Bayesian Filtering and SmoothingCambridge University Press, 05.09.2013 - 232 Seiten Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods. |
Inhalt
What are Bayesian filtering and smoothing? l | 1 |
Bayesian inference | 17 |
Batch and recursive Bayesian estimation | 27 |
Bayesian filtering equations and exact solutions | 51 |
General Gaussian filtering | 96 |
Particle filtering | 116 |
Bayesian smoothing equations and exact solutions | 134 |
Extended and unscented smoothing | 144 |
General Gaussian smoothing | 154 |
Particle smoothing | 165 |
Parameter estimation | 174 |
Epilogue | 204 |
References | 219 |
| 229 | |
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algorithm augmented backward-simulation Bayesian filtering Bayesian inference closed form cross-covariance cubature defined derivative dynamic model EM algorithm energy function ERTSS evaluated extended Kalman filter filtering and smoothing filtering distributions filtering equations filters and smoothers first order Gauss—Hermite Gaussian distribution Gaussian filter Gaussian random walk GHKF given gradient Haykin I N(Xk IEEE Transactions Implement importance distribution importance sampling integration Jacobian matrix joint distribution Kalman filter likelihood linear regression marginal marginal likelihood Markov chain MCMC mean and covariance measurement model measurement noise measurement yk methods non-additive optimal filtering P(Xk p(yk parameter estimation particle smoother polynomials posterior distribution predicted covariance predicted mean qk_1 random variable random walk Rauch—Tung—Striebel smoother recursion resampling RMSE RTS smoother Sarkka sequential importance smoothing distribution solution space model spherical cubature statistical linearization stochastic Taylor series Theorem tion unit sigma points unscented transform update steps vector weights xk_1