动态系统基于时域与频域相结合的多尺度联合滤波器

A Multiscale Associated Filter Combining Temporal Domain with Frequency Domain for Dynamic System

针对基于小波变换与Kalman滤波相结合的多尺度联合估计方法中存在的问题,本文利用新的系统分块技术与多尺度变换方法相结合,建立一个动态系统基于时域与频域相结合的多尺度联合滤波器.首先,将时域中描述的状态方程和观测方程改写为块状态方程和块观测方程;利用多尺度变换技术在时域和频域中联合描述它们;结合Kalman滤波与顺序滤波的思想,建立了一类应用于动态系统的多尺度估计联合滤波器.新滤波器不仅保留了传统Kalman滤波器的实时性和递归性等优良性质,而且在滤波过程中还具有对随机状态信号进行多尺度分析的能力.计算机仿真实验验证了利用新估计器得到的估计精度可与利用传统Kalman滤波器得到的估计精度相媲美.

According to these shortcomings exited in mulitscale associated estimation methods, a new multiscale estimator is proposed by combining wavelet transform and Kalman filtering, in which a new technology of systemic and multiscale trartsform are employed. The state equation and measure equation described only in temporal domain are rewritten down data-block equations; these dam-block equations are characterized by use of multiscale technology in both temporal and frequency domains;the new associated filter is established via using Kalman filter and sequential filter. The new filter not only holds the good characters, such as the real time and recursive, but also possesses the multiiscale analysis capability. Computer simulations Sow that the estimate accuracy of new algorithm is comparable with or little better than that of traditional Kalman filter.