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We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…

The ensemble Gaussian mixture filter (EnGMF) is a non-linear filter suited to data assimilation of highly non-Gaussian and non-linear models that has practical utility in the case of a small number of samples, and theoretical convergence to…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

The ensemble Gaussian mixture filter (EnGMF) is a powerful, convergent particle filter capable of medium-to-high dimensional non-linear filtering. The EnGMF relies on a resampling step that can generate physically unrealistic posterior…

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…

Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…