Improved Accuracy of Nonlinear Parameter Estimation with LAV and Interval Arithmetic Methods

The reliable solution of nonlinear parameter estimation problems is an important computational problem in many areas of science and engineering, including such applications as real time optimization. Its goal is to estimate accurate model parameters that provide the best fit to measured data, despite small-scale noise in the data or occasional large-scale measurement errors (outliers). In general, the estimation techniques are based on some kind of least squares or maximum likelihood criterion, and these require the solution of a nonlinear and nonconvex optimization problem. Classical solution methods for these problems are local methods, and may not be reliable for finding the global optimum, with no guarantee the best model parameters have been found. Interval arithmetic can be used to compute completely and reliably the global optimum for the nonlinear parameter estimation problem. Finally, experimental results will compare the least squares, 12, and the least absolute value 11 estimates using interval arithmetic in a chemical engineering application.