Numerical Development For Kalman Filter Factorization

S Ahmed, Ahmed; H Abid, Salah

	Numerical Development For Kalman Filter Factorization
Al Kut Journal of Economics Administrative Sciences
Article 1, Volume 0, Issue 22, 2018, Pages 169-177
Authors
Ahmed S Ahmed; Salah H Abid
Abstract
No one disagrees on the importance of the Kalman filter in the practical aspects of the various scientific fields . This importance can be noticed clearly in Grewal and Andrews (2008) which they stated that ' Practically , the kalman filter is one of the greater discoveries in the history of statistical estimation theory and possibly the greatest discovery in the twentieth century " . Due to the importance of Kalman filter , the developments is continued until now in the filter techniques and different aspects related with .For detailed review about the techniques of Kalman filter , one can see, Grewal and Andrews (2008) and Zarchan and Musoff (2009). One can also see Moreno and Pigazo (2009) and Mahmoud and Khalid (2013) for detailed review about the applications of Kalman filter . There are a lot of mathematical aspects represent the structure of Kalman filter and the basis of its work . In this paper we will discuss and then develop one of the most important of these aspects , which is the spectral matrix factorization , when the Kalman filter works in the frequency domain .At first , we will present the work mechanism of the Kalman filter in the frequency domain , access to the point of spectral matrix factorization and then discuss one of the most important method in factorization . Finally , we will present our development for this method .

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