Path Integration Errors Research Articles

Navigating without vision: basic and applied research.

We describe some of the results of our program of basic and applied research on navigating without vision. One basic research topic that we have studied extensively is path integration, a form of navigation in which perceived self-motion is integrated over time to obtain an estimate of current position and orientation. In experiments on pathway completion, one test of path integration ability, we have found that subjects who are passively guided over the outbound path without vision exhibit significant errors when attempting to return to the origin but are nevertheless sensitive to turns and segment lengths in the stimulus path. We have also found no major differences in path integration ability among blind and sighted populations. A model we have developed that attributes errors in path integration to errors in encoding the stimulus path is a good beginning toward understanding path integration performance. In other research on path integration, in which optic flow information was manipulated in addition to the proprioceptive and vestibular information of nonvisual locomotion, we have found that optic flow is a weak input to the path integration process. In other basic research, our studies of auditory distance perception in outdoor environments show systematic underestimation of sound source distance. Our applied research has been concerned with developing and evaluating a navigation system for the visually impaired that uses three recent technologies: the Global Positioning System, Geographic Information Systems, and virtual acoustics. Our work shows that there is considerable promise of these three technologies in allowing visually impaired individuals to navigate and learn about unfamiliar environments without the assistance of human guides.

Integration errors in a three-dimensional model for canopy albedos

A three-dimensional model of the radiative transfer within a vegetation canopy gives albedo and bidirectional reflectance for climate and remote-sensing applications. Major sources of numerical error in this model are evaluated in the single-scattering limit by comparison with an analytic solution, and procedures for the amelioration of these errors are developed. The model consists of a three-dimensional array of cells and treats multiple scattering by individual cells through integration over discrete angular sections and iteration of the scattering. Two distinct sources of error are identified: (i) errors in bidirectional reflectance from the integration of absorption and emission along the path of the radiation, and (ii) errors in integrating the bidirectional reflectances over solid angle to synthesize the albedo. Path integration errors may result from neglect of self-absorption by individual cells upon emission, inclusion of insufficient number of cell interactions, and inclusion of too few cells, i.e., unless cells near the outside of the canopy have leaf area index LAI ⪡ 1, the implied gradients of light attenuation are too sharp to be resolved. These errors are minimized by including a self-absorption term, ensuring that the number of interactions are sufficient, selecting enough vertical layers, and providing most resolution in LAI near the outside of the canopy. The spherical integration error results from the coarseness and arrangement of angular sectors and from the procedure used to sum their contributions. Error may be reduced by adding more spherical resolution and by changing the angular integration to one with equal increments in the cosine of the zenith angle. Higher-order integration schemes may also be helpful.