An Introduction to Identification
Advanced undergraduates and graduate students of electrical, chemical, mechanical, and environmental engineering will appreciate this text for a course in systems identification. In addition to the theoretical basis for mathematical modeling, it covers a variety of tried-and-true identification algorithms and their applications. Moreover, its broad view and fairly modest mathematical level offer readers a quick appraisal of established methods and their limitations. In addition to surveys covering classical methods of identification — including impulse, step, and sine-wave testing — and identification based on correlation function, the text examines least-squares model fitting, statistical properties of estimators, optimal estimation, and Bayes and maximum-likelihood estimators. Other topics include experiment design and choice of model structure as well as model validation. Numerical examples show students how to apply the modeling theories, and a chapter on specialized topics introduces research areas.
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algorithm analysis applied approximation asymptotic autocorrelation Bayes estimation behaviour bias Chapter coefﬁcients column computed constant continuous-time convergence correlation covariance deﬁned deﬁnition depends deterministic discrete-time elements Example ﬁnd ﬁnding ﬁnite ﬁrst ﬁt ﬁxed ﬂow frequency Gaussian gives identiﬁcation IEEE Trans ill-conditioning impulse response inﬂuence initial input input—output instrumental variables iteration Kalman ﬁlter Laplace transforms linear system linearly Ljung loss function m-sequence m.l. estimate matrix mean measurements minimise minimum-covariance model order model output model structure noise non-linear non-zero normal matrix Norton o.l.s. estimate observations obtained orthogonal output errors parameter estimates positive-deﬁnite posterior p.d.f. prediction prior p.d.f. problem random variables records recursive regression-equation error regressors residuals samples scalar Section self-tuning sequence signal signiﬁcance singular-value decomposition speciﬁed steady-state gain step stochastic stochastic approximation time-invariant time-varying transfer function transfer-function transform unbiased estimator uncorrelated updating values variance vector York z-transform zero zero-mean zero-order hold