Principles of Modern Radar - Volume 2 1891121537

714 CHAPTER 16 Human Detection With Radar: Dismount DetectionRV = v/HT. The parameter RLc can be expressed in terms of RV as RLc = 1.346 √ RV,leading to the following simplification in the expression for Dc:Dc = 1.346 √RV(s) (16.5)The duration of support, Ds, the duration of double support, Dds, and duration ofbalance are all linearly dependent upon the cycle duration and are given asDs = 0.752Dc − 0.143 (s) (16.6)Dds = 0.252Dc − 0.143 (s) (16.7)Db = 0.248Dc + 0.143 (s) (16.8)A relative time parameter, t%, is defined ast% = t(16.9)Dcwhile the relative duration of support, Ds%, is defined asDs% = Ds(16.10)DcIn both (16.9) and (16.10), the term “relative” refers to the time elapsed as being a percentageof the overall walking cycle duration.These temporal values are used in the parametric model, which produces the 3-Dkinematic equations for the time-varying change in position of certain points on the bodyas well as the time-varying angular motion of elbow, knee, and ankle joints. All motionis described relative to the origin, defined at the bottom of the spine, OS (as shown inFigure 16-3). Note that the thigh height, which is a critical parameter in the model, isdefined as the distance between the ground and the top of the thigh bones, while OS islocated higher up at the base of the spine. The kinematics governing pelvic rotations andflexing at the hip are thus also modeled.Consider the equations given by the Boulic-Thalmann model for the periodic trajectoriesthat govern the motion of the origin, OS, for the duration of one walking cycle:Vertical translation:OS V = 0.015RV (sin 2π (2t% − 0.35) − 1) (16.11)Lateral translation:⎧⎨ −0.032 for RV > 0.5OS L = A L sin 2π (t% − 0.1) , where A L =⎩−0.128RV 2 + 0.128RV for RV < 0.5(16.12)Forward/backward translation:OS FB = A FB sin 2π (2t% − 2φ FB ) (16.13){−0.021 for RV > 0.5where φ FB = 0.625 − Ds% and A FB =−0.084RV 2 + 0.084RV for RV < 0.5A plot of the trajectories of OS for varying values of RV is shown in Figure 16-4. Thesecurves are significant because when these components are combined to form the overall