In one approach to eye tracking, a contact lens contains a network of twelve accelerometers. The accelerometers are positioned within the contact lens so that the measurements of acceleration can be used to estimate a position and an orientation of the eye relative to an external reference frame. One advantage of accelerometers is that they can be made relatively small and do not require much power. However, because the contact lens has a curved shape and is relatively thin, the possible locations for the accelerometers are limited. Various geometries for the accelerometer network and approaches to optimizing these geometries are described.