Quaternion-Based Complementary Filter for Attitude Determination of a Smartphone

Abstract

A geometrically intuitive quaternion-based complementary filter has been developed, which estimates the attitude of a smartphone using signals obtained from the device's internal magnetic and inertial measurement unit. This method introduces two correction factors μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> , which governs the rate at which the accelerometer corrects the pitch/roll angle, and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> , which controls the rate at which the yaw angle is corrected by the magnetometer. The smartphone's attitude can be determined by combining information from the tri-axial gyroscope (measures the rate at which the device rotates), the tri-axial accelerometer (measures the acceleration due to gravity in the absence of body movement), and the triaxial magnetometer (can be used to determine the direction of geomagnetic north). In order to validate the algorithm, a nonferrous rectangular plate with retroreflective markers affixed at each corner was attached to the smartphone enabling its attitude to be tracked by an optical motion capture system. The accuracy of the algorithm (φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> = 3.37°, θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> = 1.84°, ψ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> = 4.83°) was assessed as ten subjects performed five normal daily activities while the smartphone was loosely fixed to the upper thigh to simulate being carried in a pants pocket. The optimal tuning parameters (μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> = 0.003 and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> = 0.001) for the algorithm across all the body movements were also identified.