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The extended Kalman filter performs badly. 2. 1. Both figures demonstrate clearly that the estimated state converge towards fixed values and gives a good fit of the measurements. 5 are used. Here, the derivatives for a chromatographic system of one peak plus baseline are given. The system transition matrix is identity and the system noise covariance the null matrix. A measurement noise variance R(k) - 10~^ is used. 25, σ - 5 , -16, measurements used are given performs badly. 4. O Q - O . lO~^. 3.

26) Sec. 5] 25 Kalman filter Note the similarity with the recursive least squares algorithm. They are the same. 26) the identities ii^(ik/fc)-is(ifc/fc), ii^(*/it + l ) - i i ( k / J k - l ) , P^(jfe/Jk)-P(ife/*) and P^(Jk/ik + l)-P(Jfc/Jfc-l). 26)) for the on-line improvement of the estimate and its covariance. It should be clear that once the loop is entered, it could be continued at infinitum. In practice, however, we always have to deal with a limited amount of measurements and the loop ends somewhere.

L/Zx(k)-x(k/k)]^p-^(k/k)[x{k)-x(k/k)] \P{k/k)\Y'^ with the mean estimate and covariance matrix defmed by the integrals: +00 +00 J. 9) -00 —00 +00 +00 E{x{k)}. 10) 54 The multicomponent system - 1 /2U{e}[x(k) -l/2ld{(2nf - x(k/k)fp~^ IP(k/k)\} + where we used the trace relation x^Ax Thus the multivariate entropy is given by: H(k)-mid{(2nef [Ch. 6 (fc /ifc)[x(jfc) - x{k/k)]]dx{k) l/2ld{e}tr{P~\k/k)P(k/k)} tr{Axx^}. Ipre{k)+I^{k) The value Ipreik) P{k Ik) 1} describes the information loss in die prediction stage of the Kalman fdter, which is in the case of multicomponent analysis equal to zero since the state is index invariant and there is no system noise.

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