State estimation for ellipsoidally constrained dynamic systems with set-membership pseudo measurements
State estimation for ellipsoidally constrained dynamic systems with set-membership pseudo measurements
复制标题
DOI：
10.1109/mfi.2015.7295824
复制
发表时间：
2015-10
期刊：
影响因子：
--
通讯作者：
B. Noack;M. Baum;U. Hanebeck
中科院分区：
文献类型：
--
作者：
B. Noack;M. Baum;U. Hanebeck
在许多动态系统中，状态的演化受到特定的约束。通常，约束不能容易地集成到卡尔曼滤波器算法的预测-校正结构中。线性等式约束是这一规则的例外，并且已经被广泛使用和研究，因为它们允许简单的封闭形式表达式。一种常见的方法是将等式约束重新表达为待估计状态的伪测量。然而，等式约束定义状态分量之间的确定性关系，这是卡尔曼滤波中的不期望的特性，因为这导致奇异协方差矩阵。第二个问题涉及识别和定义精确约束所需的知识，这些约束由系统状态满足。在本文中，引入了椭圆体约束，可用于对系统状态受约束的有界区域进行建模。这个概念构成了一个易于使用的放松等式约束。为了将椭球约束集成到卡尔曼滤波器结构中，利用了依赖于组合的随机和集成员不确定性表示的广义滤波器框架。
In many dynamic systems, the evolution of the state is subject to specific constraints. In general, constraints cannot easily be integrated into the prediction-correction structure of the Kalman filter algorithm. Linear equality constraints are an exception to this rule and have been widely used and studied as they allow for simple closed-form expressions. A common approach is to reformulate equality constraints into pseudo measurements of the state to be estimated. However, equality constraints define deterministic relationships between state components which is an undesirable property in Kalman filtering as this leads to singular covariance matrices. A second problem relates to the knowledge required to identify and define precise constraints, which are met by the system state. In this article, ellipsoidal constraints are introduced that can be employed to model a bounded region, to which the system state is constrained. This concept constitutes an easy-to-use relaxation of equality constraints. In order to integrate ellipsoidal constraints into the Kalman filter structure, a generalized filter framework is utilized that relies on a combined stochastic and set-membership uncertainty representation.