Gaussian MAP Filtering Using Kalman Optimization

Kalman filtering using pairwise Gaussian models

An important problem in signal processing consists in recursively estimating an unobservable process x = {xn}n∈IN from an observed process y = {yn}n∈IN. This is done classically in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the well-known Kalman filter. In this paper, we consider Pairwise Gaussian Models by assuming tha...

Optimization-based Sampling in Ensemble Kalman Filtering

In the ensemble Kalman filter (EnKF), uncertainty in the state of a dynamical model is represented as samples of the state vector. The samples are propagated forward using the evolution model, and the forecast (prior) mean and covariance matrix are estimated from the ensemble. Data assimilation is carried out by using these estimates in the Kalman filter formulas. The prior is given in the subs...

Kalman-filtering using local interactions

There is a growing interest in using Kalman-filter models for brain modelling. In turn, it is of considerable importance to represent Kalman-filter in connectionist forms with local Hebbian learning rules. To our best knowledge, Kalman-filter has not been given such local representation. It seems that the main obstacle is the dynamic adaptation of the Kalman-gain. Here, a connectionist represen...

On Kalman Filtering for Conditionally Gaussian Systems with Random Matrices

Efficient Spatio-Temporal Gaussian Regression via Kalman Filtering

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so...