04778nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072001700184072002300201072001600224100008200240245019200322250001800514264007500532300004400607336002600651337002600677338003600703347002400739490006400763505036700827520254201194650002503736650001903761650002003780650002303800650003203823650002903855650004203884700008003926710003404006773002604040776003604066776003604102776003604138830006404174856004604238978-3-031-61371-5DE-He21320251030112941.0cr nn 008mamaa240906s2024    sz |    s    |||| 0|eng d  a97830316137157 a10.1007/978-3-031-61371-52doi 4aTJ212-225 7aTJFM2bicssc 7aGPFC2bicssc 7aTEC0070002bisacsh 7aTJFM2thema1 aKulikov, Gennady Yu.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aState Estimation for Nonlinear Continuous–Discrete Stochastic Systemsh[electronic resource] :bNumerical Aspects and Implementation Issues /cby Gennady Yu. Kulikov, Maria V. Kulikova.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXXI, 798 p. 60 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aStudies in Systems, Decision and Control,x2198-4190 ;v5390 aNumerical Integration Methods for Ordinary Differential Equations -- Kalman Filtering for Linear Stochastic Modeling -- Extended Kalman Filtering for Nonlinear Stochastic Modeling -- Unscented Kalman Filtering for Nonlinear Stochastic Modeling -- Cubature Kalman Filtering for Nonlinear Stochastic Modeling -- Kalman-Like Filtering for Stiff Stochastic Modeling.  aThis book addresses the problem of accurate state estimation in nonlinear continuous-time stochastic models with additive noise and discrete measurements. Its main focus is on numerical aspects of computation of the expectation and covariance in Kalman-like filters rather than on statistical properties determining a model of the system state. Nevertheless, it provides the sound theoretical background and covers all contemporary state estimation techniques beginning at the celebrated Kalman filter, including its versions extended to nonlinear stochastic models, and till the most advanced universal Gaussian filters with deterministically sampled mean and covariance. In particular, the authors demonstrate that, when applying such filtering procedures to stochastic models with strong nonlinearities, the use of adaptive ordinary differential equation solvers with automatic local and global error control facilities allows the discretization error—and consequently the state estimation error—to be reduced considerably. For achieving that, the variable-stepsize methods with automatic error regulation and stepsize selection mechanisms are applied to treating moment differential equations arisen. The implemented discretization error reduction makes the self-adaptive nonlinear Gaussian filtering algorithms more suitable for application and leads to the novel notion of accurate state estimation. The book also discusses accurate state estimation in mathematical models with sparse measurements. Of special interest in this regard, it provides a means for treating stiff stochastic systems, which often encountered in applied science and engineering, being exemplified by the Van der Pol oscillator in electrical engineering and the Oregonator model of chemical kinetics. Square-root implementations of all Kalman-like filters considered and explored in this book for state estimation in Ill-conditioned continuous–discrete stochastic systems attract the authors’ particular attention. This book covers both theoretical and applied aspects of numerical integration methods, including the concepts of approximation, convergence, stiffness as well as of local and global errors, suitably for applied scientists and engineers. Such methods serve as a basis for the development of accurate continuous–discrete extended, unscented, cubature and many other Kalman filtering algorithms, including the universal Gaussian methods with deterministically sampled expectation and covariance as well as their mixed-type versions. . 0aControl engineering. 0aSystem theory. 0aControl theory. 0aSignal processing.14aControl and Systems Theory.24aSystems Theory, Control.24aDigital and Analog Signal Processing.1 aKulikova, Maria V.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303161370808iPrinted edition:z978303161372208iPrinted edition:z9783031613739 0aStudies in Systems, Decision and Control,x2198-4190 ;v53940uhttps://doi.org/10.1007/978-3-031-61371-5