Selecting optimal weighting factors in iPDA for parameter estimation in continuous-time dynamic models

Iteratively refined principal differential analysis (iPDA) is a spline-based method for estimating parameters in ordinary differential equation (ODE) models. In this article we extend iPDA for use in differential equation models with stochastic disturbances and we demonstrate the probabilistic basis for the iPDA objective function using a maximum likelihood argument. This development naturally leads to a method for selecting the optimal weighting factor in the iPDA objective function. We demonstrate the effectiveness of iPDA using a simple two-output continuous-stirred-tank-reactor example, and we use Monte Carlo simulations to show that iPDA parameter estimates are superior to those obtained using traditional nonlinear least squares techniques, which do not account for stochastic disturbances.