Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

Cai X.; Ding Y. S.; Li S. Y.

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Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

机译：Riccati方程的收敛性质及其在状态估计稳定性分析中的应用。

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Since the recursive nature of Kalman filtering always results in a growing size of the optimization problem, state estimation is usually realized by use of finite-memory, receding horizon, sliding window, or "frozen" techniques, which causes difficulties on stability analysis. This paper proposes a novel method on selection of an initial covariance matrix and a horizon for the Kalman filter to make sure that a sequence of the closed-loop Kalman filters are stable as time-invariant filters at subsequent time instant. Convergent properties of Riccati Difference Equation (RDE) are first exploited. Based on these properties, sufficient conditions for stability of a sequence of Kalman filters are obtained. Compared with the existent literature, the convergent properties and the stability conditions are less conservative since they provide analytic results and are applicable to more common cases where the RDEs are not monotonic.

机译：由于卡尔曼滤波的递归性质总是导致优化问题的规模不断扩大，因此状态估计通常是通过使用有限内存，后退地平线，滑动窗口或“冻结”技术来实现的，这给稳定性分析带来了困难。本文提出了一种新的选择卡尔曼滤波器初始协方差矩阵和视界的方法，以确保闭环卡尔曼滤波器序列在随后的时刻稳定为时不变滤波器。首先利用Riccati差分方程（RDE）的收敛性质。基于这些性质，获得了一系列卡尔曼滤波器的稳定性的充分条件。与现有文献相比，收敛性质和稳定性条件较不保守，因为它们提供了分析结果，并且适用于RDE不是单调的更常见情况。

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《Mathematical Problems in Engineering》 |2017年第6期|2367042.1-2367042.7|共7页
作者
Cai X.; Ding Y. S.; Li S. Y.;
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Donghua Univ, Coll Informat Sci & Technol, Engn Res Ctr Digitized Text & Apparel Technol, Minist Educ, Shanghai 201620, Peoples R China;

Donghua Univ, Coll Informat Sci & Technol, Engn Res Ctr Digitized Text & Apparel Technol, Minist Educ, Shanghai 201620, Peoples R China;

Shanghai Jiao Tong Univ, Dept Automat, Shanghai 200240, Peoples R China|Minist Educ, Key Lab Syst Control & Informat Proc, Shanghai 200240, Peoples R China;

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Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

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