Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
5.2 Continuous-discrete Framework
Remark 68
As for the continuous case, the convergence proof can be extended to the multiple output
case following the instructions of Section 5.1. The only difference lies in the usage of Lemma
64 with equation (5.36), where we cannot write θδt
r
since R is no longer a scalar. Since R is
definite positive, we can assume the existence of a scalar ˜r such that R>˜rId. Then (5.36)
can be written:
S −1
k
and Lemma 64 can be used.
−1
(−)Sk(+)Sk (−) ≤ S−1
k (−)+θδt
114
˜r S−1
k
(−)C ′
CS −1
k (−),