Auxiliary Location Inference for Recurrent Sparse Field Reconstruction

Sparse field reconstruction with uncertain sensor locations must distinguish prediction errors from spatial misalignment, often with only some vector components observed. We develop calibrated auxiliary location inference with sensor-block cross-fitting and incorporate its probabilities consistently into a kernel correction. On three cylinder cases, the recurrent implementation reduces aggregate NRMSE by 3.40–5.25% over the original auxiliary procedure, retaining 1.63–2.29% in a second observation batch. Matched reference comparisons and component ablations separate the roles of the auxiliary field, likelihood adjustment and stage assignment. We then connect location probabilities to the implemented field response through the observation operator, working covariance, solve and postprocessing. Controlled interventions identify two breaks in this link: physical closure can reverse a raw-field gain, and held-sensor scores can favor corrections that increase full-field error. Cross-physics evaluations show how the measured gains depend on the scene and reference quality.