Far East Journal of Dynamical Systems
Volume 3, Issue 2, Pages 175 - 204
(December 2001)
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THE EXISTENCE THEOREM OF KALMAN FILTER IN MEASUREMENT THEORY
Shiro Ishikawa (Japan)
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Abstract:
The purpose of this paper is to formulate and prove the existence theorem of Kalman filter in terms of measurements. The difficulty of this paper is not in how to prove it but in how to formulate it. We first review and further develop our idea that Bayes’s method is the dual method of Fisher’s (generalized likelihood function) method. The concept of measurements is indispensable for the complete understanding of the duality. Using the idea, we can formulate the Kalman filter in terms of subjective states as the dual theory of the Kalman filter that is described in terms of likelihood functions. We conclude that the Kalman filter always exists in sufficiently wide situations (i.e., in any classical subjective system). Thus, we hope that our result will be generally accepted as one of the most fundamental results concerning Kalman filter. |
| Keywords and phrases: Kalman filter, general system theory, subjective measurements, Bayesian statistics. |
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