Imene Goumiri, Lawrence Livermore National Laboratory; Amanda Muyskens, Lawrence Livermore National Laboratory; Benjamin Priest, Lawrence Livermore National Laboratory; Robert Armstrong, Lawrence Livermore National Laboratory
Keywords: machine learning, gaussian process, light curve, anomaly detection, space domain awareness, uncertainty quantification
Abstract:
Light curves trace apparent visual light magnitudes of space objects over a given time horizon. On can use light curves to formulate latent variable inference problems that solve Space Domain Awareness tasks such as satellite identification, pose estimation, or maneuver detection. Ground-based light curve observations from commercial off the shelf (COTS) cameras remain inexpensive compared to higher precision instruments; however, issues with COTS cameras such as limited sensor availability combined with noisier observations can produce sparse, corrupted time-series data. These external factors hinder the automation of light curve analysis, making light curve anomaly detection and forecasting crucial problems for SDA applications.
This paper presents Gaussian Processes (GPs) as a tool for light curve forecasting and anomaly detection with SDA applications. GPs are priors over function spaces and universal function approximators that compute Gaussian distributed estimates of response variables, providing both a mean estimate as well as error bars around the mean. This native uncertainty quantification is one of their most important features, which distinguishes them from most popular machine learning models. Uncertainty quantification in GP models arises directly from computable posterior variances, allowing for rigorous assessment of uncertainty in light curve forecasting settings. Moreover, posterior means and uncertainties computed from GP models can be used in anomaly detection: a real-time measurement with abnormally high deviation from the predicted mean based upon prior measurements could be the result of corruption, interference, sensor failure, or an unexpected rotation or orbit change.
This work employs MuyGPs, a scalable Gaussian process hyperparameter training and regression framework that can train large-scale light curve models in seconds on a standard workstation. We show that the native uncertainty quantification provided by MuyGPs is an invaluable tool for SDA practitioners through numerical experiments using real-world data.
Gaussian process models provide posterior means and variances via kernel functions, which are bivariate positive semi-definite functions that model the covariance between data points. The kernels and covariance structure of our model incorporate three primary features: (1) anisotropic kernels to account for different correlative length scales across different features in the training data (2) non-temporal features, e.g., solar phase angles, to yield more accurate apparent magnitude predictions by exploiting correlations between light curve magnitudes and other measurements (3) heteroscedastic noise parameters to account for the temporal variation of the response noise.
To demonstrate the efficacy of our approach, we devise a classification task where previously unseen measurements are matched against a database of past observations of several light curves to determine satellite identity. We also compare the performance of anisotropic and heteroscedastic MuyGPs models on light curve forecasting and near-real-time anomaly detection. We examine the uncertainty quantification provided by each model, with special emphasis on anomaly and maneuver detection, providing insight into its utility for machine learning practitioners in the SDA community.
Date of Conference: September 19-22, 2023
Track: Machine Learning for SDA Applications