Related papers: Nonlinear State Estimation using Gaussian Integral
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
The factor graph approach to discrete-time linear Gaussian state space models is well developed. The paper extends this approach to continuous-time linear systems/filters that are driven by white Gaussian noise. By Gaussian message passing,…
State estimation when only a partial model of a considered system is available remains a major challenge in many engineering fields. This work proposes a joint, square-root unscented Kalman filter to estimate states and model uncertainties…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated…
Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equations of rotational motion. This paper demonstrates that the…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
In this paper, we aim to propose a consistent non-Gaussian Bayesian filter of which the system state is a continuous function. The distributions of the true system states, and those of the system and observation noises, are only assumed…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
One of the most common misconceptions made about the Kalman filter when applied to linear systems is that it requires an assumption that all error and noise processes are Gaussian. This misconception has frequently led to the Kalman filter…
Online joint estimation of unknown parameters and states in a dynamical system with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to…