Adaptative high-gain extended Kalman filter and applications
Adaptative high-gain extended Kalman filter and applications
Adaptative high-gain extended Kalman filter and applications
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tel-00559107, version 1 - 24 Jan 2011<br />
Chapter 5<br />
Complements<br />
Contents<br />
5.1 Multiple Inputs, Multiple Outputs Case . . . . . . . . . . . . . . . 93<br />
5.1.1 System Under Consideration . . . . . . . . . . . . . . . . . . . . . . 93<br />
5.1.2 Definition of the Observer . . . . . . . . . . . . . . . . . . . . . . . . 94<br />
5.1.3 Convergence <strong>and</strong> Proof . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
5.1.3.1 Lemma on Innovation . . . . . . . . . . . . . . . . . . . . . 96<br />
5.1.3.2 Preparation for the Proof . . . . . . . . . . . . . . . . . . . 98<br />
5.1.3.3 Intermediary Lemmas . . . . . . . . . . . . . . . . . . . . . 100<br />
5.1.3.4 Proof of the Theorem . . . . . . . . . . . . . . . . . . . . . 101<br />
5.2 Continuous-discrete Framework . . . . . . . . . . . . . . . . . . . . 103<br />
5.2.1 System Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104<br />
5.2.2 Observer Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105<br />
5.2.3 Convergence Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 106<br />
5.2.4 Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107<br />
5.2.5 Preparation for the Proof . . . . . . . . . . . . . . . . . . . . . . . . 108<br />
5.2.6 Proof of the Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
92
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