Lesson 26 Kalman-Bucy Filtering

Summary

The Kalman-Bucy filter (KBF) is the continuous-time counterpart to the Kalman filter. It is a continuous-time minimum-variance filter that provides state estimates for continuous-time dynamical systems that are described by linear, (possibly) time-varying, and (possibly) nonstationary ordinary differential equations.

The purpose of this lesson is to derive the KBF. We do this in two different ways: (1) use of a formal limiting procedure to obtain the KBF from the KF, and (2) assumption of a linear differential equation structure for the KBF, one that contains an unknown time-varying gain matrix that weights the difference between the measurement made at time t and the estimate of that measurement, after ...

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