Recursive smoothing for discrete-time systems as a filtering problem

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Recursive smoothing for discrete-time systems as a filtering problem

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© The Institution of Electrical Engineers
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It is shown that the problem of recursive smoothing of the past states for discrete-time linear systems can be transformed to a filtering problem by introducing an enlarged state and modifying the system equations. The smoothing equations are then obtained from Kalman filter equations. Equations for the fixed-point time smoothing problem results directly from the filter equations.

Inspec keywords: state estimation; filtering and prediction theory; discrete time systems; linear systems

Other keywords: state estimation; filtering; recursive smoothing; linear systems; discrete-time systems

Subjects: Information theory; Discrete control systems; Simulation, modelling and identification

References

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      • J.S. Meditch . (1969) , Stochastic optimal linear estimation and control.
    2. 2)
      • Fraser, D.: `Discussion of optimal fixed-point continuous linear smoothing (by J.S. Meditch)', Proc. Joint Automatic Control Conf., 1967, Univ. of Pensylvania, 249.
    3. 3)
      • F.C. Schweppe . (1973) , Uncertain dynamic systems.
    4. 4)
      • Gessing, R.: `The generalized certainty equivalence principle for linear-quadratic problem', Int. Conf. Methods of Mathematical Programming, 1977, Zakopane , PWN Edition.
    5. 5)
      • A.E. Bryson , Y.C. Ho . (1969) , Applied optimal control.
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