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David Bar Moshe
David Bar Moshe
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The following paper:

http://www.cirm.univ-mrs.fr/videos/2008/exposes/287w1/Wojtkowski.pdf

provides a geometric positive answer to your question. (The paper discusses the private case where the measurement noise is of unit variance, but this isn't really a shortcoming, because the covariance matrix of the measurement noise can be diagonalized and then all the measurement equation scaled). The answer is based on the fact that geometrically the time evolution of the Riccati equation is a flow on a Grassmann manifold. In the paper, it is proved that this flow preserves the positivity and of P, and that the time evolution matrix of the estimated state vector X is decaying.

The following paper:

http://www.cirm.univ-mrs.fr/videos/2008/exposes/287w1/Wojtkowski.pdf

provides a geometric positive answer to your question. (The paper discusses the private case where the measurement noise is of unit variance). The answer is based on the fact that geometrically the time evolution of the Riccati equation is a flow on a Grassmann manifold. In the paper, it is proved that this flow preserves the positivity and of P, and that the time evolution matrix of the state vector X is decaying.

The following paper:

http://www.cirm.univ-mrs.fr/videos/2008/exposes/287w1/Wojtkowski.pdf

provides a geometric positive answer to your question. (The paper discusses the private case where the measurement noise is of unit variance, but this isn't really a shortcoming, because the covariance matrix of the measurement noise can be diagonalized and then all the measurement equation scaled). The answer is based on the fact that geometrically the time evolution of the Riccati equation is a flow on a Grassmann manifold. In the paper, it is proved that this flow preserves the positivity and of P, and that the time evolution matrix of the estimated state vector X is decaying.

Source Link
David Bar Moshe
David Bar Moshe
  • 4.6k
  • 21
  • 11

The following paper:

http://www.cirm.univ-mrs.fr/videos/2008/exposes/287w1/Wojtkowski.pdf

provides a geometric positive answer to your question. (The paper discusses the private case where the measurement noise is of unit variance). The answer is based on the fact that geometrically the time evolution of the Riccati equation is a flow on a Grassmann manifold. In the paper, it is proved that this flow preserves the positivity and of P, and that the time evolution matrix of the state vector X is decaying.