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Wind energy generation is increasing globally, and associated environmental impacts must be considered. The risk of seabirds colliding with offshore wind turbines is influenced by flight height, and flight height data usually come from observers on boats, making estimates in daylight in fine weather. GPS tracking provides an alternative and generates flight height information in a range of conditions, but the raw data have associated error., Here, we present a novel analytical solution for accommodating GPS error. We use Bayesian state-space models to describe the flight height distributions and the error in altitude measured by GPS for lesser black-backed gulls and great skuas, tracked throughout the breeding season. We also examine how location and light levels influence flight height., Lesser black-backed gulls flew lower by night than by day, indicating that this species would be less likely to encounter turbine blades at night, when birds' ability to detect and avoid them might be reduced. Gulls flew highest over land and lowest near the coast. For great skuas, no significant relationships were found between flight height, time of day and location., We consider four 'collision risk windows', corresponding to the airspace swept by rotor blades for different offshore wind turbine designs. We found the highest proportion of birds at risk for a 22-250 m turbine (up to 9% for great skuas and 34% for lesser black-backed gulls) and the lowest for a 30-258 m turbine. Our results suggest lesser black-backed gulls are at greater risk of collision than great skuas, especially by day., Synthesis and applications. Our novel modelling approach is an effective way of resolving the error associated with GPS tracking data. We demonstrate its use on GPS measurements of altitude, generating important information on how breeding seabirds use their environment. This approach and the associated data also provide information to improve avian collision risk assessments for offshore wind farms. Our modelling approach could be applied to other GPS data sets to help manage the ecological needs of seabirds and other species at a time when the pressures on the marine environment are growing. [ABSTRACT FROM AUTHOR]