As a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs, the Kitanidis filter has been designed by one-step minimization of the trace of the state estimation error covariance matrix. In this technical communiqué, it is shown that the Kitanidis filter is also optimal for the whole gain sequence in the sense of matrix positive definiteness, which notably implies that the Kitanidis filter minimizes not only the trace criterion, but also the matrix spectral norm criterion.

中文翻译：

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关于拒绝未知输入的状态估计的 Kitanidis 滤波器的最优性

作为卡尔曼滤波器对受任意未知输入影响的系统的自然扩展，Kitanidis 滤波器是通过一步最小化状态估计误差协方差矩阵的迹线来设计的。在该技术公报中，表明 Kitanidis 滤波器在矩阵正定性意义上对于整个增益序列也是最优的，这特别意味着 Kitanidis 滤波器不仅最小化了迹准则，而且最小化了矩阵谱范数准则。