位移和加速度融合的自适应多速率Kalman滤波方法

A new adaptive multi-rate Kalman filter for the data fusion of displacement and acceleration

多速率Kalman滤波方法可用于低采样率的位移和高采样率的加速度数据融合,而未知的噪声协方差信息则显著制约着多速率Kalman滤波精度.本文通过将多速率Kalman滤波转换为传统的单速率Kalman滤波,建立了Kalman滤波增益的自协方差矢量与未知的加速度谱密度和观测噪声参数间的线性函数模型,并采用最小二乘估计方法对未知的噪声协方差参数进行估计,进而有效地提高了多速率Kalman滤波精度.数值仿真和震动台实验结果验证了本文方法的正确性和有效性.

The multi-rate Kalman filter can be used for the data fusion of displacement and acceleration,which were sampled at different frequencies. However,the noise covariance matrices,especially the process noise covariance matrix,are usually unavailable in the practical applications.With inappropriate noise covariance matrices,the state estimates of multi-rate Kalman filter is suboptimal.In this paper,a new adaptive multi-rate Kalman filter,which is based on the autocovariance least-squares method,is proposed.For a given set of displacement and acceleration data sampled at different frequencies,the data fusion problem is formulated as the single-rate Kalman filter rather than the multi-rate Kalman filter.And the correlations between the innovations were used to establish a relationship to the unknown parameters aboutthe noise covariance matrices.Therefore,the unknown parameters can be estimated by solving the least-squares problem.The validity of the proposed method is demonstrated by a numerical example and an earthquake engineering test from the Large High-Performance Outdoor Shake Table.