A0557
Title: Multi-resolution filters via linear projection for large spatio-temporal datasets
Authors: Toshihiro Hirano - Kanto Gakuin University (Japan) [presenting]
Tsunehiro Ishihara - Takasaki City University of Economics (Japan)
Abstract: Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatiotemporal 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, an online filtering inference is considered 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, a multi-resolution filter is proposed 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, the 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, extensions of the MRF-lp to a nonlinear and non-Gaussian case are discussed. Simulation studies and real data analysis for total precipitable water vapor demonstrate that the proposed approach performs well compared with the related methods.
