基于PCA的有色噪声环境下卡尔曼滤波算法

A PCA-based algorithm for Kalman filtering in colored noise environments

针对卡尔曼滤波处理有色噪声存在精度和可靠性不高的问题,提出了利用主成分分析(PCA)处理卡尔曼滤波的算法。该算法充分利用卡尔曼滤波的预测功能,以卡尔曼预测值为中心对接收信号进行加窗处理,对窗口内的数据进行主成分分析得到预测值,然后对预测值进行修正,在滤波过程中不断在窗口内估计修正参数,既可以减少运算复杂度,又可以避免过分依赖模型先验知识。最后给出了仿真实验,结果表明,该算法实现简单,均方误差低,稳定性好,大大减少了计算复杂度,能更为有效地对系统进行状态估计。

Principal component analysis （PCA） was used to improve Kalman filtering＇ s precision and reliability performance in a colored noise environment. With the predictive function of Kalman filters, this method processes the sig- nal in a window which determines the Kalman predictive center. Then the PCA is used in the data of the window, and the prediction value is corrected. In the process of filtering, the parameters are continually estimated in the window. This method does not depend on the future knowledge of noise dynamics and heavy computational effort needed. The simulation results show that the algorithm can be easily implemented, and it has low mean square and good stability. Experimental results show that the PCA Kalman filtering model could perform better for the state estimation with low complexity.