By Peter S. Maybeck
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Extra resources for Stochastic models, estimation and control, Vol.2
2 3 4 7 = 8 9 10 10- 4 , Qd = 0: D. forward filter; 14 8. 3 The previous examples, cases in which smoothing significantly improves the filter estimate, as shown in Figs. 6, are characterized by both the filter and smoother quickly reaching steady state operation. For these cases, the Qd/R ratio is large: the uncertainty in the state propagation is large compared to relatively accurate measurements, so the new estimate is much more heavily dependent upon the new measurement than prior estimates; this combined with noise stationarity caused the filter to reach steady state operation quickly.
Control AC-22 (3), 443-447 (1977). Maybeck, P. , "Stochastic Models, Estimation, and Control," Vol. I. Academic Press, New York, 1979. Meditch, J. , Optimal fixed point continuous linear smoothing, Proc. Joint Automat. , Univ. of Pennsylvania, Philadelphia, Pennsyluania pp. 249-257 (June 1967). Meditch, J. , On optimal fixed-point linear smoothing, Int. J. Control, 6, 189 (1962). 19 PROBLEMS 20. Meditch, J. , On optimal linear smoothing theory, Inform. and Control 10, 598-615 (1967). 21. Meditch, J.
5 (Volume I), alternative models of a bias of b(tJ = 0 and bit) = wit), with w(·,·) a zero-mean white Gaussian noise, were discussed and resulting filter performance depicted. The latter model can be interpreted as the original bit) = 0, but with pseudonoise added to reflect a conviction that this basic model is not totally adequate. Without the pseudonoise addition, the filter would compute a variance of the error in estimating bias that converged to zero. Simultaneously, the filter gain on that state channel would be zeroed, thereby precluding use of further measurement data to maintain a viable estimate.