Abstract
The general state estimation problem for linear systems is formulated and discussed in this section.
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Bibliography
The results given in this chapter can be found in various textboks on stochastic systems and estimation. For some historical benchmark papers, see Kailath, T. (Ed.), 1977. Linear Least-Squares Estimation, Dowden, Hutchinson and Ross, Inc., Stroudsburg, PA.
Sorenson, H.W. (Ed.), 1985. Kalman Filtering: Theory and Application. IEEE Press, New York.
Alternative treatments and derivations of the optimal state estimate can be found in Anderson, B.D.O., Moore, J.B., 1979. Optimal Filtering. Prentice Hall, Englewood Cliffs, NJ.
Åström, K.J., 1970. Introduction to Stochastic Control. Academic Press, New York.
Brown, R.G., 1983. Introduction to Random Signal Analysis and Kaiman Filtering. John Wiley & Sons, New York.
Chui, C.K., Chen, G., 1987. Kaiman Filtering with Real-Time Application. Springer-Verlag, Berlin.
Gelb, A. (Ed.), 1975. Applied Optimal Estimation. MIT Press, Cambridge, MA.
Grimble, M.J., Johnson, M.A., 1988. Optimal Control and Stochastic Estimation, vol. 2. John Wiley & Sons, Chichester, UK.
Kailath, T., Sayed, A.H., Hassibi, B., 2000. Linear Estimation. Prentice Hall, Upper Saddle River, NJ.
Kay, S.M., 1993. Fundamentals of Statistical Signal Processing: Estimation Theory. PTR Prentice Hall, Englewood Cliffs, NJ.
Lewis, F.L., 1986. Optimal Estimation. John Wiley k Sons, New York.
Maybeck, P.S., 1979–82. Stochastic Models, Estimation and Control, vols 1 and 2. Academic Press, New York.
A comprehensive treatment of the Riccati equation and its properties is given in
A comprehensive treatment of the Riccati equation and its properties is given in Bittanti, S., Laub, A.J., Willems, J.C., (Eds), 1991. The Riccati Equation. Springer-Verlag, Heidelberg.
Implementation aspects, notably the U-D algorithm mentioned in Section 6.8.1, are treated in Bierman, G.J., 1977. Factorization Methods for Discrete Sequential Estimation. Academic Press, New York.
Fundamental aspects on numerical algorithms for solving the ARE are given in Arnold,III, W.F., Laub, A.J., 1984. Generalized eigenproblem algorithms and software for algebraic Riccati equations. IEEE Proceedings, vol 72, 1746–1754.
There seem to have been several persons who derived the optimal state estimate around 1960. The optimal filter is named after Kaiman, who gave the fundamental description in
There seem to have been several persons who derived the optimal state estimate around 1960. The optimal filter is named after Kalman, who gave the fundamental description in Kalman, R.E., 1960. A new approach to linear filtering and prediction problems. Transactions of ASME, Journal of Basic Engineering, Series D, vol 82, 342–345. Kalman also cooperated with R. S. Bucy. The optimal filter of continuous-time systems is often called the Kalman-Bucy filter.
Kalman also cooperated with R. S. Bucy. The optimal filter of continuous-time systems is often called the Kalman-Bucy filter.
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Söderström, T. (2002). Optimal State Estimation for Linear Systems. In: Discrete-time Stochastic Systems. Advanced Textbooks in Control and Signal Processing. Springer, London. https://doi.org/10.1007/978-1-4471-0101-7_6
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DOI: https://doi.org/10.1007/978-1-4471-0101-7_6
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