Smoother based 3 - D Attitude Estimation for Mobile

The mobile robot localization problem is decomposed and treated as a two-stage iterative process. The attitude is estimated rst and is then used for position estimation. The innovation of our method presented in the sequel is the incorporation of a smoother, in the attitude estimation loop that outperforms in estimate accuracy any other Kalman ter based technique. The smoother is ideally suited for this application because it can exploit the special nature of the data fused. These data are either provided by inertial sensors and, in general, appear with high frequency, or result from absolute orientation measuring devices and arrive at lower rates. Two Kalman lters form the smoother. During each time interval one of them propagates the attitude estimate forward in time until it is updated (by an absolute orientation sensor). Then, the second lter propagates the recently renewed estimate backwards this time. Combining the outcome of the two lters, the smoother optimally exploits the limited (only at certain time instances) observability of the system. The backward lter propagation is particularly beneecial for those parts of the trajectory that exhibit lower levels of accuracy as these were determined during the forward lter propagation. This way the estimates across each time interval, are smoothed and thus a more uniform and better quality orientation estimate is achieved. Another prominent feature of this new approach is that the frequency of the absolute orientation sensors can be used as a design parameter. The desired level of accuracy for the attitude estimation and subsequently for the three-dimensional position estimation can be preset. At the system model level, gyro modeling is used which relies on the integration of the kinematic equations to propagate the attitude estimates. Thus, the Indirect (error state) form of the Kalman lter is developed for both the forward and the backward parts of the smoother. The main beneet of this choice is that the tedious and highly sensitive dynamic modeling of the mobile robot and its environment is avoided. The proposed implementation is independent of the structure of the vehicle or the morphology of the ground. It can easily be transfered to another mobile platform provided that it carries an equivalent set of sensors. Finally, instead of Euler angles mostly found in the relevant robotics literature, quaternions are selected for the three-dimensional attitude representation. The quaternion parameterization was chosen mainly for three practical reasons. First, the prediction equations are treated linearly, …