On the Use of Gaussian Random Processes for Probabilistic Interpolation of CubeSat Data in the Presence of Geolocation Error

Abstract

With their greatly reduced sizes, low development cost, and rapid construction time, CubeSats have merged as a platform of considerable interest for a wide range of applications, including remote sensing. Many applications require the interpolation of sensor data into a regularly spaced grid for the development of downstream scientific products. This problem is complicated for CubeSat platforms due to potentially significant uncertainties associated with the spatial position of the satellite. In this paper, we present a probabilistic approach to the data interpolation problem in which we estimate both the platform location and data samples on a regular grid given observations corrupted by noise and location error. Our approach is based on a Gaussian process model to connect the measured data to the values on the grid. Two statistical models for positional uncertainties are considered, one based on an assumption of independent errors and another motivated by positional errors associated with a specific platform of interest, the MicroMAS radiometer. In each case, the maximum a posteriori estimate of the positions and the data is generated using an optimized Gaussian process regression (OGPR) method resulting in two algorithms: OGPR-IID and OGPR-PCA. The performance of this approach is tested on both simulated data and advanced technology microwave sounder data where significant improvements both qualitatively and quantitatively relative to traditional interpolation methods are observed.