A Probabilistic Analysis of Positional Errors on Satellite Remote Sensing Data Using Scattered Interpolation

With the recent development of CubeSats, several ultracompact, low cost, and rapidly deployable satellites have been developed for earth observation missions. Because of the geometry of the acquisition process, measurements are irregularly sampled, whereas in meteorological applications, data are preferred on a regular grid. This problem is further complicated by the fact that, due to CubeSats' compact sizes and constraints, such as limited power, errors occur in geolocation calibration, resulting in positional errors. In this letter, we analyze how the commonly used triangulation-based linear data interpolation scheme behaves under probabilistic models for the positional errors. The derived distribution of interpolation error caused by positional error is intractable even under a Gaussian distribution for positional errors. To address this problem, we developed an analytical closed-form solution to the first two moments of the interpolation error. Using models for positional errors motivated by our prior work, experimental results show that, compared with the first-order linear model, the second-order one provides a better approximation in terms of the mean and variance, which is very close to that is obtained using more computationally intensive Monte Carlo simulations. This model also allows for the closed-form calculation of mean squared interpolation error, which can be of use in the context of system design where the impact of positional errors on remote sensing products must be considered.