Online noise parameters estimation for sigma-point Kalman filter using sequential importance resampling

The sigma-point Kalman filter (SPKF) is a widely-used method for system state and structural parameters estimation. It assumes that the state prediction errors are minimized when the structural parameters correspond to the noise covariance matrices. However, in practice, the covariance matrices for process noise and measurement noise are usually unknown. Arbitrary selection of these covariance matrices may lead to unreliable state predictions and potentially diverging estimation results. To address this problem, we propose a method by integrating the sequential importance resampling algorithm into the traditional SPKF for the estimation of the noise covariance matrices based on the acceleration response measurement. The effectiveness of the proposed Sequential Importance Resampling Sigmapoint Kalman Filter (SIR-SPKF) is demonstrated through a numerical application to a bridge structure and a laboratory experiment involving a 3 degrees of freedom model.