Abstract: To improve the speed and robustness of Recursive Least Squares (RLS) algorithm with forgetting factor in the parameter identification of ship course motion mathematical model, an RLS algorithm with dynamic forgetting factor based on fuzzy control was proposed. Firstly, the residual between the theoretical model output and actual model output was calculated. Secondly, an evaluation function was constructed on the basis of the residual, to assess the parameter identification error. Then, a fuzzy controller with evaluation function and its change rate as two inputs was adopted to realize the dynamic adjustment of the forgetting factor. Combined with designed fuzzy control rule table, the modification of the forgetting factor was obtained by the fuzzy controller at last. Simulation results show that the forgetting factor can be adjusted according to the parameter identification error in the presented algorithm, which achieves higher precision and faster parameter identification than RLS algorithm with constant forgetting factor.

Key words: dynamic forgetting factor, Recursive Least Squares (RLS) algorithm, fuzzy control, ship course model, parameter identification

摘要： 为提高遗忘因子递推最小二乘（RLS）算法辨识船舶航向运动数学模型参数的快速性和鲁棒性，在分析遗忘因子大小对算法特性影响的基础上，提出一种基于模糊控制的动态遗忘因子RLS算法。该算法从理论模型输出与实际模型输出之间的残差入手来构造评估参数辨识误差大小的评价函数，并将评价函数及其变化率作为模糊控制器的输入，利用模糊控制器结合制定的规则表进行模糊推理并计算遗忘因子的修正量，从而实现遗忘因子的动态调整。仿真结果表明，与恒定遗忘因子RLS算法的对比，该算法能够根据参数辨识误差实时调整遗忘因子的大小，使算法在模型参数平稳时有更高的辨识精度，在模型参数突变时有更快的收敛速度，验证了所提算法的优越性。

关键词: 动态遗忘因子, 递推最小二乘算法, 模糊控制, 船舶航向模型, 参数辨识