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Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition by Jerry M. Mendel - Department of Electrical Engineering, University of Southern California, Los Angeles, California

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Lesson 19 State Estimation: Steady-state Kalman Filter and Its Relationship to a Digital Wiener Filter

Summary

In this lesson we study the steady-state Kalman filter from different points of view, and we then show how it is related to a digital Wiener filter.

What is a steady-state Kalman filter? We have already noted that a Kalman filter is a time-varying recursive digital filter. It is time-varying because the Kalman gain matrix, K(k), varies with time. If our basic state-variable model is time invariant and stationary, then (under some additional system-theoretic conditions), after an initial interval of time during which K(k) does vary with time, K(k) reaches a steady state in which all its elements are constants. The steady-state Kalman ...

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