Data fusion based multi-rate Kalman filtering with unknown input for on-line estimation of dynamic displacements

Structural dynamic displacement is one of the most important measurands that describe the dynamic characteristics of a structure. However, accurate measurement of dynamic displacements of a civil infrastructure is still a challenging task. To solve the difficulties and drawbacks of direct dynamic displacement measurement, the approach of multi-rate Kalman filtering for the data fusion of displacement and acceleration measurement was developed. Recently, an improved technique for dynamic displacement estimation by fusing biased high-sampling rate acceleration and low-sampling rate displacement measurements has been proposed. However, this technique can only take constant acceleration bias into account. In this paper, based on the algorithm of Kalman filter with unknown input recently developed by the authors, dynamic displacement is on line estimated based on multi-rate data fusion of high-sampling rate acceleration with time-varying bias and low-sampling rate displacement measurements. The time history of time-varying acceleration bias is treated as “unknown input” in the algorithm of Kalman filter with unknown input to overcome the limitations of the previous technique. Some numerical examples with linear or polynomial acceleration bias are used to demonstrate the effectiveness of the proposed approach for on line estimation of structural dynamic displacement.