On the Use of Gaussian Process Models for Problems in CubeSat Data Interpolation
Thursday, October 25, 2018 - 4:10pm - 5:00pm
Within the context of satellite remote sensing, a common processing problem is the interpolation of irregularly sampled sensor data onto a regularly spaced grid as required for use in downstream scientific data products. Motivated by the need to solve this problem in the context of CubeSat radiometer platforms under development at MIT Lincoln Laboratory (MIT LL), here we explore the use of Gaussian Process (GP) models to address a couple of challenges. The first is specifically associated with the CubeSat architecture itself. For this class of sensors, there exist potentially significant geolocation uncertainties which if left unattended, will negatively impact the interpolation performance. We describe the Optimized Gaussian Process Regression (OGPR) approach which combines data interpolation with geolocation correction. A Maximum a Posteriori estimation problem is formulated and solved that couples a GP-based statistical model for spatial variations in the sensor data with a stochastic model for positional uncertainties. The second challenge, while motivated by our work with the MIT LL CubeSats, is a bit more generic and concerns multi-channel interpolation. Rather than collecting a single dataum (here brightness temperature) at each spatial location, the CubeSat radiometers of interest to us collects data from multiple frequency channels. For the resulting multi-channel interpolation problem, we propose a Gaussian Process Mixture Model (GPMM) that extends the naive GP model by constructing a space-frequency covariance matrix as a superposition of Kronecker products between spatial variations for each output channel and weight matrices allowing for mixing across channels. For both problems, we compare the performance of the proposed approached with a number of alternative schemes using both simulated data as well as real data collected by an in-service platform.