CHAPTER 4
 RESULTS

 Synthetic Marker Data without Noise

 For synthetic motions without noise, each two-level optimization precisely

recovered the original marker trajectories to within an arbitrarily tight tolerance (on the

order of le-13 cm), as illustrated in Figure 3-9. At the termination of each optimization,

the optimum model parameters for the hip, knee, and ankle were recovered with mean

rotational errors less than or equal to 0.0450 and mean translational errors less than or

equal to 0.0077 cm (Appendix C).

 Synthetic Marker Data with Noise

 For synthetic motions with noise, the two-level optimization of the hip, knee, and

ankle resulted in mean marker distance errors equal to 0.46 cm, which is of the same

order of magnitude as the selected random continuous noise model (Table 4-1). The

two-level approach determined the original model parameters with mean rotational errors

less than or equal to 3.730 and mean translational errors less than or equal to 0.92 cm

(Appendix D). The outer-level fitness history converged rapidly (Figure 4-1) and the hip,

knee, and ankle optimizations terminated with a mean wall clock time of 41.02 hours.

 Experimental Marker Data

 For multi-cycle experimental motions, the mean marker distance error of the

optimal hip, knee, and ankle solutions was 0.41 cm, which is a 0.43 cm improvement

over the mean nominal error of 0.84 cm (Table 4-2). For each joint complex, the

optimum model parameters improved upon the nominal parameter data (or values found