Characterization of Exponential Divergence of the Kalman Filter for Time-Varying Systems
Characterization of Exponential Divergence of the Kalman Filter for Time-Varying Systems
复制标题
时变系统卡尔曼滤波器指数发散的表征
DOI：
10.1137/080717055
复制
发表时间：
2010
影响因子：
2.2
通讯作者：
Costa E
中科院分区：
文献类型：
--
作者：
Costa E
本文研究了线性时变（LTV）、可能不可测系统在不正确噪声信息下的递归卡尔曼滤波器的半稳定性。半稳定性是一个关键属性，因为它确保了实际的估计误差不会以指数方式发散。我们探讨了该滤波器的结构性质，得到了该滤波器是半稳定的一个充分必要条件。该条件不涉及限制增益，也不涉及Riccati方程的解，因为它们可能难以数值获得并且可能不存在。我们还比较了半稳定性的稳定性和稳定性w.r.t.初始误差协方差，我们表明，半稳定性在某种意义上使持久和非持久不正确的噪声模型之间没有区别，而不是稳定。在线性时不变的情况下，我们得到代数，易于测试的条件，半稳定性和稳定性，这补充的结果可检测系统的背景下。说明性的例子包括在内。
This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.