Bayesian state-space models reveal unobserved off-shore nocturnal migration from Motus data

•State-space models for Motus data from migratory birds.•Simple localization routine predicts bird location and spatial uncertainty.•New movement models for migratory birds flying at night.•Estimate unobserved locations and behaviors (e.g. migration and foraging).•Red-eyed Vireos performed most migratory flights at night and over water.