Is. Chan et al., SENSOP - A DERIVATIVE-FREE SOLVER FOR NONLINEAR LEAST-SQUARES WITH SENSITIVITY SCALING, Annals of biomedical engineering, 21(6), 1993, pp. 621-631
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.