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Research Papers

Motion Estimation Using Point Cluster Method and Kalman Filter

[+] Author and Article Information
M. Senesh

Biorobotics and Biomechanics Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

A. Wolf1

Biorobotics and Biomechanics Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israelalonw@technion.ac.il

1

Corresponding author.

J Biomech Eng 131(5), 051008 (Apr 13, 2009) (7 pages) doi:10.1115/1.3116153 History: Received August 20, 2007; Revised September 14, 2008; Published April 13, 2009

The most frequently used method in a three dimensional human gait analysis involves placing markers on the skin of the analyzed segment. This introduces a significant artifact, which strongly influences the bone position and orientation and joint kinematic estimates. In this study, we tested and evaluated the effect of adding a Kalman filter procedure to the previously reported point cluster technique (PCT) in the estimation of a rigid body motion. We demonstrated the procedures by motion analysis of a compound planar pendulum from indirect opto-electronic measurements of markers attached to an elastic appendage that is restrained to slide along the rigid body long axis. The elastic frequency is close to the pendulum frequency, as in the biomechanical problem, where the soft tissue frequency content is similar to the actual movement of the bones. Comparison of the real pendulum angle to that obtained by several estimation procedures—PCT, Kalman filter followed by PCT, and low pass filter followed by PCT—enables evaluation of the accuracy of the procedures. When comparing the maximal amplitude, no effect was noted by adding the Kalman filter; however, a closer look at the signal revealed that the estimated angle based only on the PCT method was very noisy with fluctuation, while the estimated angle based on the Kalman filter followed by the PCT was a smooth signal. It was also noted that the instantaneous frequencies obtained from the estimated angle based on the PCT method is more dispersed than those obtained from the estimated angle based on Kalman filter followed by the PCT method. Addition of a Kalman filter to the PCT method in the estimation procedure of rigid body motion results in a smoother signal that better represents the real motion, with less signal distortion than when using a digital low pass filter. Furthermore, it can be concluded that adding a Kalman filter to the PCT procedure substantially reduces the dispersion of the maximal and minimal instantaneous frequencies.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Experiment setup: (a) system setup, (b) sliding mass, (c) static part, and pendulum hinge

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Figure 2

Frequency backbones: (a) pendulum and (b) slider mass

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Figure 3

Real angle: (a) static part of the pendulum and (b) pendulum hinge

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Figure 4

PCT estimated angle: (a) static part of the pendulum and (b) pendulum hinge

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Figure 5

Kalman filter followed by PCT estimated angle: (a) static part of the pendulum and (b) pendulum

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Figure 6

Maximal angular amplitudes: (+) real angle, (○) PCT estimated angle, and (*) Kalman filter followed by PCT estimated angle

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Figure 7

Relative error between the real and estimated angle: (○) Kalman filter followed by PCT estimated angle and (+) PCT estimated angle

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Figure 8

Closer look at the signals: (−) real angle, (…) PCT estimated angle, and (--) Kalman filter followed by PCT estimated angle

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Figure 9

Instantaneous frequency: (a) instantaneous maximal frequency, (b) instantaneous minimal frequency. (○) real angle, (+) PCT estimated angle, and (*) Kalman filter followed by PCT estimated angle

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Figure 10

Low pass filter followed by PCT estimated angle: (a) static part of the pendulum and (b) pendulum

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Figure 11

The bone is represented by a rigid rod and the soft tissues are represented by a combination of springs and slider mass

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