A Kalman filter for linear systems driven by time-space Brownian sheet
Probability
2024-07-10 v1
Abstract
We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the conditional value of the signal given the observation, which can be considered a time-space analogue of the classical Kalman filter. The result is illustrated with examples of the filtering problem involving noisy observations.
Cite
@article{arxiv.2407.06386,
title = {A Kalman filter for linear systems driven by time-space Brownian sheet},
author = {Nacira Agram and Bernt Øksendal and Frank Proske and Olena Tymoshenko},
journal= {arXiv preprint arXiv:2407.06386},
year = {2024}
}