The Generalized HR $q$ -Derivative and Its Application to Quaternion Least Mean Square Algorithm
IEEE Signal Processing Letters(2022)
摘要
Quaternion adaptive filters have been widely used in processing three-dimensional and four-dimensional signals. To improve the performance of quaternion adaptive filtering algorithms, this letter first proposes a novel derivation rule named generalized HR (GHR)
$q$
-derivative based on the concept of
$q$
-derivative and quaternion GHR derivative. Then, the product rules of GHR
$q$
-derivative are deduced, and the results of GHR
$q$
-derivative regarding some common univariate and multivariable functions are given. In addition, based on the proposed GHR
$q$
-derivative, the cost function of the quaternion least mean square (QLMS) algorithm is minimized to generate the
$q$
-QLMS algorithm. Finally, an example of Lorentz chaotic time-series prediction verifies the effectiveness of the proposed
$q$
-QLMS algorithm.
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关键词
Quaternion adaptive filters, $q$ -derivative,GHR $q$ -derivative,quaternion least mean square (QLMS), $q$ -QLMS
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