LEADER 05390nam 22006614a 450 001 9910877505803321 005 20200520144314.0 010 $a1-280-50795-0 010 $a9786610507955 010 $a0-470-04534-5 010 $a1-61583-476-1 010 $a0-470-04533-7 035 $a(CKB)1000000000355271 035 $a(EBL)265855 035 $a(SSID)ssj0000215745 035 $a(PQKBManifestationID)11208070 035 $a(PQKBTitleCode)TC0000215745 035 $a(PQKBWorkID)10204533 035 $a(PQKB)11726097 035 $a(MiAaPQ)EBC265855 035 $a(PPN)170227774 035 $a(OCoLC)85821130 035 $a(FR-PaCSA)41001009 035 $a(EXLCZ)991000000000355271 100 $a20060209d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOptimal state estimation $eKalman, H [infinity] and nonlinear approaches /$fDan Simon 210 $aHoboken, N.J. $cWiley-Interscience$dc2006 215 $a1 online resource (554 p.) 300 $aOn t.p. "[infinity]" appears as the infinity symbol. 311 $a0-471-70858-5 320 $aIncludes bibliographical references (p. 501-520) and index. 327 $aOptimal State Estimation; CONTENTS; Acknowledgments; Acronyms; List of algorithms; Introduction; PART I INTRODUCTORY MATERIAL; 1 Linear systems theory; 1.1 Matrix algebra and matrix calculus; 1.1.1 Matrix algebra; 1.1.2 The matrix inversion lemma; 1.1.3 Matrix calculus; 1.1.4 The history of matrices; 1.2 Linear systems; 1.3 Nonlinear systems; 1.4 Discretization; 1.5 Simulation; 1.5.1 Rectangular integration; 1.5.2 Trapezoidal integration; 1.5.3 Runge-Kutta integration; 1.6 Stability; 1.6.1 Continuous-time systems; 1.6.2 Discrete-time systems; 1.7 Controllability and observability 327 $a1.7.1 Controllability1.7.2 Observability; 1.7.3 Stabilizability and detectability; 1.8 Summary; Problems; 2 Probability theory; 2.1 Probability; 2.2 Random variables; 2.3 Transformations of random variables; 2.4 Multiple random variables; 2.4.1 Statistical independence; 2.4.2 Multivariate statistics; 2.5 Stochastic Processes; 2.6 White noise and colored noise; 2.7 Simulating correlated noise; 2.8 Summary; Problems; 3 Least squares estimation; 3.1 Estimation of a constant; 3.2 Weighted least squares estimation; 3.3 Recursive least squares estimation; 3.3.1 Alternate estimator forms 327 $a3.3.2 Curve fitting3.4 Wiener filtering; 3.4.1 Parametric filter optimization; 3.4.2 General filter optimization; 3.4.3 Noncausal filter optimization; 3.4.4 Causal filter optimization; 3.4.5 Comparison; 3.5 Summary; Problems; 4 Propagation of states and covariances; 4.1 Discrete-time systems; 4.2 Sampled-data systems; 4.3 Continuous-time systems; 4.4 Summary; Problems; PART II THE KALMAN FILTER; 5 The discrete-time Kalman filter; 5.1 Derivation of the discrete-time Kalman filter; 5.2 Kalman filter properties; 5.3 One-step Kalman filter equations; 5.4 Alternate propagation of covariance 327 $a5.4.1 Multiple state systems5.4.2 Scalar systems; 5.5 Divergence issues; 5.6 Summary; Problems; 6 Alternate Kalman filter formulations; 6.1 Sequential Kalman filtering; 6.2 Information filtering; 6.3 Square root filtering; 6.3.1 Condition number; 6.3.2 The square root time-update equation; 6.3.3 Potter's square root measurement-update equation; 6.3.4 Square root measurement update via triangularization; 6.3.5 Algorithms for orthogonal transformations; 6.4 U-D filtering; 6.4.1 U-D filtering: The measurement-update equation; 6.4.2 U-D filtering: The time-update equation; 6.5 Summary; Problems 327 $a7 Kalman filter generalizations7.1 Correlated process and measurement noise; 7.2 Colored process and measurement noise; 7.2.1 Colored process noise; 7.2.2 Colored measurement noise: State augmentation; 7.2.3 Colored measurement noise: Measurement differencing; 7.3 Steady-state filtering; 7.3.1 ?-? filtering; 7.3.2 ?-?-? filtering; 7.3.3 A Hamiltonian approach to steady-state filtering; 7.4 Kalman filtering with fading memory; 7.5 Constrained Kalman filtering; 7.5.1 Model reduction; 7.5.2 Perfect measurements; 7.5.3 Projection approaches; 7.5.4 A pdf truncation approach; 7.6 Summary; Problems 327 $a8 The continuous-time Kalman filter 330 $aA bottom-up approach that enables readers to master and apply the latest techniques in state estimationThis book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering.While there are other textbooks that treat state estimation, this one offers special features and a uniqu 606 $aKalman filtering 606 $aNonlinear systems 606 $aMathematical optimization 615 0$aKalman filtering. 615 0$aNonlinear systems. 615 0$aMathematical optimization. 676 $a629.8/312 700 $aSimon$b Dan$f1960-$0856795 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877505803321 996 $aOptimal state estimation$94191156 997 $aUNINA