By Linda E. Brackenbury
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Extra resources for Design of Very Large Scale Integration Systems
We can consider the regularization process to be an input of some alternative data. To show this, let us discuss the time update of the information matrix V. * (27) ' An analogous square-root decomposition may be used for V. - § = [ 1'[ ~ + ,/~(i,s)[ v,. ~r ]',/~(i,s)[ v,. ena v(k + ~lk):= ~: b) (28) c) The first formula (28 a) results from (26) and (10). The relation for the recursive regularization (28 b) has the same form as the formula of exponential update (20 b). The only difference is that forgetting is not applied to the information matrix, but to the input data.
Automatica, 1986, Vol. l, pp. 43-57. J. Chen, K. ", Proc. 1st Int. Workshop on Systolic Arrays, Oxford, 1986, pp. 161-170. I3] P. E. G. J. ", Proc. Int. Conf. on Systolic Arrays, Killarney, Ireland, May 1989, pp. 42-51. T. E. Mead and L. Conway, Addison-Wesley, 1980. F. W. ", IEE Proceedings-D Control theory and applications, Vol. 137, No. 4, pp. 235-244, 1990. W. ", to be presented at IEEE European Workshop on Computer-Intensive Methods in Control and Signal Processing, Prague, September 1994.
2, but the forgetting factor is not included for simplicity. The notation used in the figure refers to the data update, nonetheless, the same formulae are also used for regularization. ~ Propagation of Forgetting. If we assume A to be time variable, we have to synchronize its changes in the array with the propagation of the rotations (25). For this reason, it is entered in the upper left cell and propagated through the array as shown in Fig. 3. Because A(k) is used to compute the accumulated forgetting coefficient A(1, N) (20 c), it cannot be entered in the square-rooted and inverted form.