Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition
Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition
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DOI：
10.1109/jas.2021.1004362
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Kun Zhu;Chengpu Yu;Yiming Wan
中科院分区：
文献类型：
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作者：
Kun Zhu;Chengpu Yu;Yiming Wan
本文针对多输出系统提出了一种新的具有变向遗忘（VDF）的递归最小二乘（RLS）识别算法。目标是增强非持续激励下的参数估计性能。所提出的算法对信息矩阵进行倾斜投影分解，使得遗忘仅应用于接收到新信息的方向。理论证明表明，即使没有持续激励，信息矩阵仍保持下限和上限，并且估计误差方差收敛到有限范围内。此外，还进行了详细分析，与最近报道的利用特征值分解的 VDF 算法（VDF-ED）进行比较。结果表明，在非持续激励下，VDF-ED 算法中的部分遗忘子空间可以在不接收新数据的情况下折扣旧信息，这可能会产生比我们提出的算法更病态的信息矩阵。数值模拟结果证明了我们提出的算法相对于最近的 VDF-ED 算法的有效性和优势。
In this paper, a new recursive least squares (RLS) identification algorithm with variable-direction forgetting (VDF) is proposed for multi-output systems. The objective is to enhance parameter estimation performance under non-persistent excitation. The proposed algorithm performs oblique projection decomposition of the information matrix, such that forgetting is applied only to directions where new information is received. Theoretical proofs show that even without persistent excitation, the information matrix remains lower and upper bounded, and the estimation error variance converges to be within a finite bound. Moreover, detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition (VDF-ED). It is revealed that under non-persistent excitation, part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data, which could produce a more ill-conditioned information matrix than our proposed algorithm. Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.