一种多新息分数阶的辨识算法

An Identification Algorithm Based on Multi-innovation and Fractional Order

针对传统分数阶最小均方算法收敛性能较差的问题,提出了一种改进型分数阶最小均方算法。首先,利用分数阶微积分和多新息理论,从新息修正的角度提出了一种基于辅助模型多新息分数阶的最小均方算法(auxiliary model least mean square identification algorithm with multi-innovation and fractional order,AM-MFLMSI)。该算法在每次迭代时既使用当前数据,又使用了历史的数据,提高了收敛速度,同时还改善了参数估计精度。其次,分析了AM-MFLMSI的收敛性。然后,通过选取不同的分数阶和新息长度,比较分析了两者对算法性能的影响。最后,通过仿真实例,将AM-MFLMSI与其他分数阶算法作比较,进一步验证了所提算法的有效性。

An improved fractional order least mean square identification was presented to solve the poor convergence performance of traditional fractional least mean square algorithm.Firstly,using fractional calculus and multi-innovation theory,a based auxiliary model least mean square identification algorithm with multi-innovation and fractional order(AM-MFLMSI)was presented from the perspective of innovation modification.Both the current data and the historical data at each iteration were used in the proposed algorithm,the convergence velocity and precision was improved by the proposed algorithm.After that,the convergence of AM-MFLMSI was analyzed.Then,by taking different fractional order and innovation length,the influence of them on the performance of the algorithm was analyzed.Finally,compared AM-MFLMSI with other fractional order algorithms,the effectiveness of the proposed algorithm was verified by a simulation example.