Optimal Accelerometer Layouts for Data Recovery in Signature Verification

Current experimental use of pen acceleration data for signature verification has prompted the mathematical theory of our recent paper on the subject, expounding motion recovery techniques for a special pen with imbedded accelerometers. This continuation seeks to optimize the instrument layout as a mechanical filter which serves to extract the kinematic observables from the experimental noise. Our early sections, through various algebraic postulates, determine a simplest function of the layout geometry expressing the relative desirability of an accelerometer configuration. Any nontrivial layout demands some off-axial instruments, but natural “feel” requires few such placements. Hence, our middle sections prove mathematical results under various geometric assumptions which yield optimal layouts with one, two, or three off-axial instruments. Our final sections discuss the further constraint that all accelerometers measure just three directions. They assume not more than two off-axial instruments and obtain the best configurations of these tridirectional types.