Improved Kalman filter with unknown inputs based on data fusion of partial acceleration and displacement measurements

The classical Kalman filter (KF) provides a practical and efficient state estimation approach for structural identification and vibration control. However, the classical KF approach is applicable only when external inputs are assumed known. Over the years, some approaches based on Kalman filter with unknown inputs (KF-UI) have been presented. However, these approaches based solely on acceleration measurements are inherently unstable which leads poor tracking and so-called drifts in the estimated unknown inputs and structural displacement in the presence of measurement noises. Either on-line regularization schemes or post signal processing is required to treat the drifts in the identification results, which prohibits the real-time identification of joint structural state and unknown inputs. In this paper, it is aimed to extend the classical KF approach to circumvent the above limitation for real time joint estimation of structural states and the unknown inputs. Based on the scheme of the classical KF, analytical recursive solutions of an improved Kalman filter with unknown excitations (KF-UI) are derived and presented. Moreover, data fusion of partially measured displacement and acceleration responses is used to prevent in real time the so-called drifts in the estimated structural state vector and unknown external inputs. The effectiveness and performance of the proposed approach are demonstrated by some numerical examples.