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Related papers: Closed-form Filtering for Non-linear Systems

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In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

Methodology · Statistics 2023-04-28 Konstantinos E. Tatsis , Vasilis K. Dertimanis , Eleni N. Chatzi

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…

Machine Learning · Statistics 2015-10-13 Yves-Laurent Kom Samo , Stephen J. Roberts

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…

Computation · Statistics 2021-03-24 Sara Pérez-Vieites , Joaquín Míguez

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

Machine Learning · Computer Science 2025-10-20 Tengjie Zheng , Haipeng Chen , Lin Cheng , Shengping Gong , Xu Huang

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…

Optimization and Control · Mathematics 2016-06-28 Sze Zheng Yong , Minghui Zhu , Emilio Frazzoli

Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Wenhan Cao , Tianyi Zhang , Zeju Sun , Chang Liu , Stephen S. -T. Yau , Shengbo Eben Li

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…

Methodology · Statistics 2013-02-05 Simo Särkkä Jouni Hartikainen

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…

Dynamical Systems · Mathematics 2016-04-05 Juha Ala-Luhtala , Simo Särkkä , Robert Piché

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

Machine Learning · Computer Science 2025-11-17 John Paisley , Wei Zhang , Brian Barr

The optimality of Bayesian filtering relies on the completeness of prior models, while deep learning holds a distinct advantage in learning models from offline data. Nevertheless, the current fusion of these two methodologies remains…

Signal Processing · Electrical Eng. & Systems 2024-03-11 Shi Yan , Yan Liang , Le Zheng , Mingyang Fan , Xiaoxu Wang , Binglu Wang

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

Numerical Analysis · Mathematics 2026-04-21 Kasper Bågmark , Adam Andersson , Stig Larsson

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

Machine Learning · Statistics 2021-11-24 Jarrad Courts , Adrian Wills , Thomas B. Schön

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…

Computation · Statistics 2022-01-13 Hamza Ruzayqat , Aimad Er-Raiy , Alexandros Beskos , Dan Crisan , Ajay Jasra , Nikolas Kantas

Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…

Computation · Statistics 2012-08-02 Hatef Monajemi , Peter K. Kitanidis

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable…

We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows…

Methodology · Statistics 2022-05-23 Beniamino Hadj-Amar , Jack Jewson , Mark Fiecas

State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose…

Machine Learning · Computer Science 2025-06-02 Yuta Tarumi , Keisuke Fukuda , Shin-ichi Maeda

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…

Information Theory · Computer Science 2010-11-04 Mr. Chong Han , Dr. Ido Nevat , Dr. Gareth Peters , Prof. Jinhong Yuan

Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…

Optimization and Control · Mathematics 2013-01-22 T R Bewley , A S Sharma

We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…

Mathematical Physics · Physics 2024-07-09 Di Qi , Jian-Guo Liu