This paper develops a filtering-based iterative algorithm for the combined parameter and state estimation problems of bilinear state-space systems, taking account of the moving average noise. In order to deal with the correlated noise and unknown states in the parameter estimation, a filter is chosen to filter the input-output data disturbed by colored noise and a Kalman state observer (KSO) is designed to estimate the states by minimizing the trace of the error covariance matrix. Then, a KSO extended gradient-based iterative (KSO-EGI) algorithm and a filtering based KSO-EGI algorithm are presented to estimate the unknown states and unknown parameters jointly by the iterative estimation idea. The simulation results demonstrate the effectiveness of the proposed algorithms.

针对移动线性噪声，针对双线性状态空间系统的参数和状态估计问题，提出了一种基于滤波的迭代算法。为了处理参数估计中的相关噪声和未知状态，选择了一个滤波器来过滤有色噪声干扰的输入输出数据，并设计了卡尔曼状态观测器（KSO）通过最小化跟踪来估计状态。误差协方差矩阵。然后，提出了一种KSO扩展的基于梯度的迭代算法（KSO-EGI）和一种基于滤波的KSO-EGI算法，以迭代估计的思想联合估计未知状态和未知参数。仿真结果证明了所提算法的有效性。