Multiple output Gaussian process regression algorithm for multi-frequency scattered data interpolation

Abstract

In recent years, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. Of specific interest in this paper are data processing challenges associated with the MIT's Microwave Atmospheric Satellite (MicroMAS). Due to the motion of MicroMAS and the geometry of the data acquisition process, measurements are not collected on a regular grid of spatial locations as required by most applications. Thus, a fundamental problem in processing these data is that of interpolation. The problem is further complicated by the fact that MicroMAS collects data from several frequencies at a single location. A baseline algorithm that can be used to solve this multi-frequency scattered data interpolation problem is to fit data from each frequency via independent Gaussian Process (GP) and apply standard GP regression to estimate unknown data on the regular grid for each frequency separately. However, this approach ignores the correlation between frequencies. From the covariance structure in the aforementioned Independent Multiple output GP Regression (IMGPR) algorithm, we proposed a Correlated Multiple output GP Regression (CMGPR) algorithm which replaces a set of delta vectors with parameterized weight vectors learned from the dataset. To test the effectiveness of our proposed algorithms, we use NOAA's ATMS temperature data. According to the experimental results, the CMGPR algorithm performs better than the IMGPR.