双线性状态空间系统的状态观测器设计

State observers for bilinear state-space systems

针对受过程噪声和量测噪声干扰的双线性状态空间系统,研究其状态估计算法.借助双线性系统的特殊结构,将其等价表示为线性时变模型,推导基于Kalman滤波的状态估计算法.针对线性时变模型中存在的未知变量,基于辅助模型辨识思想,通过构造一个辅助模型,将未知变量用该模型的输出代替,提出基于辅助模型的双线性系统状态估计算法.构造双线性状态观测器,引入delta算子极小化状态估计误差协方差矩阵,从而得到最优状态估计增益,并提出基于delta算子的双线性系统状态估计算法.所提出的算法能够避免线性化过程带来的估计精度差的问题,提高双线性系统的状态估计精度.通过仿真实验验证了所提出算法的有效性,并对比分析了不同噪声情况下所提出算法的估计效果.

This paper studies state estimation algorithms for a bilinear state-space system disturbed by process noise and measurement noise.Because of the special structure of bilinear systems,this paper transforms the considered system into its equivalent linear parameter-varying model and presents the Kalman filter based state estimation algorithm.For the unknown term existing in the linear parameter varying model,we construct an auxiliary model and use its output to take the place of the unknown term,and present the auxiliary model-based state estimation algorithm.Finally,this paper constructs a bilinear state observer and computes the optimal state estimation gain by introducin g the delta operator to minimize the covariance matrix of the state estimation error,and derives the delta operator-based state estimation algorithm.The proposed algorithms avoid the poor estimation accuracy caused by the linearization model and improve the state estimation accuracy of bilinear systems.The simulation results show the effectiveness of the proposed algorithms and the state estimation accuracy under different noise conditions.