Related papers: Numerical Gaussian process Kalman filtering

The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…

State-space models (SSMs) are a broad class of probabilistic models for dynamical systems with many applications in engineering and science. Bayesian filtering is analytically tractable only in the linear-Gaussian setting, where the Kalman…

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…

The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…

Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple…

Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of…

This paper introduces the concept of the Gaussian integral filter (GIF), the limit of the Gaussian sum filter (GSF) for when the number of mixands tends to infinity. The GIF is obtained via a combination of GSF, quadrature, and…

The Kalman Filter is a widely used approach for the linear estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks.…

Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian…