A Kalman filter for linear systems driven by time-space Brownian sheet

Nacira Agram; Bernt Øksendal; Frank Proske; Olena Tymoshenko

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arXiv · 2407.06386

A Kalman filter for linear systems driven by time-space Brownian sheet

Nacira Agram·Bernt Øksendal·Frank Proske·Olena Tymoshenko

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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.

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Nacira Agram, Bernt Øksendal, Frank Proske, Olena Tymoshenko. 2024-07-08. A Kalman filter for linear systems driven by time-space Brownian sheet. https://arxiv.org/abs/2407.06386

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