PGCFlow: Observation-Grounded Conditional Ensemble Generation of Spaceborne GNSS-R BRCS Delay–Doppler Maps

Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) archives usually provide only one delay–Doppler map (DDM) for each recorded observation condition, limiting the representation of residual DDM variability. This study proposes a Position-Guided Conditional Normalizing Flow (PGCFlow) for observation-grounded probabilistic expansion of ocean bistatic radar cross section (BRCS) DDMs. PGCFlow uses four invertible affine coupling blocks to map a 17×11 DDM to an equal-dimensional Gaussian latent space. Wind–Auxiliary Condition Modulation incorporates a seven-dimensional condition vector into affine-parameter prediction, while Position-Guided Cross-Partition Aggregation (PGCA) uses deterministic grid descriptors to retain explicit cell locations and facilitate spatial-dependence modeling. Experiments used 5,819,042 quality-controlled CYGNSS observations from 2024. PGCFlow was compared with a conditional variational autoencoder and a generic conditional invertible neural network on 8000 held-out recorded conditions drawn from the same empirical observation domain, with 16 generated DDMs per condition. Although the cVAE achieved the highest balanced-aggregate structural similarity (SSIM) of 0.9396, PGCFlow obtained the lowest Fair Energy Score (FES) and Variogram Score (VS) of 0.2242 and 0.0641 and the closest relative local-neighborhood dispersion to unity at 1.0501. It also achieved the lowest frozen-estimator response RMSE and response MAE of 1.1900 and 0.9129 m/s, respectively. Ablation results indicated individual contributions from both proposed modules. Overall, PGCFlow achieved a favorable trade-off among the evaluated fidelity, dependence, dispersion, and response-consistency measures.