Related papers: Model error covariance estimation in particle and …
Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…
A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an…
Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper…
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…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…
This paper presents preliminary work on computing upper bounds on the estimation error covariance in the framework of the extended Kalman filter. The approach taken is using quadratic constraints to bound the dynamic nonlinearities and use…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations…
The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning…
Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…