A framework for propagation of uncertainties in the Kepler data analysis pipeline

Abstract

The Kepler space telescope is designed to detect Earth-like planets around Sun-like stars using transit photometry by simultaneously observing more than 100,000 stellar targets nearly continuously over a three-and-a-half year period. The 96.4-megapixel focal plane consists of 42 Charge-Coupled Devices (CCD), each containing two 1024 x 1100 pixel arrays. Since cross-correlations between calibrated pixels are introduced by common calibrations performed on each CCD, downstream data processing requires access to the calibrated pixel covariance matrix to properly estimate uncertainties. However, the prohibitively large covariance matrices corresponding to the ~75,000 calibrated pixels per CCD preclude calculating and storing the covariance in standard lock-step fashion. We present a novel framework used to implement standard Propagation of Uncertainties (POU) in the Kepler Science Operations Center (SOC) data processing pipeline. The POU framework captures the variance of the raw pixel data and the kernel of each subsequent calibration transformation, allowing the full covariance matrix of any subset of calibrated pixels to be recalled on the fly at any step in the calibration process. Singular Value Decomposition (SVD) is used to compress and filter the raw uncertainty data as well as any data-dependent kernels. This combination of POU framework and SVD compression allows the downstream consumer access to the full covariance matrix of any subset of the calibrated pixels which is traceable to the pixel-level measurement uncertainties, all without having to store, retrieve, and operate on prohibitively large covariance matrices. We describe the POU framework and SVD compression scheme and its implementation in the Kepler SOC pipeline.