Stochastic Models, Estimation and Control Volume 1 by Peter S. Maybeck

By Peter S. Maybeck

From Contents: advent; Deterministic method versions; chance idea and Static versions; Stochastic tactics and Linear Dynamic method types; optimum Filtering and Linear procedure versions; layout and function research of Kalman Filters; sq. Root Filtering. (Description via http-mart)

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A strong foundation in deterministic models provides invaluable insights into, and motivation for, stochastic models to be developed subsequently. algorithm, considerably more detail will be developed herein than might be expected of a review. 2 develops continuous-time dynamic models, perhaps the most natural description of most problems of practical interest. Attention progresses from linear, time-invariant, single input-single output systems models through nonlinear state models, exploiting as many analytical tools as practical to gain insights.

7. Gelb, A. ), Applied Optimal Estimation. T. Press, Cambridge, Massachusetts, 1974. 8. Jazwinski, A. H.. Stochastic Processes and Filtering Theory. Academic Press, New York, 1970. 9. , Linear Optimal Control Systems. Wiley, New York, 1972. 10. Lee, R. C . , Oprimal Estimation, Identification ant! Control. T. Press. Cambridge, Massachusctts, 1964. 11. Liebelt, P. , An Introduction to Optimal Estimation. Addison-Wesley, Reading. Massachusetts, 1967. 12. Maybeck, P. , “The, Kalman Filter-An Introduction for Potential Users,” TM-72-3.

DETERMINISTIC SYSTEM MODELS The standard obserziable form derives its name analogously, and for minimal representations it is described by the same F matrix as in the standard controllable form, but has different forms for b and h: 0 0 1 0 0 1 '.. ' 1 -ao -a, 1 0 z(t) = [ - a 2 . . -an-l- 0 ... ] X(t) 0 (2-14) Again F is derived by inspection from either the differential equation or transfer function, and the bj's are obtained by long division to generate the Laurent series for C(s): + . . + b,C" + .

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