS; VECTORS;

AUTOREGRESSIVE MOVING AVERAGE; COVARIANCE FITTING; LINEAR MATRIX INEQUALITIES; SCHUR STABILIZATION; SEMIDEFINITE PROGRAMMING; VECTOR VALUED LINEAR STOCHASTIC SYSTEMS;

SIGNAL PROCESSING;

EID: 0033716743     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.847793     Document Type: Article

References (57)

1. E. J. Hannan and M. Deistler, The Statistical Theory of Linear Systems. New York: Wiley, 1988.
2. K. Glover and J. Willems, "Parametrizations of linear dynamical systems : Canonical forms and identifiability," IEEE Trans. Automat. Contr., vol. AC-19, pp. 640-645, 1974.
3. M. Hazewinkel and R. Kaiman, Invariants, Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems, G. Maresini and S. K. Mitter, Eds. Berlin, Germany: Springer Verlag, 1976, pp. 48-60.
4. R. J. Ober, "Balanced parametrization of classes of linear systems," SIAM J. Contr. Optim., vol. 29, pp. 2049-2073, 1991.
5. J. J. Fuchs, "Structure and order estimation of multivariable stochastic processes," IEEE Trans. Automat. Contr., vol. 35, pp. 1338-1341, 1990.
6. T. McKelvey and A. Helmersson, "System identification using an over-parametrized model class-Improving the optimization algorithm," in P roc. 36th IEEE Conf. Decision Contr, San Diego, CA, 1997, pp. 2984-2989.
7. J. A. Cadzow, "High performance spectral estimation-A new ARMA method," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 524-529, 1980.
8. P. Van Overschee and B. De Moor, "N4SID: subspace algorithms for the identification of combined deterministic and stochastic systems," Automatica, vol. 30, pp. 75-93, 1994.
9. _, Subspace Identification for Linear Systems-Theory, Implementation, Applications. Boston, MA: Kluwer , 1996.
10. A. Dahlén, A. Lindquist, and J. Mari, "Experimental evidence showing that stochastic subspace identification methods may fail," Syst. Contr. Lett., vol. 34, pp. 303-312, 1998.
11. J. Durbin, "The fitting of time-series models," Rev. Inst. Int. Stat., vol. 47, pp. 223-243, 1960.
12. D. Q. Mayne and F. Firoozan, "Linear identification of ARMA processes," Automatica, vol. 18, pp. 461-4166, 1982.
13. P. Stoica and R. Moses, Introduction to Spectral Analysis, NJ: PrenticeHall, 1997.
14. A. Swami and J. M. Mendel, "ARMA parameter estimation using only output cumulants," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1257-1265, 1990.
15. C. L. Nikias and J. M. Mendel, Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework. Englewood Cliffs, NJ: PrenticeHall, 1993.
16. P. Faurre, "Identification par minimization d'une representation markovienne de processus aléatoires," in Proc. Symp. Optimiz., Nice, France, 1969.
17. R. E. Kaiman, P. L. Falb, and M. A. Arbib, Topics in Mathematical Systems Theory. New York: McGraw-Hill, 1969.
18. B. D. O. Anderson, "The inverse problem of stationary covariance generation,"/ Stat. Phys., vol. 1, pp. 133-147, 1969.
19. H. Akaike, "Canonical correlation analysis of time series and the use of an information criterion," in System Identification: Advances and Case Studies. New York: Academic, 1976.
20. R. E. Kaiman, "On partial realizations, transfer functions and canonical forms," Acta Polytech. Scand., vol. MA31, pp. 9-39, 1979.
21. B. L. Ho and R. E. Kaiman, "Efficient construction of linear state variable models from input/output functions," Regelungstechnik, vol. 14, pp. 545-548, 1966.
22. M. Aoki, State Space Modeling of Time Series. Berlin, Germany: Springer Verlag, 1987.
23. W. E. Larimore, "System identification, reduced ordered filtering and modeling via canonical variate analysis," in Proc. Amer. Contr. Conf., San Francisco, CA, 1983.
24. P. Van Overschee and B. De Moor, "Subspace algorithms for the stochastic identification problem," in Proc. 30th Conf. Decision Contr., Brighton, U.K., 1991.
25. C. F. Van Loan, "How near is a stable matrix to an unstable matrix?," in Linear Algebra and its Role in Systems Theory, B. N. Datta, Ed. New York: Amer. Math. Soc., 1985.
26. S. Boyd, L. El Ghaoui, E. Feron, and V Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
27. P. Stoica, T. McKelvey, and J. Mari, "MA estimation in polynomial time," IEEE Trans. Signal Processing, vol. 48, pp. 1999-2012, July 2000.
28. T. McKelvey, P. Stoica, and J. Mari, "A semidefinite programing approach to ARMA estimation," presented at the SYSID, 2000.
29. J. L. Doob, Stochastic Processes. New York: Wiley, 1953.
30. R. Bröckelt, Finite Dimensional Linear Systems. New York: Springer Verlag, 1970.
31. P. E. Caines, Linear Stochastic Systems. New York: Wiley, 1988.
32. P. Faurre, M. Clerget, and F. Germain, Opérateurs Rationnels Postitifs. Paris, France: Dunod, 1979.
33. A. Lindquist and G. Picci, "Canonical correlation analysis, approximate covariance extension, and identification of stationary time series," Automatica, vol. 32, no. 5, pp. 709-733, 1996.
34. G. H. Golub and C. F. van Loan, Matrix Computations. Baltimore, MD: John Hopkins Univ., 1989.
35. B. C. Moore, "Singular value analysis of linear systems," Proc. IEEE CDC, pp. 66-73, 1978.
36. P. Van Dooren, "A generalized eigenvalue approach for solving Riccati equations," SIAM J. Sci. Stat. Comput., vol. 2, pp. 121-135, 1981.
37. T. Söderstrom and P. Stoica, System Identification. London, U.K.: Prentice-Hall, 1989.
38. J. Mari, "Modifications of rational transfer matrices to achieve positive realness," Signal Process., vol. 80, no. 4, pp. 615-635, 2000.
39. _, "Rational modeling of time series and applications of geometric control," Ph.D. dissertation, Royal Inst. Technol., Stockholm, Sweden, 1998.
40. T.Kailalh, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
41. R. V Patel, "Computation of matrix fraction descriptions of linear time-invariant systems," IEEE Trans. Automat. Contr, vol. AC-26, pp. 148-161, 1981.
42. P. Van Dooren, "Rational and polynomial matrix factorizations via recursive pole-zero cancellation," Linear Algebra Appl., vol. 137, pp. 663-697, 1990.
43. J. J. Fuchs, "ARMA order estimation via matrix perturbation theory," IEEE Trans. Automat. Contr., vol. AC-32, pp. 358-361, 1987.
44. P. Stoica and M. Cedervall, "Detection tests for array process in unknown correlated noise fields," IEEE Trans. Signal Processing, vol. 45, pp. 2351-2362, Sept. 1997.
45. J. Sorelius, T. Söderstrom, P. Stoica, and M. Cedervall, "Comparative study of rank test methods for ARMA order estimation," in Statistical Methods in Control and Signal Processing, T. Katayama and S. Sugimoto, Eds. New York: Marcel Dekker, 1997, pp. 179-216.
46. D. Bauer, M. Deistler, and W. Scherrer, "The analysis of the asymptotic variance of subspace algorithms," in Preprints llth IFAC Symp. Syst. Identif., Yoshikazu, Sawaragi, andS. Sagara, Eds., 1997, pp. 1087-1091.
47. P. Stoica and R. Moses, "On the unit circle problem: the Schur-Cohn procedure revisited," Signal Process., vol. 26, pp. 95-118, 1990.
48. J. M. Maciejowski, "Guaranteed stability with subspace methods," Syst. Contr. Lett., vol. 26, pp. 153-156, 1995.
49. N. L. C. Chui and J. M. Maciejowski, "Realization of stable models with subspace methods," Automation, vol. 32, no. 11, pp. 1587-1595, 1996.
50. J. L. Willems, Stability Theory of Dynamical Systems. London, U.K.: Nelson, 1970.
51. T. Pappas, A. Laub, and N. Sandell, "On the numerical solution of the discrete-time algebraic Riccati equation," IEEE Trans. Automat. Contr, vol. AC-25, pp. 631-641, 1980.
52. W. E. Roth, "On direct product matrices," Bull. Amer. Math. Soc., vol. 40, pp. 461-468, 1934.
53. P. Gahinet and A. Nemirovsky, "The projective method for solving linear matrix inequalities," Math. Program., vol. 77, pp. 163-190, 1997.
54. Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming. Philadelphia, PA: SIAM, 1994.
55. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 38, pp. 49-95, 1996.
56. P. Gahinet, A. Nemirovsky, and A. Laub, LMI Control Toolbox User's Guide. Natick, MA: The Math Works, Inc., 1995.
57. M. Overton. SDPpack: A package for semidefinite-quadratic-linear programming (SQLP). Online http://www.cs.nyu.edu/faculty/overton/sdppack/.