Estimation and tests of hypotheses for the initial mean and covariance in the kalman filter model

作者: R. H. Shumway , D. E. Olsen , L. J. Levy

DOI: 10.1080/03610928108828137

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摘要: Kalman filtering techniques are widely used by engineers to recursively estimate random signal parameters which essentially coefficients in a large-scale time series regression model. These Bayesian estimators depend on the values assumed for mean and covariance associated with initial state of signal. This paper considers likelihood approach estimation tests hypotheses involving critical means covariances. A computationally simple convergent iterative algorithm is generate only standard filter outputs at each successive stage. Conditions given under maximum consistent asymptotically normal. The procedure illustrated using typical data set 10-dimensional vectors.

参考文章(19)
David A. Harville, Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems Journal of the American Statistical Association. ,vol. 72, pp. 320- 338 ,(1977) , 10.1080/01621459.1977.10480998
T. W. Anderson, Asymptotically Efficient Estimation of Covariance Matrices with Linear Structure Annals of Statistics. ,vol. 1, pp. 135- 141 ,(1973) , 10.1214/AOS/1193342389
P. L. Odell, T. O. Lewis, Best Linear Recursive Estimation Journal of the American Statistical Association. ,vol. 66, pp. 893- 896 ,(1971) , 10.1080/01621459.1971.10482366
A. P. Dempster, N. M. Laird, D. B. Rubin, Maximum Likelihood from Incomplete Data Via theEMAlgorithm Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 39, pp. 1- 22 ,(1977) , 10.1111/J.2517-6161.1977.TB01600.X
Johannes Ledolter, A recursive approach to parameter estimation in regression and time series models Communications in Statistics - Theory and Methods. ,vol. 8, pp. 1227- 1245 ,(1979) , 10.1080/03610927908827825
H. O. HARTLEY, J. N. K. RAO, Maximum-likelihood estimation for the mixed analysis of variance model Biometrika. ,vol. 54, pp. 93- 108 ,(1967) , 10.1093/BIOMET/54.1-2.93
T. W. Anderson, Repeated Measurements on Autoregressive Processes Journal of the American Statistical Association. ,vol. 73, pp. 371- 378 ,(1978) , 10.1080/01621459.1978.10481585
N. Gupta, R. Mehra, Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations IEEE Transactions on Automatic Control. ,vol. 19, pp. 774- 783 ,(1974) , 10.1109/TAC.1974.1100714