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Solar archival tags (henceforth called geolocators) are tracking devices deployed on animals to reconstruct their long-distance movements. The increased use of geolocators on small birds has created a need for analytical tools to produce accurate and objective estimates of migration routes that are explicit in their uncertainty about the position estimates. We present a hidden Markov chain model for the analysis of geolocator data. This model estimates tracks for animals with complex migratory behaviour by combining: (1) a shading-insensitive, template-fit physical model that includes migratory and sedentary behavioural states, (2) an uncorrelated random walk movement model, and (3) spatially explicit behavioural masks. We use the particle filter (PF) algorithm to provide relatively fast model posterior computation. We illustrate our modelling approach with analysis of simulated data for stationary tags and for real tracks of both a Tree Swallow Tachycineta bicolor migrating along the east and a Golden-Crowned Sparrow Zonotrichia atricapilla migrating along the west coast of North America. Our model increases accuracy in analyses of noisy data and movements of animals with complicated migration behaviour. It also provides posterior distributions for the positions of animals, their behavioural states (e.g., migrating or sedentary), and distance and direction of movement.