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An exact equivalence between the discrete- and continuous-time formulations of the Kalman filter

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  • Smith, M.W.A.
  • Roberts, A.P.

Abstract

It is shown that if the definition of the covariance of a white noise sequence in discrete-time is derived from the accepted mathematical description for the covariance of a white noise process in continuous-time, compatibility between the discrete- and continuous-time versions of the Kalman filter is complete. Consequently the approach to the limit of the discrete-time filter to obtain its continuous-time equivalent no longer depends on Kalman's non-rigorous argument for dividing the covariance of a white noise sequence by the sampling interval Δt. Such an exact equivalence is essential for comparing the accuray of discrete-time computations with results obtained by numerically integrating the continuous-time filter equations. This approach provides a pragmatic technique for the determination of the most suitable sampling interval for discrete-time Kalman filtering.

Suggested Citation

  • Smith, M.W.A. & Roberts, A.P., 1978. "An exact equivalence between the discrete- and continuous-time formulations of the Kalman filter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(2), pages 102-109.
    • Handle: RePEc:eee:matcom:v:20:y:1978:i:2:p:102-109
    DOI: 10.1016/0378-4754(78)90033-2
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    Cited by:

    1. Smith, M.W.A. & Roberts, A.P., 1978. "A Kalman filter type of extension to a deterministic gradient technique for parameter estimation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 291-300.
    2. Eugene A. Morelli, 2021. "Optimal Input Design for Aircraft Stability and Control Flight Testing," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 415-439, December.
    3. Woolfson, M.S. & Hui, S.Y.R., 1996. "Application of the transmission line method to the solution of the continuous Kalman filter equations of general order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(1), pages 15-33.

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