Deep Sigma Point Processes for RCS Modeling in Spaceborne SAR Imagery

Radar Cross Section (RCS) modeling is foundational to advancing the utility and sensitivity of spaceborne radar systems. This study introduces a Deep Sigma Point Process (DSPP) model for predicting RCS in Synthetic Aperture Radar (SAR) imagery, using a RADARSAT-2 dataset containing 208,191 verified ships. The DSPP model not only strives for predictive accuracy but ventures to characterize the uncertainty inherent in the intricate relationships among radar signals, ship parameters, and environmental conditions. Unlike traditional approaches relying on deterministic equations with static parameters, the DSPP leverages a hierarchical Gaussian Process framework with Bayesian inference to capture variability and uncertainty in RCS predictions. By generating predictive distributions rather than single estimates, the model effectively accounts for the complex dynamics governing radar returns. Using a Matérn kernel with Automatic Relevance Determination, the DSPP identifies and ranks critical features across radar, operational, and environmental domains, ensuring transparency and interpretability. Performance evaluations demonstrate the model's superiority over linear regression baselines, achieving a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$20.83\%$</tex-math></inline-formula> reduction in Root Mean Squared Error (RMSE), a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$25.89\%$</tex-math></inline-formula> increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R^{2}$</tex-math></inline-formula>, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$44.4\%$</tex-math></inline-formula> reduction in both residual Interquartile Range (IQR) and Median Absolute Deviation (MAD) on test data. By providing calibrated uncertainty bounds, the DSPP enhances prediction reliability and supports robust decision-making. This work marks a shift toward probabilistic models that incorporate the inherent uncertainty of complex phenomena. Transitioning from fixed equations to distributions over outcomes, the DSPP fosters a deeper understanding of RCS behavior, enabling systems to thrive in dynamic operational environments.