Simplified Ellipsoid Fitting-Based Magnetometer Calibration for Pedestrian Dead Reckoning

Abstract

Pedestrian dead reckoning (PDR) is a relative positioning technique, which determines the relative location of a pedestrian by using step detection, step length estimation, and heading estimation. Since step can be accurately detected and step length can be well modelled, the heading estimation is the dominant element affecting the positioning accuracy. However, heading estimation using magnetometer is seriously influenced by diversity of indoor electromagnetic environment. In order to calibrate the magnetometer measurement, we introduce an ellipsoid equation to represent the error model of magnetometer measurement, and utilize the Singular Value Decomposition and the Cholesky Decomposition for solving the equation in this paper. To achieve an accurate error model, the state-of-the-art magnetometer calibration methods need to obtain massive samples of magnetic field. To collect the data from magnetometer more efficiently, we propose a simplified method to rotate smartphone two circles around arbitrary two of three axes in a 3D space. This data collection method can provide adequate samples to determine the ellipsoid equation within a short period. The experimental results shows that the variance of data applied with proposed method is reduced by 94.08 % on an average, while data collected by six-direction method is reduced by 91.73 % and ∞ shape method by 49.83 % averagely. The calibration process takes just 2–4 s, while the conventional methods need at least 10 s. Compared to 4.59 m of the 95th percentile error without calibration, the PDR field tests show a 1.62 m error with proposed method.