An Algorithm for Least Squares Estimation of Nonlinear Parameters When Some of the Parameters Are Linear

Abstract

An algorithm is presented for nonlinear least squares estimation in which the parameters to be estimated can be regarded as all nonlinear (the traditional approach) or reclassified as linear-nonlinear. The theoretical basis for the reclassification approach is given and examples are presented which allow a comparison of the all nonlinear to the linear-nonlinear method employing two widely used iterative techniques, Hartley and Marquardt. The reclassification method reduces the dimensionality of the vector of iterants and thus the number of initial guesses to be made. Improved results (less iterations and computer run time) are obtained for the linear-nonlinear method when using the Hartley technique, but are not when using the Marquardt technique.

Key Words:

• Nonlinear
• Least Squares
• Estimation
• Parameter Reclassification
• Linear-Nonlinear
• Algorithm
• Mathematical Model