Input and State Estimation for Linear Discrete-Time Systems without Direct Feedthrough

The classical Kalman filter (KF) is an effective approach of state estimation for linear discrete-time systems, but classical KF is applicable only when external inputs are measured. So far, some studies of Kalman filter with unknown inputs (KF-UI) have been proposed. However, previous KF-UI approaches based solely on acceleration measurements are inherently unstable which leads to poor tracking and fictitious drifts in the identified structural displacements and unknown inputs in the presence of measurement noises. Moreover, it is necessary to have the measurements of acceleration responses at the locations where unknown inputs applied, direct feedthrough of the unknown inputs to the output measurements are required in these approaches. In this paper, it aims to extend the classical KF approach to circumvent the above limitations for Input and state estimation for linear discrete-time systems without direct feedthrough. Based on the scheme of the classical KF, a Kalman filter with unknown excitations (KF-UI) is derived for linear discrete-time systems without direct feedthrough. Then, data fusion of acceleration and displacement or strain measurements is used to prevent the drifts in the identified structural state and unknown inputs. In addition, dynamic displacement is one of the crucial physical parameters for bridge rating, seismic risk assessment, structural health monitoring of structures. However, it is challenging to measure dynamic displacement because displacement is a relative quantity and requires a fixed reference point Some researchers have investigated dynamic displacement estimation by fusing biased high-sampling rate acceleration and low-sampling rate non-contact displacement measurements. In this 1) Professor, Corresponding author, mail: *[email protected] 2) Graduate Student paper, the proposed KF-UI is used to identify the dynamic displacement by fusing biased high-sampling rate acceleration and low-sampling rate displacement measurements with consideration of bias in acceleration measurements as “unknown input”. Numerical examples are used to demonstrate the effectiveness of the proposed approach.