This article addresses the combined estimation issues of parameters and states for multivariable systems in the state‐space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF‐PC‐RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi‐innovation partially coupled recursive generalized extended least‐squares algorithm to enhance the parameter estimation accuracy of the KF‐PC‐RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.

中文翻译：

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存在有色噪声的多变量状态空间系统的参数和状态的组合估计

本文讨论了受噪声影响的状态空间形式的多变量系统的参数和状态的组合估计问题。利用卡尔曼滤波原理和耦合识别概念，推导了基于卡尔曼滤波的部分耦合递归广义扩展最小二乘算法（KF-PC-RGELS），以共同估计参数和状态。利用过去和当前的数据进行参数估计，我们提出了一种基于卡尔曼滤波的多创新部分耦合递归广义扩展最小二乘算法，以提高KF-PC-RGELS算法的参数估计精度。最后，提供了一个仿真示例来测试和比较所提出算法的性能。