@article{COCV_1999__4__609_0, author = {Zhou, Yishao}, title = {On the phase portrait of the fast filtering algorithms}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {609--630}, publisher = {EDP-Sciences}, volume = {4}, year = {1999}, mrnumber = {1746170}, zbl = {0937.93050}, language = {en}, url = {http://www.numdam.org/item/COCV_1999__4__609_0/} }
Zhou, Yishao. On the phase portrait of the fast filtering algorithms. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 609-630. http://www.numdam.org/item/COCV_1999__4__609_0/
[1] The geometry of matrix eigenvalue methods. Acta Appl. Math. 5 ( 1986) 239-279. | MR | Zbl
and ,[2] A Hamiltonian approach to the factorization of the matrix Riccati equation. Math. Programming Stud. 18 ( 198227-38. | Zbl
and ,[3] A complete parametrization of all positive rational extensions of a covariance sequence. IEEE Trans. Automat. Control AC-40 ( 1995) 1841-1857. | MR | Zbl
, , and ,[4] On the partial stochastic realization problem. IEEE Trans. Automat. Control AC-42 ( 1997) 1049-1070. | MR | Zbl
and ,[5] Predictability and unpredictability in Kalman filtering. IEEE Trans. Automat. Control 36 ( 1991) 563-579. | MR | Zbl
, and ,[6] Stable, unstable and center manifolds for fast filtering algorithms. Modeling, Estimation and Control of Systems with Uncertainty, G.B. Di Masi, A. Gombani and A. Kurzhanski, Eds., Birkhäuser Boston Inc. ( 1991). | MR | Zbl
, and ,[7] On the nonlinear dynamics of fast filtering algorithms. SIAM J. Control Optim. 32 ( 1994) 744-789. | MR | Zbl
, and ,[8] An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge ( 1956). | MR | Zbl
,[9] On the well-posedness of the rational covariance extension problem, Tech. Report TRITA/MAT-96-OS5, Department of Mathematics, KTH, Royal Institute of Technology, Stockholm, Sweden ( 1996). | MR | Zbl
, and ,[10] A convex optimization approach to the rational covariance extension problem, Tech. Report TRITA/MAT-97-OS9, Department of Mathematics, KTH, Royal Institute of Technology, Stockholm, Sweden ( 1997).
, and ,[11] Opérateurs Rationnels Positifs, Dunod ( 1979). | MR | Zbl
, and ,[12] Some problems of Diophantine approximation. Acta Math. 37 ( 1914) 155-239. | JFM | MR
and ,[13] An Introduction to the Theory of Numbers, Oxford at the Clarendon Press ( 1954). | MR | Zbl
and ,[14] Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations, I: General Lie-theoretic methods. Math. Systems Theory 15 ( 1982) 277-284. | MR | Zbl
and ,[15] Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations. II. Math. Systems Theory 16 ( 1983) 297-306. | MR | Zbl
and ,[16] Diophantische Approximationen, Chelsea Publishing Company, New York ( 1936). | JFM | Zbl
,[17] Canonical forms for symplectic and Hamiltonian matrices. Celestial Mech. 9 ( 1974) 213-238. | MR | Zbl
and ,[18] A new algorithm for optimal filtering of discrete-time stationary processes. SIAM J. Control 12 ( 1974) 736-746. | MR | Zbl
,[19] Some reduced-order non-Riccati equations for linear least-squares estimation: the stationary, single-output case. Int. J. Control 24 ( 1976) 821-842. | MR | Zbl
,[20] Grassmannian manifolds, Riccati equations, and feedback invariants of linear systems, Geometrical Methods for the Theory of Linear Systems, C.I. Byrnes and C. Martin, Eds., Reidel Publishing Company ( 1980) 195-211. | MR | Zbl
,[21] Diophantine Approximations, Interscience Publishers, New York, London ( 1956). | MR | Zbl
,[22] Basic Algebraic Geometry, Springer-Verlag, Heidelberg ( 1974). | MR | Zbl
,[23] Phase portrait of the matrix Riccati equations. SIAM J. Control Optim. 24 ( 1986) 1-65. | MR | Zbl
,[24] Monotonicity and finite escape time of solutions of the discrete-time riccati equation, to appear in proceedings of European Control Conference, Karlsruhe ( 1999).
,