Convergence analysis of the RLS identification algorithm with exponential forgetting in stationary ARX-structures

International Journal of Adaptive Control and Signal Processing

Volumn 13, Issue 1, 1999, Pages 1-22

  Lindoff, B ^a,b   Holst, J ^a  

^a LUND INSTITUTE OF TECHNOLOGY   (Sweden)

^b ERICSSON RESEARCH   (Sweden)

Author keywords

Convergence analysis; Exponential forgetting; Recursive least squares estimation

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; LEAST SQUARES APPROXIMATIONS; REGRESSION ANALYSIS; STOCHASTIC CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS;

COVARIANCE FUNCTION; EXPONENTIAL FORGETTING; GAUSSIAN AUTOREGRESSION ANALYSIS; RECURSIVE LEAST SQUARES (RKS) ALGORITHM;

PARAMETER ESTIMATION;

EID: 0033075095     PISSN: 08906327     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1115(199902)13:1<1::AID-ACS520>3.0.CO;2-V     Document Type: Article

References (22)

1. Ljung, L. and T. Söderström, Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983.
2. Ljung, L. and S. Gunnarsson, 'Adaption and tracking in system identification - a survey', Automatica, 26, 7-22 (1990).
3. Bittanti, S. and M. Campi, 'Bounded error identification of time-varying parameters by RLS techniques', IEEE Trans. Automat. Control, AC-39, 1106-1110 (1994).
4. Canetti, R. M. and M. D. Espana, 'Convergence analysis of the least-squares identification algorithm with a variable forgetting factor for time-varying linear systems', Automatica, 25, 609-612 (1989).
5. Niedzwiecki, M. and L. Guo, 'Nonasymptotic results for finite-memory WLS filters', IEEE Trans. Automat. Control, AC-36, 198-206 (1991).
6. Gerencsér, L., 'Fixed gain off-line estimators of ARMA parameters', J. Math. System Estimation Control, 4, 249-252 (1994).
7. Arvastson, L., H. Olsson and J. Holst, 'Asymptotic bias in parameter estimation of AR-processes using RLS with exponential forgetting', Scandinavian Journal of Statistics (1999), in press.
8. Porat, B., 'Second-order equivalence of rectangular and exponential windows in least-squares estimation of Gaussian autoregressive processes', IEEE Trans. Acoust. Speech Signal Process, ASSP-33, 1209-1212 (1985).
9. Stoica, P. and A. Nehorai, 'On the asymptotic distribution of exponentially weighted prediction error estimators', IEEE Trans. Acoust. Speech Signal Process., ASSP-36, 136-139 (1988).
10. Lindoff, B. and J. Holst, 'Bias and covariance of the recursive least squares estimator with exponential forgetting in vector autoregressions', J. Time Series Anal. 17, 553-570 (1996).
11. Guo, L. and L. Ljung, 'Performance analysis of general tracking algorithms', 33rd Conf. on Decision and Control, 1994, pp. 2851-2855.
12. Guo, L. and L. Ljung, 'Performance analysis of general tracking algorithms', IEEE Trans. Automat. Control, 40, 1388-1402 (1995).
13. Guo, L., L. Ljung and P. Priouret, 'Performance analysis of the forgetting factor RLS algorithm', Int. J. Adapt. Control Signal Process., 7, 525-537 (1993).
14. Lindoff, B., 'On the optimal choice of forgetting factor in the recursive least squares estimator', Technical Report 1997:10, Department of Mathematical Statistics, Lund Institute of Technology, Lund, Sweden, 1997.
15. Lindoff, B. and J. Holst, 'Distribution of the RLS-estimator in a time-varying AR(1)-process', 5th IFAC Symp. on Adaptive Systems in Control and Signal Processing, Budapest, Hungary, 1995, pp. 135-140.
16. Lindoff, B. and J. Holst, 'Exact distribution and moments for the RLS estimate in a time-varying AR(1) process', Automatica, 32, 429-433 (1996).
17. Sayed, A. H. and T. Kailath, 'A state-space approach to adaptive RLS-filtering', IEEE Signal Process. Mag., 12(1), 18-60 (1994).
18. Reinsel, G., Elements of Multivariate Time-Series Analysis, Springer, New York, 1993.
19. Cryer, J. D., J. C. Nankervis and N. E. Savin, 'Mirror-image and invariant distributions in ARMA models', Econometric Theory, 5, 36-52 (1989).
20. Nicholls, D. F. and A. L. Pope, 'Bias in the estimation of multivariate autoregressions', Australian J. Statist., 30A, 296-309 (1988).
21. Pope, A. L., 'Biases of estimators in multivariate non-Gaussian autoregressions', J. Time Series Anal., 11, 249-258 (1990).
22. Fuller, W.A. and D.P. Hasza, 'Properties of predictors for autoregressive time series', J. Amer. Statist. Assoc. 76, 155-161 (1981).