Because of the product item of the control input and the state vector, the identification of bilinear systems is difficult. This paper considers the combined parameter and state estimation problems of bilinear state‐space systems. On the basis of the observability canonical form and the model transformation, an identification model with a linear combination of the system parameters is obtained. Using the hierarchical principle, the identification model is decomposed into three submodels with fewer variables, and a three‐stage least squares‐based iterative (3S‐LSI) algorithm is presented to estimate the system parameters. Furthermore, we derive a state estimator (SE) for estimating the unknown states, and present an SE‐3S‐LSI algorithm for estimating the unknown parameters and states simultaneously. After that, the least squares‐based iterative algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can identify the bilinear system effectively but the 3S‐LSI algorithm can improve the computational efficiency. The simulation results indicate the effectiveness of the proposed algorithms.

中文翻译：

---

基于双线性状态估计器的三线性最小二乘迭代估计算法

由于控制输入和状态向量的乘积项，因此很难识别双线性系统。本文考虑了双线性状态空间系统的组合参数和状态估计问题。基于可观测性规范形式和模型转换，获得了系统参数线性组合的辨识模型。使用分层原理，将识别模型分解为变量较少的三个子模型，并提出了一种基于最小二乘的三阶段迭代（3S-LSI）算法来估计系统参数。此外，我们推导了用于估计未知状态的状态估计器（SE），并提出了一种SE-3S-LSI算法，用于同时估计未知参数和状态。之后，提出了基于最小二乘的迭代算法作为比较。通过分析估计结果和计算量，这两种算法可以有效地识别双线性系统，但是3S-LSI算法可以提高计算效率。仿真结果表明了所提算法的有效性。