164 A.R. Ortiz et al. 20.4 Results The pedestrian’s Center of Mass (CoM) is identified and traced for the pedestrian walking along a 9 m pathway. The pathway is a rigid ground slab, stiff enough to avoid the human-structure interaction phenomenon. The pedestrian is a man, 29 years old, with a mass of 69 kg. Axial (xr), transversal (yr) and vertical (zr) components of the tracked trajectory are shown in Fig.20.4. The velocity of the pedestrian is approximately constant as can be seen in the slope of the first plot in Fig. 20.4. The total distance recorded by the Kinect sensor is around 6.0 m. The vertical and transversal movement of the pedestrian is shown in the last two plots of Fig. 20.4. The movement of the pedestrian’s CoM is somehow following sinusoidal functions where the main frequency of the vertical movement (zr) is around twice the main frequency of the transversal movement (yr). This is in accordance with the assumption of the model described in section two, however there is not a unique frequency, fact notably seen in the vertical component. The analytical model used for modeling the pedestrian’s trajectory (described by Eqs. (20.2)–(20.4)) is updated based on the experimental data showed in Fig. 20.4. Model’s parameters are updated using a probabilistic approach based on Bayesian theory as described in the methodology section. The prior distributions P.‚jMj/ of the parameters {‚=ax, ay, az, av, v0 and z0} are presented in Table 20.1. Figure 20.5 shows the marginals histogram of each parameter (along the diagonal) and the relation between parameters (plots outside the diagonal). A total of 100,000 samples were used. Other 400,000 were used for thinning as burning samples. Figure 20.5 shows a strong correlation between the parameters av and v0. This means that the model could be reduced to five parameters using a relation between av and v0. Beyond this correlation, parameters look independent to each other’s. Fig. 20.4 CoM trajectories of the pedestrian Table 20.1 Prior PDFs used for updating the parameters Parameter Units PDF Parameters ax m Uniform lower D0:3, upper D1:0 ay m Normal D0:02, D0:005 az m Normal D0:02, D0:005 av m/s Normal D0:3, D0:07 v0 m/s Normal D1:0, D0:25 z0 m Uniform lower D0:8, upper D0:9
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