Geolocation data were recovered from archival tags applied to bigeye tuna near Hawaii. A state-space Kalman filter statistical model was used to estimate geolocation errors, movement parameters, and most probable tracks from the recovered data. Standard deviation estimates ranged from 0.5° to 4.4° latitude and from 0.2° to 1.6° longitude. Bias estimates ranged from −1.9° to 4.1° latitude and from −0.5° to 3.0° longitude. Estimates of directed movement were close to zero for most fish reaching a maximum magnitude of 5.3 nm day−1 for the one fish that moved away from its release site. Diffusivity estimates were also low, ranging from near zero to 1000 nm2 day−1. Low values of the estimated movement parameters are consistent with the restricted scale of the observed movement and the apparent fidelity of bigeye to geographical points of attraction. Inclusion of a time-dependent model of the variance in geolocation estimates reduced the variability of latitude estimates. The state-space Kalman filter model appears to provide realistic estimates of in situ geolocation errors and movement parameters, provides a means to avoid indeterminate latitude estimates during equinoxes, and is a potential bridge between analyses of individual and population movements.