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

M.W.A. Smith and A.P. Roberts

Mathematics and Computers in Simulation (MATCOM), 1978, vol. 20, issue 2, 102-109

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.

Date: 1978
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:20:y:1978:i:2:p:102-109

DOI: 10.1016/0378-4754(78)90033-2

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