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本文提出了利用定常卡尔曼滤波来实现任意一维平稳随机过程递推最佳滤波的方法。该法首先对已知非有理功率谱进行有理谱逼近,并将有理谱进行乘性谱分解,得到相应的ARMA模型,然后将ARMA模型转化为扩充维数形式的马尔可夫状态空间模型,再利用定常卡尔曼滤波递推公式进行递推滤波。文中给出了模拟计算结果,并与维纳滤波法给出的结果进行了比较,数值计算结果表明,两种方法的结果完全一致。
In this paper, we propose a method to realize recursive optimal filtering of any one-dimensional stationary stochastic process by using the stationary Kalman filter. In the method, the rational spectral approximation of known un-rational power spectrum is firstly performed, and the rational spectrum is decomposed by multiplication spectrum to obtain the corresponding ARMA model. Then, the ARMA model is transformed into an extended Markov state-space model Recursive Filtering Using Recurring Kalman Filter Recursion Formulas. The simulation results are given in the paper, and compared with the results given by the Wiener filter method. The numerical results show that the two methods are completely consistent.