is of full rank where M j = It can be easily shown that if u is sufficiently general, then (B8) implies b, = a,l = = . . . = = 0, tf q and i. Hence * = 0, and @B = 0, @AB = O,.*.,@A"-'B I 0 ( B W that is 8[BIABIAeBl. . . IA"-lB] = 0 .If the plant. is assumed to be completely controllable, the controllsbility matrix is of rank n and hence, (B11) implies that 8 = 0.Hence, e 3 O=) @ = 0, * = 0, which proves the asymptot,ic stability of the identification scheme. REFERENCES J. S. Pazdem and H. J. Pottinger, "Linear system identification via Lyapunor design technlques." in Proc. lMh Ann. J o i d Automatic Control Conf.. P. Kudva and K. S. Narendra, "An identification procedure for linear multi-1969. pp. i95-801. variable systems," Yale Univ.. Kew Haven, Conn., Becton Center Tech. Rep. CT-48, Aprt6 19i2, J. M. hlendel. Gradlent error-correction identification algorithms," Inform.Abstract-The problem of estimating the state of a linear dynamic system driven by additive Gaussian noise with unknown time varying statistics is considered. Estimates of the state of the system are obtained which are based on all past observations of the system. These observations are linear functions of the state contaminated by additive white Gaussian noise. A previously developed algorithm designed for use in the case of stationary noise is modified to allow estimation of an unknown Kalman gain and thus the system state linear function of the stat.e contaminated by additive white Gaussian
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