J-spectral factorization for general discrete rational matrices is considered in this paper. We propose a simple approach based on the Kalman filtering in Krein space. The main idea is to construct a stochastic state space filtering model in Krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized. The spectral factor is then easily derived by using the generalized Kalman filtering in Krein space, which is similar to the H/sub 2/ spectral factorization. Our approach unifies the treatment of the H/sub 2/ spectral factorization and the J-spectral factorization. The applications of the derived results in H/sub /spl infin// and risk-sensitive estimation for both nonsingular and singular systems are demonstrated.
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机译：本文考虑了一般离散有理矩阵的J谱分解。我们提出了一种基于Kerin空间中的Kalman滤波的简单方法。主要思想是在Kerin空间中构建随机状态空间滤波模型，以使输出的谱矩阵等于要分解的有理矩阵。然后，可以通过在Kerin空间中使用广义卡尔曼滤波轻松地得出光谱因子，这类似于H / sub 2 /光谱因子分解。我们的方法统一了H / sub 2 /频谱分解和J频谱分解的处理。证明了所得结果在H / sub / spl infin //中的应用以及对非奇异系统和奇异系统的风险敏感估计。
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