线性系统状态估计及传感器选择方法

Linear Systems State Estimation and Sensor Selection

针对线性时不变系统状态估计及传感器选择问题进行研究,提出了线性时不变系统状态估计及传感器选择方法。首先给出了系统和观测序列的一致可探测性定义以及误差协方差矩阵收敛的条件,接着指出了一致可探测性观测序列存在条件并根据定义进行了证明,然后在一致可探测性观测序列存在的条件下提出了一种改进贪婪算法确定传感器选择方案,以此生成该一致可探测性观测序列,并分析了该算法的完全性和复杂度。仿真结果表明,当在一致可探测性观测序列存在的条件下求解传感器选择方案时,与基本的贪婪算法和长时选择方法相比,本文算法综合性能最优,求解速度和求解质量均较好。

Aiming at the state estimation of linear time invariant systems and sensor selection method,a state estimation and sensor selection method for linear time invariant systems was proposed.Firstly,the detectability of a system,the detectability of a sequence of observations and the boundedness of the error covariance were defined.Secondly,the existence conditions of a detectable sequence of observations was given and proved according to the definition of the detectability of a sequence of observations.Thirdly,a improved greedy algorithm to find out a detectable sequence of observations was put forward if there exits one.Simulations showed that when there exited detectable sequences of observations,the comprehensive performance of the algorithm in this paper outperformed the basic greedy algorithm and the non-myopic sensor selection algorithm with a fast computation speed and a good solution quality.