Gaussian Process Regression for CubeSat Data Interpolation with Uncertain Inputs and Multi-channel Outputs - Ruan, Weitong. (2018)
Abstract: With their greatly reduced sizes, low development cost and rapid construction time, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. Many applications require the interpolation of irregularly sampled (scattered) sensor data onto a regularly spaced grid for the development of downstream scientific products. This problem is further complicated for the CubeSat platform by two factors. First, there exist potentially significant uncertainties associated with the spatial position of the satellite sensor, which if left unattended, will negatively impact the interpolation performance. Second, instead of collecting a data point from each sampling location, the CubeSat radiometer usually captures data from multiple frequency channels, which turns the scattered data interpolation problem from single output to multi-channel outputs. In this thesis, models and associated algorithms based on the framework of Gaussian Process (GP) Regression are provided to solve both problems. The Optimized Gaussian Process Regression (OGPR) approach provides both estimation of the value on the grid and the geolocation by forming a Maximum A Posterior (MAP) estimation which couples the statistical model for spatial variations in the sensor data field provided by a GP model with a stochastic model for positional uncertainties. For the multi-channel interpolation problem, we propose a Gaussian Process Mixture Model (GPMM) that extends the naive GP model by constructing the covariance matrix as a superposition of Kronecker products between spatial variations for each output channel and weight matrices allowing for mixing across channels. Both approaches are proven to provide superior performance compared with traditional approaches in real data experiments. Although the algorithms that we discuss in this thesis are motivated from the CubeSat application, they can be used in anywhere where the model is applicable.; Thesis (Ph.D.)--Tufts University, 2018.; Submitted to the Dept. of Electrical Engineering.; Advisor: Eric Miller.; Committee: William Blackwell, Mai Vu, and Liping Liu.; Keyword: Electrical engineering.