Note that known initial conditions can be forced as constraints in the AMLE minimization problem (Varziri et al.
The corresponding AMLE estimated trajectories are presented in Figure G.
Like the AMLE method proposed in this article, the CSTM software can accommodate unknown initial conditions for state variables, irregularly sampled data and unknown disturbance intensities.
The AMLE algorithm is easier to set up and converges faster than the classical ML-based method of Kristensen et al.
The algorithm, which is an extension of the AMLE algorithm previously proposed by Varziri et al.
The proposed AMLE parameter estimates are much easier to compute than the corresponding classical ML parameter estimates because it does not require recursive solution of Riccati equations to obtain the state covariance matrix.
Overall, AMLE did a good job in jointly estimating the model parameters, state trajectories and process noise intensities.
Further studies are underway to investigate the performance of AMLE in practical problems with larger numbers of inputs, outputs, and parameters, and disturbances.
i]s Abbreviations AMLE approximate maximum likelihood estimation CSTR continuous stirred tank reactor MAP maximum A posteriori MIMO multi-input multi-output ML maximum likelihood ODE ordinary differential equation PEN model-based penalty SISO single-input single-output SSE sum of squared errors