An impact load identification method based on augmented steady smooth Kalman filter under limited measurements

The Kalman filter has been widely used in structural dynamic load identification. However, traditional methods based on the augmented Kalman filter are unable to fully utilize measurement data and perform poorly when measurement capabilities are limited, leading to reduced accuracy. One way to better utilize measurement data is through the RTS smoothing filter. However, this improvement introduces significant computational overhead due to recursive covariance matrix operations. Additionally, state augmentation leads to filtering instability. To address these issues, we propose an Augmented Steady Smooth Kalman Filter (ASSKF), which improves estimation accuracy by incorporating additional response data. To enhance efficiency, a stable Kalman gain matrix is integrated into both forward and backward filtering operations, achieving computational efficiency without sacrificing accuracy. Furthermore, the stability of the augmented Kalman filter is analyzed theoretically and the filter is stabilized using pseudo-measurements when only limited measurements are available. Experimental validations confirm the accuracy and feasibility of the ASSKF. Compared to traditional Kalman and smoothing filters, the method proposed in this paper effectively strikes a balance between computational accuracy and speed.