A parameter estimation method based on discontinuous unscented Kalman filter for non-smooth gap systems

Internal parameters of non-smooth systems, such as hysteresis and gap systems, are unable to be measured when the system is enclosed. For a non-smooth gap system, the actual system state is difficult to be evaluated due to state transitions and the coupled internal mechanical and geometric parameters. Moreover, the system state evaluation directly affects the parameter estimation result, which, in turn, will affect the evaluation of the system state at the next time instant. The interdependence between the estimated parameters and the subsequent state evaluation creates a large challenge for the traditional filter method. Based on the idea of estimating system parameters at different states from the discontinuous extended Kalman filter (DEKF) and the discontinuous unscented Kalman filter (DUKF), a parameter estimation algorithm, namely DBAA-DUKF, is proposed herein by introducing a dynamic boundary approximation algorithm (DBAA) to address this contradiction. Firstly, three evaluation conditions are presented for the system state identification. Then, DBAA-DUKF adjusts the state transition parameters and their upper and lower limits according to the difference between the evaluation results of the system state and filtering results. The parameter estimation accuracy of DBAA can be improved by adjusting the upper and lower limits of state transition parameters to constrain them in a narrow range. Finally, a single-sided nonlinear impact system with a significant gap and a double-sided gap system with small gaps are used to verify the effectiveness and feasibility of the algorithm. The results show that DBAA-DUKF can effectively solve the parameter estimation problem in the uncertain state transition conditions of non-smooth gap systems and can obtain better estimation results than DEKF and DUKF.