SENSOP - A DERIVATIVE-FREE SOLVER FOR NONLINEAR LEAST-SQUARES WITH SENSITIVITY SCALING

Nonlinear least squares optimization is used most often in fitting a c omplex model to a set of data. An ordinary nonlinear least squares opt imizer assumes a constant variance for all the data points. This paper presents SENSOP, a weighted nonlinear least squares optimizer, which is designed for fitting a model to a set of data where the variance ma y or may not be constant. It uses a variant of the Levenberg-Marquardt method to calculate the direction and the length of the step change i n the parameter vector. The method for estimating appropriate weightin g functions applies generally to 1-dimensional signals and can be used for higher dimensional signals. Sets of multiple tracer outflow dilut ion curves present special problems because the data encompass three t o four orders of magnitude; a fractional power function provides appro priate weighting giving success in parameter estimation despite the wi de range.