Multi-rate Kalman filtering for the data fusion of displacement and acceleration response measurements in dynamic system monitoring

Many damage detection and system identification approaches benefit from the availability of both acceleration and displacement measurements. This is particularly true in the case of suspected non-linear behavior and permanent deformations. In civil and mechanical structural modeling accelerometers are most often used, however displacement sensors, such as non-contact optical techniques as well as GPS-based methods for civil structures are becoming more common. It is suggested, where possible, to exploit the inherent redundancy in the sensor information and combine the collocated acceleration and displacement measurements in a manner which yields highly accurate motion data. This circumvents problematic integration of accelerometer data that causes low-frequency noise amplification, and potentially more problematic differentiation of displacement measurements which amplify high-frequency noise. Another common feature of displacement-based sensing is that the high-frequency resolution is limited, and often relatively low sampling rates are used. In contrast, accelerometers are often more accurate for higher frequencies and higher sampling rates are often available. The fusion of these two data types must, therefore, combine data sampled at different frequencies. A multi-rate Kalman filtering approach is proposed to solve this problem. In addition, a smoothing step is introduced to obtain improved accuracy in the displacement estimate when it is sampled at lower rates than the corresponding acceleration measurement. Through trials with simulated data the procedure's effectiveness is shown to be quite robust at a variety of noise levels and relative sample rates for this practical problem.