Best Linear Unbiased Estimation by Recursive Methods

Previous article Next article Best Linear Unbiased Estimation by Recursive MethodsMarvin BlumMarvin Blumhttps://doi.org/10.1137/0114014PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Carl Frederick Gauss, Theoria Combinationis Observationum Erroribus Minimus Obnoxiac, French transl., Methods des Moindres CarrésMemoires sur la combination des observations, Bertrand, Göttingen, Paris, 1855 Google Scholar[2] A. C. Aitken, On least squares and linear combination of observations, Proc. Roy. Soc. Edinburgh Sect. A, 55 ((1934–1935)), 42–48 0011.26603 CrossrefGoogle Scholar[3] Ulf Grenander and , Murray Rosenblatt, Statistical analysis of stationary time series, John Wiley & Sons, New York, 1957, 300– MR0084975 0080.12904 Google Scholar[4] Norbert Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, John Wiley, New York, 1950 Google Scholar[5] A. Kolmogoroff, Interpolation und Extrapolation von stationären zufälligen Folgen, Bull. Acad. Sci. URSS Sér. Math. [Izvestia Akad. Nauk. SSSR], 5 (1941), 3–14 MR0004416 0024.15901 Google Scholar[6] M. Blum, Fixed memory least squares filters using recursive methods, IRE Trans. Information Theory, IT-3 (1957), 178–182 10.1109/TIT.1957.1057412 CrossrefISIGoogle Scholar[7] Marvin Blum, On exponential digital filters, J. Assoc. Comput. Mach., 6 (1959), 283–304 MR0103136 0156.17701 CrossrefISIGoogle Scholar[8] P. Swerling, First order error propagation in a stagewise smoothing procedure for satellite observations, J. Astronaut. Sci., 6 (1959), 46–52 Google Scholar[9] R. E. Kalman, A new approach to linear filtering and prediction problems, J. Basic Engrg., Trans. ASME, 820 (1960), 34–45 Google Scholar[10] R. H. Battin, A statistical optimization navigation procedure for space flight, ARS J., 32 (1962), 1681–1696 0115.18503 CrossrefGoogle Scholar[11] Marvin Blum, A stagewise parameter estimation procedure for correlated data, Numer. Math., 3 (1961), 202–208 10.1007/BF01386020 MR0126319 0129.11302 CrossrefGoogle Scholar[12] P. Whittle, Prediction and Regulation by Linear Least-Squares Methods, Van Nostrand, Princeton, 1963 Google Scholar[13] Marvin Marcus, Basic theorems in matrix theory, Nat. Bur. Standards Appl. Math. Ser., 57 (1960), iv+27 MR0109824 0086.32502 Google Scholar[14] G. E. Forsythe, Theory of selected methods of finite matrix inversion and decomposition, INA-52-5, National Bureau of Standards, 1951 Google Scholar[15] B. Freidman, Principles and Techniques of Applied Mathematics, John Wiley, New York, 1957 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A New Algorithm of the Recursive Generalized Least-squares MethodIFAC Proceedings Volumes, Vol. 21, No. 9 | 1 Aug 1988 Cross Ref Best Linear Recursive EstimationJournal of the American Statistical Association, Vol. 66, No. 336 | 1 Dec 1971 Cross Ref Modern state estimation methods from the viewpoint of the method of least squaresIEEE Transactions on Automatic Control, Vol. 16, No. 6 | 1 Dec 1971 Cross Ref Some computer-aided estimators in stochastic control systems identification†International Journal of Control, Vol. 12, No. 3 | 1 Sep 1970 Cross Ref A Recursive Method for Signal ResolutionIEEE Transactions on Aerospace and Electronic Systems, Vol. AES-5, No. 1 | 1 Jan 1969 Cross Ref On observability of stochastic discrete-time dynamic systemsJournal of the Franklin Institute, Vol. 286, No. 1 | 1 Jul 1968 Cross Ref Volume 14, Issue 1| 1966SIAM Journal on Applied Mathematics History Submitted:30 September 1963Published online:13 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114014Article page range:pp. 167-180ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics