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<p><strong>Abstract.</strong> When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to <i>N</i><sup>+</sup> + N<sup>0</sup> where <i>N</i><sup>+</sup> and <i>N</i><sup>0</sup> are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is thedoi:10.5194/npg-18-243-2011 fatcat:dfk5ld37kra7lba3zi42d7tktm