Multi-resolution filters via linear projection for large spatio-temporal datasets

Toshihiro Hirano; Tsunehiro Ishihara

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arXiv · 2401.05315

Multi-resolution filters via linear projection for large spatio-temporal datasets

Toshihiro Hirano·Tsunehiro Ishihara

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Abstract

Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatio-temporal datasets with coordinates. Since such datasets are often incomplete and noisy, it is useful to create the prediction surface of a spatial field. To this end, we consider an online filtering inference by using the Kalman filter based on linear Gaussian state-space models. However, the Kalman filter is impractically time-consuming when the number of locations in spatio-temporal datasets is large. To address this problem, we propose a multi-resolution filter via linear projection (MRF-lp), a fast computation method for online filtering inference. In the MRF-lp, by carrying out a multi-resolution approximation via linear projection (MRA-lp), the forecast covariance matrix can be approximated while capturing both the large- and small-scale spatial variations. As a result of this approximation, our proposed MRF-lp preserves a block-sparse structure of some matrices appearing in the MRF-lp through time, which leads to the scalability of this algorithm. Additionally, we discuss extensions of the MRF-lp to a nonlinear and non-Gaussian case. Simulation studies and real data analysis for total precipitable water vapor demonstrate that our proposed approach performs well compared with the related methods.

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Toshihiro Hirano, Tsunehiro Ishihara. 2024-01-10. Multi-resolution filters via linear projection for large spatio-temporal datasets. https://arxiv.org/abs/2401.05315

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