For many of the numeric optimizations within SA, the partials matrix is computed using numerical differentiation. A value is changed by a delta (referred to as a perturbation), and the result is computed. The deltas used to offset the values in an optimization are set here. At each step, one portion of the partials matrix is populated. If these values are too small, you can experience sensitivity problems. The perturbation may be so small that the change in the objective is negligible and therefore the optimization proceeds without accurate direction. If the values are too large, it is possible to miss nuances in the solution space by moving over the ideal solutions.
Adjusting the Perturbation/Damping Values
Length Perturbation. The length perturbation is the amount of perturbation along the X, Y, and Z axes. In the case of a best- fit transformation, for example, the X value is adjusted by the length perturbation. The objective function is recomputed, and this process is repeated with adjustments to the Y and Z values.
Angular Perturbation. After perturbing X, Y, and Z, the Rx value is perturbed by the angular perturbation, then Ry, then Rz. At each step, one part of the partials matrix is populated. If these values are too small, you can experience sensitivity problems. The perturbation may be so small that the change in the objective is negligible and therefore the optimization proceeds without accurate direction. If the values are too large, it is possible to miss nuances in the solution space by moving over the ideal solutions.
Damping. Once the partials matrix is computed for a given step in an optimization, the matrix is inverted, and multiplied by the residual errors. This results in a vector describing how to move the input variables to minimize the objective is the system were truly linear. Since the systems we deal with in coordinate metrology are usually non-linear, the delta vector will most likely not move to the optimal solution. For this reason, we scale the vector by the damping factor to retard its effect. After making the move, the partial determination process repeats until an acceptable solution is reached.