Multiple-Model Linear Kalman Filter Framework for Unpredictable Signals

This paper presents sensor fusion techniques for systems where the process model is a function of the human input and, therefore, unpredictable. The system consists of free and user-driven motion regimes. The free regime can be modeled as a damped sinusoidal waveform, while the driven regime and the transitions between regimes do not respect any sort of probability, pattern, or sequence. The quantity of interest is the deflection of a clamped beam, measured using three sensor technologies: 1) strain gages; 2) infrared; and 3) Hall effect sensors. Experiments using infrared-based motion capture as reference measuring system show that: 1) none of the sensors present optimal performance for both motion regimes and 2) measurement errors of each sensor differ significantly according to the motion regime. These findings suggest the use of sensor fusion techniques with low processing cost, compatible with real-time embedded applications. Our solution is based on a multiple-model linear Kalman filter in combination with motion segmentation. The motion segmentation discriminates gestures according to the knowledge of their process model. This allows a more predictive estimation during periods of free motion, while relying on a less predictive approach for unknown user-driven signals. In addition, we propose a framework on evaluation and selection of process models for unpredictable signals. The implementation was compared with single-sensor and single-model filter designs. Results based on human subject data reveal that the proposed method improves the error covariance of the estimate by a factor of 2.2 for driven motions and 12.7 for free motions in comparison with single-sensor filter design.