Application of heuristic scaling and null parameter space for efficient parameter estimation

Abstract

In parameter estimation problem, two factors which cause difficulties can be considered. One of those is an order-of-magnitude difference in parameter values. The order-of-magnitude difference in parameter values makes it difficult to find the optimum because parameter estimation problem can be ill-conditioned by the difference. To avoid the difficulty, a proper scaling factor of parameter should be introduced into parameter estimation. The other factor is an inefficient search direction generated by algorithm is used during the optimization. Parameters changed by inefficient search directions cannot improve the objective function of parameter estimation problem. For this reason, efficient search directions should be selected by systematic approach to estimate the optimal parameter efficiently. In this work, a new heuristic method for determining the scaling factor which converts parameter estimation problem well-conditioned and a new decision method for efficient parameter search direction are proposed.