RESEARCH ARTICLE A Bayesian model of the disambiguation of gravitoinertial force by visual cues Paul R. MacNeilage Æ Martin S. Banks Æ Daniel R. Berger Æ Heinrich H. Bu ¨ lthoff Received: 7 September 2005 / Accepted: 31 October 2006 / Published online: 30 November 2006 Ó Springer-Verlag 2006 Abstract The otoliths are stimulated in the same fashion by gravitational and inertial forces, so otolith signals are ambiguous indicators of self-orientation. The ambiguity can be resolved with added visual information indicating orientation and acceleration with respect to the earth. Here we present a Bayesian model of the statistically optimal combination of noisy vestibular and visual signals. Likelihoods associated with sensory measurements are represented in an ori- entation/acceleration space. The likelihood function associated with the otolith signal illustrates the ambi- guity; there is no unique solution for self-orientation or acceleration. Likelihood functions associated with other sensory signals can resolve this ambiguity. In addition, we propose two priors, each acting on a dimension in the orientation/acceleration space: the idiotropic prior and the no-acceleration prior. We conducted experiments using a motion platform and attached visual display to examine the influence of visual signals on the interpretation of the otolith signal. Subjects made pitch and acceleration judgments as the vestibular and visual signals were manipulated independently. Predictions of the model were con- firmed: (1) visual signals affected the interpretation of the otolith signal, (2) less variable signals had more influence on perceived orientation and acceleration than more variable ones, and (3) combined estimates were more precise than single-cue estimates. We also show that the model can explain some well-known phenomena including the perception of upright in zero gravity, the Aubert effect, and the somatogravic illusion. Keywords Self-motion  Body orientation  Bayesian estimation  Gravitoinertial force  Optic flow  Acceleration  Vestibular system Introduction Knowing the body’s orientation in world coordinates is essential for a range of behaviors including guidance of self-motion and vehicle operation. One way that hu- mans and other animals estimate body orientation is from the direction of gravity. Because gravity’s direc- tion is constant in world coordinates, knowing the direction in body coordinates is sufficient for knowing body orientation in world coordinates. However, gravitational force and inertial force from self-accel- eration cannot be measured independently because of the equivalence principle (Einstein 1907): Only the resultant force—the gravitoinertial force (Fig. 1a, blue vector)—can be measured. Said another way, during self-acceleration other forces act on the body’s gravi- tational sensors, or ‘‘graviceptors’’ (the otoliths, and kinesthetic and somatosensory signals), so they cannot signal orientation unambiguously. P. R. MacNeilage (&)  M. S. Banks Vision Science Program, University of California, Berkeley, CA 94720, USA e-mail: pogen@berkeley.edu M. S. Banks Department of Psychology and Wills Neuroscience Institute, University of California, Berkeley, CA 94720, USA D. R. Berger  H. H. Bu ¨ lthoff Max Planck Institute for Biological Cybernetics, Spemannstr. 38, 72076 Tu ¨ bingen, Germany 123 Exp Brain Res (2007) 179:263–290 DOI 10.1007/s00221-006-0792-0