Validation of Thigh Angle Estimation Using Inertial Measurement Unit Data against Optical Motion Capture Systems

Abstract

Inertial measurement units are commonly used to estimate the orientation of sections of sections of human body in inertial navigation systems. Most of the algorithms used for orientation estimation are computationally expensive and it is difficult to implement them in real-time embedded systems with restricted capabilities. This paper discusses a computationally inexpensive orientation estimation algorithm (Gyro Integration-Based Orientation Filter-GIOF) that is used to estimate the forward and backward swing angle of the thigh (thigh angle) for a vision impaired navigation aid. The algorithm fuses the accelerometer and gyroscope readings to derive the single dimension orientation in such a way that the orientation is corrected using the accelerometer reading when it reads gravity only or otherwise integrate the gyro reading to estimate the orientation. This strategy was used to reduce the drift caused by the gyro integration. The thigh angle estimated by GIOF was compared against the Vicon Optical Motion Capture System and reported a mean correlation of 99.58% for 374 walking trials with a standard deviation of 0.34%. The Root Mean Square Error (RMSE) of the thigh angle estimated by GIOF compared with Vicon measurement was 1.8477°. The computation time on an 8-bit microcontroller running at 8 MHz for GIOF is about a half of that of Complementary Filter implementation. Although GIOF was only implemented and tested for estimating pitch of the IMU, it can be easily extended into 2D to estimate both pitch and roll.

Keywords: human gait analysis; inertial measurement units; sensor fusion.

Figure 1

(a) Thigh angle of a subject during a single trial measured from the motion analysis lab (MAL). (b) Thigh angle measuring reference.

Figure 2

Thigh angle synchronized with the vertical and forward movements of the foot. Vertical and forward movements of the foot is used to identify the key points of the thigh angle waveform.

Figure 3

Thigh angle of left and right legs. This indicates that the toe off of one leg is synchronized with the initial contact of the other leg as shown by vertical dashed lines.

Figure 4

Marker and IMU placement. (a) Full placement. (b) Marker cluster attached to the left thigh of subject and the markers on it. (c) Custom-made IMU attached on the right thigh and the markers placed on it. (d) Markers attached to the heels.

Figure 5

Reference axis of IMU data.

Figure 6

Gyro Integration-Based Orientation Filter (GIOF). $a_{i_k}$ ($i=x,y,z)$ is the acceleration of $i$ axis measured at time stamp k; $g_{k_z}$ and $g_{{\left(k-1\right)}_z}$ are gyroscope $z$ axis reading measured at time stamps k and (k − 1); $t_k$ and $t_{k-1}$ are the time values of time stamps k; and (k − 1); ${\theta }_{k-1}$ is the previous estimation of thigh angle and ${\theta }_k$ is the current estimation of thigh angle.

Figure 7

Thigh angle computed from MAL data $\left({\theta }_{MAL}\right)$ and IMU data $\left({\theta }_{IMU}\right)$ for a sample trial. Correlation coefficient of the two waveforms is 0.99932 and the root mean square error (RMSE) is 1.0675 for this trial.

Figure 8

Histograms of positive and negative peak angle errors.

Figure 9

Distributions of correlation and RMSE between ${\theta }_{IMU}$ and ${\theta }_{MAL}$ for vision impaired subjects.

Figure 10

Thigh angle estimated in real-time in the IMU by GIOF and complementary filter captured for a trial when walking on a corridor.

Figure 11

Normalized thigh angle, gyro signal, and time derivative of gyro signal.