# Bayesian Filtering and Smoothing

@inproceedings{Srkk2013BayesianFA, title={Bayesian Filtering and Smoothing}, author={Simo S{\"a}rkk{\"a}}, booktitle={Institute of Mathematical Statistics textbooks}, year={2013} }

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…

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## 1,209 Citations

Robust Bayesian Filtering and Smoothing Using Student's t Distribution

- Computer ScienceArXiv
- 2017

The use of Student's t distribution is described to develop robust, scalable, and simple filtering and smoothing algorithms that closely resemble the Kalman filter and the Rauch-Tung-Striebel smoother except for a nonlinear measurement-dependent matrix update.

Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systems

- Mathematics
- 2015

This work considers approximate maximum likelihood parameter estimation in nonlinear state-space models and discusses both direct optimization of the likelihood and expectation--maximization (EM), and focuses on using Gaussian filtering and smoothing algorithms that employ sigma-points to approximate the required integrals.

Nonlinear Bayesian estimation: from Kalman filtering to a broader horizon

- MathematicsIEEE/CAA Journal of Automatica Sinica
- 2018

A systematic introduction to the Bayesian state estimation framework is offered and various Kalman filtering U+0028 KF U-0029 techniques are reviewed, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KFFor nonlinear systems.

Recursive Bayesian Filtering Through a Mixture of Gaussian and Discrete Particles

- Computer Science, Engineering
- 2017

A new type of filter is proposed where particles in addition to a (linearized) Gaussian component are tracked, which can be seen as a parallel solution to the estimation problem, each component can be separately filtered and constituent outputs summed up to form the filtering distribution.

Bayesian quadrature in nonlinear filtering

- Mathematics2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO)
- 2015

This paper improves estimation of covariances in quadrature-based filtering algorithms by taking into account the integral variance, and applies the proposed modifications to the Gauss-Hermite Kalman filter and the unscented Kalmanfilter algorithms.

Kalman filters as the steady-state solution of gradient descent on variational free energy

- Computer ScienceArXiv
- 2021

This work presents a straightforward derivation of Kalman filters consistent with active inference via a variational treatment of free energy minimisation in terms of gradient descent, offering a more direct link between models of neural dynamics as gradient descent and standard accounts of perception and decision making based on probabilistic inference.

The Level Set Kalman Filter for State Estimation of Continuous-Discrete Systems

- Computer ScienceIEEE Transactions on Signal Processing
- 2022

The LSKF improves the time-update step compared to existing methods, such as the continuous-discrete cubature Kalman filter (CD-CKF), by reformulating the underlying Fokker-Planck equation as an ordinary differential equation for the Gaussian, thereby avoiding the need for the explicit expression of the higher derivatives.

Approximate Inference and Learning of State Space Models With Laplace Noise

- Computer ScienceIEEE Transactions on Signal Processing
- 2021

This paper presents a new approximate inference algorithm for state space models with Laplace-distributed multivariate data that is robust to a wide range of non-Gaussian noise, and presents a maximum posterior expectation-maximization (EM) algorithm that provides better model estimation than existing methods for the Gaussian model.

Accurate State Estimation in Continuous-Discrete Stochastic State-Space Systems With Nonlinear or Nondifferentiable Observations

- EngineeringIEEE Transactions on Automatic Control
- 2017

A novel method of nonlinear Kalman filtering, which unifies the best features of the accurate continuous-discrete extended and cubature Kalman filters, which is particularly effective for continuous-Discrete stochastic systems with nonlinear and/or nondifferentiable observations.

Major development under Gaussian filtering since unscented Kalman filter

- Computer ScienceIEEE/CAA Journal of Automatica Sinica
- 2020

Significant developments made under Gaussian filtering since the proposition of UKF are reviewed, particularly focused on advancing the numerical approximation methods; modifying the conventional Gaussian approach to further improve the filtering performance; and constrained filtering to address the problem of discrete-time formulation of process dynamics.

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