Extending the Kalman filter for structured identification of linear and nonlinear systems

Abstract

This paper considers a novel approach to system identification which allows accurate models to be created for both linear and nonlinear multi-input/output systems. In addition to conventional system identification applications, the method can also be used as a black-box tool for model order reduction. A nonlinear Kalman filter is extended to include slow-varying parameter states in a canonical model structure. Interestingly, in spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100% accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical structure ensures a well-conditioned model which simultaneously provides valuable dynamic information to the engineer. After extensive testing of a linear example, the model structure is extended to a generalised nonlinear form, which is shown to accurately identify the handling response of a full vehicle model.