Abstract We are interested in the optimal filter in a continuous time setting. We want to show that the optimal filter is stable with respect to its initial condition. We reduce the problem to a discrete time setting and apply truncation techniques. Due to the continuous time setting, we need a new technique to solve the problem. In the end, we show that the forgetting rate is at least a power of the time t. The results can be re-used to prove the stability in time of a numerical approximation of the optimal filter.

中文翻译：

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连续时间最优滤波器的稳定性：超越 Beneš 滤波器

摘要 我们对连续时间设置中的最优滤波器感兴趣。我们想证明最优滤波器相对于其初始条件是稳定的。我们将问题简化为离散时间设置并应用截断技术。由于连续的时间设置，我们需要一种新的技术来解决这个问题。最后，我们证明了遗忘率至少是时间 t 的幂。结果可以重复使用以证明最优滤波器的数值逼近的时间稳定性。