Investigation of simultaneous estimation of state and unknown parameters using a modified Kalman filter incorporating with moment equations in the prediction step

Abstract

The modified Kalman filter, incorporating stochastic dynamic analysis in the prediction step, was introduced in a previous paper to systematically deal with nonlinear and parameter uncertainty excitation systems. In addition, the KF-SDA filter was extended to parameter estimation problems. However, the problem of simultaneous estimation of state and unknown parameters has not been developed in previous research. The problem of simultaneous estimation of state and unknown parameters is of great engineering significance as a method of state estimation and system identification under the limitation of the number and types of sensors. This paper deals with a method to apply KF-SDA to the problem of simultaneous estimation of state and unknown parameters. As a basic verification of the proposed method, numerical simulations are performed for a single-degree-of-freedom system which is subject to random noise excitation of parameters. Furthermore, the cases that the estimated value and the true value agree and the cases that they do not agree are considered using the time required for convergence.