Accounting for Input Noise in Gaussian Process Parameter Retrieval

TL;DR

This paper introduces a method to incorporate input noise into Gaussian Process models, improving the accuracy of uncertainty estimates in temperature prediction from infrared data.

Contribution

It presents a novel formulation for Gaussian Processes that accounts for input noise, enhancing error propagation analysis in earth observation applications.

Findings

More accurate predictive variance estimates achieved

Improved error characterization in temperature retrieval

Demonstrated effectiveness on infrared sounding data

Abstract

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data.