Comparison of the extended kalman filter and marquardt algorithms for processing kinetic data

The extended Kalman filter and Marquardt's gradient expansion algorithm for nonlinear least squares are compared with respect to accuracy and precision of parameter extimates, computational burden, sensitivity to initial parameter estimates and ability to indicate model errors. Fits of synthetic first-order data and combined first- and zero-order data produce estimates of equivalent precision and accuracy in most cases. Similar results were obtained for both simulated and experimental data for combined zero-order/first-order processes. However, for the simulated zero-order/first-order data with small zero-order components processed over two half-lives of the first-order process, the Kalman filter overestimated the zero-order rate constant by a substantially larger amount than the Marquardt algorithm. Significant differences in computational burden and sensitivity to initial parameter estimates are demonstrated; however, neither algorithm has a significant advantage over the other for the detection of model error.