Kalman Filtering: Theory and Practice Using MATLAB

Book•

Kalman Filtering: Theory and Practice Using MATLAB

16 Jan 2001-

TL;DR: Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering and appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.

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Abstract: The definitive textbook and professional reference on Kalman Filtering fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.

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Journal Article•DOI•

Cubature Kalman Filters

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Ienkaran Arasaratnam¹, Simon Haykin¹•Institutions (1)

McMaster University¹

27 May 2009-IEEE Transactions on Automatic Control

TL;DR: A third-degree spherical-radial cubature rule is derived that provides a set of cubature points scaling linearly with the state-vector dimension that may provide a systematic solution for high-dimensional nonlinear filtering problems.

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Abstract: In this paper, we present a new nonlinear filter for high-dimensional state estimation, which we have named the cubature Kalman filter (CKF) The heart of the CKF is a spherical-radial cubature rule, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear Bayesian filter Specifically, we derive a third-degree spherical-radial cubature rule that provides a set of cubature points scaling linearly with the state-vector dimension The CKF may therefore provide a systematic solution for high-dimensional nonlinear filtering problems The paper also includes the derivation of a square-root version of the CKF for improved numerical stability The CKF is tested experimentally in two nonlinear state estimation problems In the first problem, the proposed cubature rule is used to compute the second-order statistics of a nonlinearly transformed Gaussian random variable The second problem addresses the use of the CKF for tracking a maneuvering aircraft The results of both experiments demonstrate the improved performance of the CKF over conventional nonlinear filters

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2,597 citations

Cites background from "Kalman Filtering: Theory and Practi..."

...The reason is that the use of a forced symmetry on the solution of the matrix Ricatti equation improves the numerical stability of the Kalman filter [36], whereas the underlying meaning of the covariance is embedded in the positive definiteness....
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DOI•

Bayesian Filtering and Smoothing

[...]

Simo Särkkä

31 May 2023

TL;DR: 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 and learns what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.

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Abstract: Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

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1,373 citations

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

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Simo Särkkä

01 Jan 2015

TL;DR: 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 and learns what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.

...read moreread less

Abstract: 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.

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1,102 citations

Cites methods from "Kalman Filtering: Theory and Practi..."

...Non-linear extensions of the Kalman filter, the extended Kalman filter (EKF), the statistically linearized filter (SLF), and the unscented Kalman filter (UKF) are presented in Chapter 5....
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...2 Extended Kalman filter The extended Kalman filter (EKF) (see, e.g., Jazwinski, 1970; Maybeck, 1982b; Bar-Shalom et al., 2001; Grewal and Andrews, 2001) is an extension of the Kalman filter to non-linear filtering problems....
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.../ k i th predicted sigma point of the measurement yk at step k Z Normalization constant Zk Normalization constant at the time step k 1 Infinity www.cambridge.org© in this web service Cambridge University Press Cambridge University Press 978-1-107-03065-7 - Bayesian Filtering and Smoothing Simo Särkkä Frontmatter More information Symbols and abbreviations xxi Abbreviations ADF Assumed density filter AM Adaptive Metropolis (algorithm) AMCMC Adaptive Markov chain Monte Carlo AR Autoregressive (model) ARMA Autoregressive moving average (model) ASIR Auxiliary sequential importance resampling BS-PS Backward-simulation particle smoother CDKF Central differences Kalman filter CKF Cubature Kalman filter CLT Central limit theorem CPF Cubature particle filter CRLB Cramér–Rao lower bound DLM Dynamic linear model DOT Diffuse optical tomography DSP Digital signal processing EC Expectation correction EEG Electroencephalography EKF Extended Kalman filter EM Expectation–maximization EP Expectation propagation ERTSS Extended Rauch–Tung–Striebel smoother FHKF Fourier–Hermite Kalman filter FHRTSS Fourier–Hermite Rauch–Tung–Striebel smoother fMRI Functional magnetic resonance imaging GHKF Gauss–Hermite Kalman filter GHPF Gauss–Hermite particle filter GHRTSS Gauss–Hermite Rauch–Tung–Striebel smoother GPB Generalized pseudo-Bayesian GPS Global positioning system HMC Hamiltonian (or hybrid) Monte Carlo HMM Hidden Markov model IMM Interacting multiple model (algorithm) INS Inertial navigation system IS Importance sampling InI Inverse imaging KF Kalman filter LMS Least mean squares LQG Linear quadratic Gaussian (regulator) www.cambridge.org© in this web service Cambridge University Press Cambridge University Press 978-1-107-03065-7 - Bayesian Filtering and Smoothing Simo Särkkä Frontmatter More information xxii Symbols and abbreviations LS Least squares MA Moving average (model) MAP Maximum a posteriori MC Monte Carlo MCMC Markov chain Monte Carlo MEG Magnetoencephalography MH Metropolis–Hastings MKF Mixture Kalman filter ML Maximum likelihood MLP Multi-layer perceptron MMSE Minimum mean squared error MNE Minimum norm estimate MSE Mean squared error PF Particle filter PMCMC Particle Markov chain Monte Carlo PMMH Particle marginal Metropolis–Hastings PS Particle smoother QKF Quadrature Kalman filter RAM Robust adaptive Metropolis (algorithm) RBPF Rao–Blackwellized particle filter RBPS Rao–Blackwellized particle smoother RMSE Root mean squared error RTS Rauch–Tung–Striebel RTSS Rauch–Tung–Striebel smoother SDE Stochastic differential equation SIR Sequential importance resampling SIR-PS Sequential importance resampling particle smoother SIS Sequential importance sampling SLDS Switching linear dynamic system SLF Statistically linearized filter SLRTSS Statistically linearized Rauch–Tung–Striebel smoother SMC Sequential Monte Carlo TVAR Time-varying autoregressive (model) UKF Unscented Kalman filter UPF Unscented particle filter URTSS Unscented Rauch–Tung–Striebel smoother UT Unscented transform www.cambridge.org© in this web service Cambridge University Press Cambridge University Press 978-1-107-03065-7 - Bayesian Filtering and Smoothing Simo Särkkä Frontmatter More information...
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Book•

Bayesian Filtering and Smoothing

[...]

Simo Srkk¹•Institutions (1)

Aalto University¹

01 Sep 2013

TL;DR: 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, learning what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.

...read moreread less

Abstract: 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.

...read moreread less

879 citations

Journal Article•DOI•

Detailed Real-Time Urban 3D Reconstruction from Video

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Marc Pollefeys¹, David Nister², Jan-Michael Frahm¹, Amir Akbarzadeh², Philippos Mordohai¹, Brian Clipp¹, Chris Engels², David Gallup¹, Seon Joo Kim¹, Paul Merrell¹, C. Salmi¹, Sudipta N. Sinha¹, B. Talton¹, Wang Liang², Qingxiong Yang², Henrik Stewenius², Ruigang Yang², Gregory F. Welch¹, Herman Towles¹ - Show less +15 more•Institutions (2)

University of North Carolina at Chapel Hill¹, University of Kentucky²

01 Jul 2008-International Journal of Computer Vision

TL;DR: A system for automatic, geo-registered, real-time 3D reconstruction from video of urban scenes that extends existing algorithms to meet the robustness and variability necessary to operate out of the lab and shows results on real video sequences comprising hundreds of thousands of frames.

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Abstract: The paper presents a system for automatic, geo-registered, real-time 3D reconstruction from video of urban scenes. The system collects video streams, as well as GPS and inertia measurements in order to place the reconstructed models in geo-registered coordinates. It is designed using current state of the art real-time modules for all processing steps. It employs commodity graphics hardware and standard CPU's to achieve real-time performance. We present the main considerations in designing the system and the steps of the processing pipeline. Our system extends existing algorithms to meet the robustness and variability necessary to operate out of the lab. To account for the large dynamic range of outdoor videos the processing pipeline estimates global camera gain changes in the feature tracking stage and efficiently compensates for these in stereo estimation without impacting the real-time performance. The required accuracy for many applications is achieved with a two-step stereo reconstruction process exploiting the redundancy across frames. We show results on real video sequences comprising hundreds of thousands of frames.

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846 citations

Cites background or methods from "Kalman Filtering: Theory and Practi..."

...Many of the surface fusion algorithms reported in the literature are limited to single objects and are not applicable to our datasets due to computation and memory requirements....
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...For a detailed introduction to Kalman filtering (Grewal and Andrews 2001) is suggested....
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Kalman Filtering: Theory and Practice Using MATLAB

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