A Generalized Gauss-Newton Procedure for Multiresponse Parameter Estimation

A method is presented for calculating the gradient and an approximate Hessian of the Box-Draper multi-response parameter estimation criterion using only the first-order derivatives of the model functions. This is an analogue of the Gauss-Newton iterative procedure for nonlinear least squares. We also describe an implementation based on a $QR$ decomposition of the residual matrix which allows incorporation of a regularization procedure similar to the Levenburg-Marquardt method in nonlinear least squares. The method incorporates a convergence criterion based on a comparison of the increment size to the statistical variability of the estimates.