Metaheuristics for Medicine and Biology by Amir Nakib & El-Ghazali Talbi

Metaheuristics for Medicine and Biology by Amir Nakib & El-Ghazali Talbi

Author:Amir Nakib & El-Ghazali Talbi
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg


(5.21)

(5.22)

where and are the process and the observation noises which are both assumed to be zero mean multivariate Gaussian noise with covariance and , respectively. In the prediction phase, the state is predicted using:

(5.23)

and the predicted covariance matrix is estimated by using:

(5.24)

The predicted state is updated using

(5.25)

where is the optimal Kalman gain, is the measurement residual and is the residual covariance

(5.26)

(5.27)

(5.28)

To use these equations, it is necessary that the functions f and h are locally linearized. Thus, the transition matrix and the observation matrix are obtained by taking the partial derivative of the nonlinear equations. The state transition and observation matrices are defined to be the following Jacobians



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