Development of Block Iterated Extended Kalman Filter for Recursive Estimation of ARMAX Model Parameters

Online estimation of dynamic model parameters using recursive techniques is at the heart of any adaptive control scheme. The majority of the available recursive parameter estimation schemes update model parameters at the same rate as that of the model time update. In many continuously operated processes, however, the system operates at one operating point for a considerable time before setpoints changes are made. Thus, the model parameter changes occur at a significantly slower rate when compared to the model time update. In this work, we develop a shifting window-based block recursive parameter estimation scheme for tracking parameters of a MISO ARMAX model. The variation of the model parameters is modeled as a slow rate random walk process over shifting time windows. Since ARMAX is a nonlinear-in-parameter model, iterated extended Kalman filter (IEKF) algorithm available in the literature for dealing with nonlinear measurement models is adopted to develop a Block IEKF for tracking the ARMAX model parameters. The efficacy of the proposed approach is demonstrated by a simulation study carried out on an artificial system with time-varying model parameters and experimental data obtained from the benchmark quadruple tank system. Analysis of the simulation and experimental results reveals that the proposed Block IEKF scheme, with a judicious tuning of the random walk model, is able to track time-varying parameters of ARMAX models quickly.