通讯约束下的线性系统状态降维与估计

摘要

本文面向状态估计,考察了通讯功率受限时线性动态系统状态的降维问题.为了满足平行信道传输数据的维数限制和通讯功率约束,采取降低状态维数的方法,通过传输信号的新息,提高传输效率,利用有限的通信资源,使得接收端的状态估计达到最优.本文采用差分脉冲编码调制系统（DPCM）,基于最小误差熵估计准则和Kalman估计算法,得出了最优的状态降维矩阵的设计方法,并且对随机系统的可估计性以及对相应确定性系统的能观性进行了分析.分析和仿真结果表明,这种设计方法在传输信号满足通讯功率限制的条件下可以使接收端的状态估计性能达到最优.%We investigate how to reduce the state dimensions when estimating the states of a linear dynamic system with channel communication power constraints.To meet the requirements on the dimension number and communication power constraints of the parallel channels,we adopt the structure of differential pulse code modulation（DPCM） to produce the innovation as the transmitted signal;and a new method of state-dimension reduction is derived under the minimum error entropy estimation（MEEE） criterion of filtering at receiver.Furthermore,the problem of state estimability of the stochastic system and the observability of the corresponding deterministic system are analyzed by using information theoretic method.Analysis and simulation results show that the estimation performance of Kalman filter is optimal under communication power constraint when this dimension reduction method is applied.