Evaluating Tracking Rotations Using Maximal Entropy Distributions for Smartphone Applications

Recursive attitude estimation of a rigid body from inertial measurements is a crucial component of many modern systems and as such, has a rich historical background of proposed techniques. Recent work has been done on tracking rotations using maximal entropy distributions. However, there has been no evaluation done on the performance of this approach using real inertial data. In this work, we investigate the performance and limitations of classical and modern probabilistic Bayesian approaches and provide a rigorous comparison to attitude estimation on the special rotation group $\mathcal {SO}(3)$ using maximal entropy distributions. The extended Kalman Filter and the unscented Kalman filter are derived as benchmarks in attitude estimation from low-cost inertial measurement units, commonly found in smartphones. To evaluate robustness over multiple sampling intervals, we generated synthetic directional inertial measurements from a typical low-cost 3-axes inertial measurement unit and use the Frobenius Norm as our primary metric. To further our evaluation, we took advantage of a publicly available dataset where inertial measurements are recorded from a number of off-the-shelf smartphones and the ground truth is calculated using a Motion Capture system. Our experiments demonstrate that tracking rotations using maximum entropy distributions produce a more accurate and robust solution in contrast to alternate proven Kalman approaches.