Estimation of Heading Angle Difference Between User and Smartphone Utilizing Gravitational Acceleration Extraction

When a user walks with a smartphone, acceleration is divided into three components. Two of the components are the vertical and horizontal accelerations according to walking dynamics, while the third is gravitational acceleration. Gravitational acceleration cannot be separated from the other two using only an accelerometer, because all accelerations are measured simultaneously. To separate the gravitational acceleration, a projection of all accelerations onto the vertical axis should be carried out using a coordinate transformation. However, the coordinate transformation itself also requires the accurate gravitational acceleration, which is a dilemma. To solve the problem, we propose a new method to extract the gravitational acceleration from additional accelerations based on a simplified walking model. The main idea is to find two time points to eliminate the additional accelerations with respect to two newly defined coordinates. The proposed method theoretically provides an optimal solution for the extraction of gravitational acceleration under the simplified model. It was mathematically analyzed and applied to the estimation problem of angle difference between the user's heading and the heading of a smartphone. The other contribution of this paper is in bandpass filtering to mitigate the estimation error of angle difference. Its center frequency is adaptively changed according to the step frequency. In experiments, the gravitational acceleration was extracted with remarkable accuracy. Therefore, the estimation of angle difference between the user's heading and the heading of a smartphone yielded stable and accurate performance.