"加权正交约束的ICA修正RLS算法"

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The modified Recursive Least Squares (RLS) algorithm for Independent Component Analysis (ICA) with Weighted Orthogonal Constraint is a unique approach to blind source separation in signal processing. This algorithm, developed by Jianwei E, combines the power of RLS with the constraint of weighted orthogonality to effectively separate mixed signals into their original source components. The Weighted Orthogonal Constraint ICA Modified RLS algorithm begins by estimating the mixing matrix that relates the observed mixed signals to the original source signals. This matrix is iteratively updated using the RLS algorithm with the added constraint of weighted orthogonality. This constraint ensures that the estimated sources are not only statistically independent but also orthogonal to each other, improving the accuracy of the separation process. By incorporating the weighted orthogonal constraint into the RLS algorithm, Jianwei E's method is able to achieve better separation performance compared to traditional ICA methods. The weighted orthogonality constraint helps to alleviate the permutation and scaling indeterminacies commonly encountered in ICA, resulting in more reliable and consistent source separation results. Overall, the Modified RLS Algorithm for ICA with Weighted Orthogonal Constraint is a promising approach for blind source separation in signal processing applications. Its innovative combination of RLS and weighted orthogonality constraint offers a more robust and accurate solution for separating mixed signals and extracting the underlying source components. This algorithm has the potential to improve the performance of various signal processing systems, making it a valuable contribution to the field of circuits, systems, and signal processing.

Circuits, Systems, and Signal Processing

out underlying inﬂuence factors from the crude oil price sequence, and further these

factors were utilized to predict the trend of crude oil price [11]. In communication, ICA

improved the effectiveness of communication system via the code division multiple

access (CDMA) technique [12]. In the ﬁeld of machine learning, Reza and Ma [14]

integrated ICA and PCA to implement feature extraction for classiﬁcation and so on.

With the development of the BSS techniques, many algorithms are introduced to

separate the independent components (ICs) from the observed s ignals. Comon [ 5]

analyzed the linear instantaneous mixed model of the BSS and ﬁrstly gave the concept

of the ICA. In 1995, a maximum entropy ICA algorithm based on information theory

was proposed [3]. However, this method needs to calculate the inverse of demixing

matrix, and it suffers from the poor stability. To overcome these shortcomings, adaptive

algorithms, which are called equivariant adaptive separation via independence (EASI)

[4] and natural gradient algorithm [1], respectively, were put forward almost at the same

time. On the basis of the above algorithms, a fast growing number of journal articles

were presented in the next decades. Typically, fast ﬁxed-point algorithm (FastICA)

based on maximum negentropy [9] was presented by Hyvärinen and Oja in 1997. In

the same year, a semiparametric statistical approach based on gradient learning rule

was analyzed by [2]. Later, Zhu et al. [24] generated an adaptive RLS learning rule

for BSS with pre-whitening. And the authors veriﬁed that the RLS-type algorithm

had faster convergence than LMS-type algorithm. Nevertheless, the algorithms with

pre-whitened signal lack the equivariance characteristic; Zhu et al. [25,26] proposed

another adaptive RLS learning rule for the BSS with observed signals directly. And

the results of experiments demonstrated that the new learning rule outperformed those

algorithms with pre-whitening process. Further, Ye et al. [23] ﬁrstly developed an

adaptive weighted orthogonal constrained algorithm for BSS with the natural gradient.

Tang [17] employed exponentials of sparse antisymmetric matrices to separate source

signals. Su et al. [16] proposed a class of novel underdetermined complex-valued ICA

algorithms. Zhu et al. [27] presented a novel algorithm to accomplish single-channel

source separation via the generalized period character of radar signals. Unfortunately,

they did not give the analysis of stability in convergence. Therefore, we analyze the

behavior of the RLS algorithm with weighted orthogonal constraint at the convergent

point. Further, for improving the stability, a modiﬁed RLS algorithm for ICA, a novel

criterion of separation matrix updating based on the behavior of RLS algorithm at the

convergent point, is proposed in the following sections.

Section 2 recalls ICA with weighted orthogonal constraint. To accelerate the con-

vergence speed in iteration numbers, a modiﬁed RLS algorithm for ICA with weighted

orthogonal constraint is proposed in Sect. 3. Section 4 compares the LMS-type and

RLS-type algorithms. The simulations are designed to prove the performance of the

proposed algorithm in Section 5. Conclusions are made in Sect. 6.

2 ICA with Weighted Orthogonal Constraint

The purpose of ICA is to extract the ICs from the observed signals. In general, ICA

model is established by the linear instantaneous mixture of source signals as follows

[10]:

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