不确定模型参数和噪声方差多传感器广义系统鲁棒估计算法

The state estimation for descriptor system has received great attention in recent years, due to the existence in the electrical network, economic systems, aerospace and other fields. In the past, when the state estimators of descriptor system were designed, it was always assumed that model parameters and noise variances of the system were precisely known. However, due to various uncertain factors in the external environment, it is very difficult to estimate the descriptor system in the theoretical analysis and engineering practice. Robust estimation has received extensive attention due to the advantages in dealing with uncertainty, and it has been successfully applied in some engineering fields. In this project, robust fused estimation algorithm is presented for multisensor descriptor system with uncertain noise variances and model parameters. Using minimax robust estimation principle and the weighted least squares method, based on the worst-case conservative system with the conservative upper bounds of noise variances, the local and five weighted fused robust time-varying and steady-state Kalman estimators are designed, which include robust centralized fusers, weighted measurement fusers and three weighted state fusers. The robustness is proved by the Lyapunov equation approach. The accuracy relations are given. The convergence in a realization between the time-varying and steady-state robust estimators is proved by the dynamic error system analysis and the dynamic variance error system analysis method. A large number of simulation examples show the effectiveness and correctness of the proposed results.

广义系统状态估计在电网络、经济系统和航空航天等领域广泛存在，近年来受到极大关注。以往设计广义系统状态估值器时，系统的模型参数和噪声方差精确已知。由于外界环境的各种不确定性因素，广义系统估计在理论分析和工程实际中存在很大困难。鲁棒估计由于在处理不确定性方面的优点受到广泛重视，并且在一些工程领域获得了成功应用。本项目针对不确定模型参数和噪声方差的多传感器广义系统，提出鲁棒融合估计算法。应用极大极小鲁棒估计原理和加权最小二乘法，基于带噪声方差保守上界的最坏情形保守系统，设计了局部和五种加权融合鲁棒时变和稳态Kalman估值器，包括鲁棒集中式融合器、加权观测融合器和三种加权状态融合器。基于Lyapunov方程方法证明鲁棒性，给出估值器之间的精度关系。应用动态误差系统分析和动态方差误差系统分析方法证明时变和稳态鲁棒估值器之间的按实现收敛性。大量仿真例子验证算法的正确性。

广义系统在机器人、电网络、经济系统、航空航天等领域有着广泛应用背景，因其描述的实际问题比正常系统更加广泛，已日益引起国内外学者的广泛关注。目前广义系统状态估计取得了很多研究成果。而以往设计广义系统状态估值器时，系统的模型参数和噪声方差要求精确已知。由于外界环境的各种不确定性因素，广义系统估计在理论分析和工程实际中存在很大困难。鲁棒估计由于在处理不确定性方面的优点受到广泛重视，并且在一些工程领域获得了成功应用。. 本项目分别针对：带丢包、乘性噪声和输入和观测白噪声线性相关、丢失观测以及观测有色噪声等不确定模型参数和噪声方差的多传感器广义系统，提出鲁棒局部和融合估计算法。利用矩阵的非奇异线性变换，通过增广状态方法和虚拟噪声技术等方法，将原系统转化为两个仅带有不确定噪声方差的降阶非广义子系统。根据极大极小鲁棒估计原理，基于带噪声方差保守上界的最坏情形子系统，得到子系统的鲁棒时变Kalman预报器。根据降阶子系统和原广义系统之间的关系，给出原系统的局部、集中式和加权观测融合鲁棒时变和稳态Kalman估值器和估值误差方差阵。基于Lyapunov方程方法证明鲁棒性，并给出估值器之间的精度关系。应用动态误差系统分析和动态方差误差系统分析方法证明时变和稳态鲁棒估值器之间的按实现收敛性。大量仿真例子验证算法的正确性。. 另外，本项目针对带有混合不确定性的多传感器网络化随机系统，采用增广方法、去随机方法和虚拟噪声方法相结合的模型转换方法，将原多传感器系统转换为只具有不确定噪声方差的多传感器系统。根据极大极小鲁棒估计原理，提出鲁棒局部和融合Kalman估值器。应用增广噪声方法、非负定矩阵分解方法和Lyapunov方程方法，证明估值器的鲁棒性。