An Application of Partial Update Kalman Filter for Bilinear System Modelling

Abstract

Bilinear models are a special class of nonlinear models significant for nonlinear systems’ parameter estimation and control design. This study proposes a novel application of partial update Kalman filter (PUKF) where the PUKF profoundly enhances the accuracy of bilinear systems modelling. In the PUKF approach, only a subset of the parameter state vector is updated at each epoch, which could decrease the computational burden compared to the traditional Kalman filter. Moreover, this work uses a preaching optimisation algorithm (POA) to tune the PUKF parameters adaptively based on the estimation problem. The adequately adjusted adaptive PUKF provide good estimation results, stable filtering operation and quick convergence. A new objective function is formulated based on correlation functions and an error between the estimated and actual outputs. The new objective function significantly improved the quality of the solution. The sensitivity of POA on solution quality is analysed using various statistical parameters. The efficacy and correctness of the proposed algorithm are verified on a numerical plant and two real-time benchmark systems. The quantitative analysis based on the proposed scheme is examined with distinct standard metrics and robustness verified at different Gaussian noise variance levels. The accuracy, stability, and consistency of the proposed algorithm performance are verified through the Diebold–Mariano hypothesis test, results from several independent runs, and tenfold cross-validation tests. The simulation results manifest that the POA-assisted PUKF method is much more effective and better compared to other existing and employed benchmark metaheuristic techniques such as self-adaptive differential evolution, crow search algorithm, and POA methods.