矩阵遗忘的递归最小二乘

Adam L. Bruce, A. Goel, D. Bernstein
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引用次数: 12

摘要

本文考虑递推最小二乘(RLS)的扩展,其中代价函数被修改为包含矩阵遗忘因子。修正代价函数的最小化为可变速率和可变方向组合遗忘(RLS-VRDF)提供了一个框架。这种RLS的扩展同时解决了标准RLS中的两个关键问题,即由于植物参数变化而需要进行可变速率遗忘,以及由于持久性损失而需要进行可变方向协方差更新。通过实例说明了RSL-VRDF在参数突变和持久性损失情况下的性能。
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Recursive Least Squares with Matrix Forgetting
This paper considers an extension of recursive least squares (RLS), where the cost function is modified to include a matrix forgetting factor. Minimization of the modified cost function provides a framework for combined variable-rate and variable-direction (RLS-VRDF) forgetting. This extension of RLS simultaneously addresses two key issues in standard RLS, namely, the need for variable-rate forgetting due to changing plant parameters as well as the need for variable-direction covariance updating due to the loss of persistency. The performance of RSL-VRDF is illustrated by an example with abrupt parameter changes and loss of persistency.
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