Therefore, multiplication has been entirely eliminated. The output, y( n), is computed by a sequence of memory fetches, shifts, and adds. The structure for the resulting filter is shown in Fig.
The problem has been called pole-zero pairing, and at the present time there does not appear to be a known analytical technique to determine the correct pairing for minimum-error performance. 25 are implemented, as well as the pairing of the numerator and denominator factors, greatly affects quantization error accumulation and represents an additional design parameter for cascade filters. This feature, together with the fact that extra adders are required at the output of the parallel structure, has resulted in more popularity of the cascade structure. In certain types of filter functions (elliptic), it is found that a oj = a 2 j, so that one multiply can be eliminated. Also, in general, the two forms require the same number of multiplications because the feed-forward multiplies make up for the lower-order numerators of the parallel second-order sections. The KF for use in meteorology has recently been addressed in work of Cohn and Parrish who discussed the propagation of error covariances in a 2D linear model.īoth the parallel and cascade structures are convenient for multiplexing the hardware of one second-order section. Ghil discussed the KF as a data assimilation method in oceanography and used it with a simple linear barotropic model. promoted first the use of KF along with Cohn, Ghil and Isaacson and Cohn. He provided a derivation of the KF equations. Miller used a 1D linear barotropic QG model to investigate the properties of the KF.
In oceanography, the KF has been used by Budgell to describe nonlinear and linear shallow water wave propagation in branched channels, using one-dimensional (1D) cross-sectionally integrated equations. The KF has been derived in a number of books on control theory, e.g., Gelb, Kasper, Nash, Price and Sutherland and Jazwinski to mention but a few.
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The KF is an efficient recursive filter that estimates the state of a dynamic system from a series of incomplete and noisy measurements. Michael Navon, in Handbook of Numerical Analysis, 2009 7.2 The KF
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