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Stability of the Kalman Filter for Output Error Systems *

机译：输出错误系统的卡尔曼滤波器的稳定性 *

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摘要

Optimality and numerical efficiency are well known properties of the Kalman filter, whereas its stability property, though equally classical and important in practice, is less often mentioned in the recent literature. The stability of the Kalman filter is usually ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. Such classical results cannot be applied to output error systems, in which the process noise is totally absent. It is shown in this paper that the uniform complete observability is sufficient to ensure the stability of the Kalman filter applied to time varying output error systems, regardless of the stability of the considered system itself.
机译：最优性和数值效率是卡尔曼滤波器的众所周知的特性，而其稳定性特性虽然在实践中同样经典且很重要，但在最近的文献中却很少提及。卡尔曼滤波器的稳定性通常由关于过程噪声的一致的完全可控制性和线性时变系统的一致的完全可观察性来确保。这样的经典结果不能应用于输出误差系统，在该系统中完全没有过程噪声。本文表明，统一的完全可观性足以确保应用于时变输出误差系统的卡尔曼滤波器的稳定性，而与所考虑的系统本身的稳定性无关。

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