Fast Sparse RLS Algorithms

We present a new, doubly fast algorithm for recursive least-squares (RLS) adaptive filtering that uses displacement structure and subsampled-updating. The fast subsampled-updating stabilized fast transversal filter (FSU SFTF) algorithm is mathematically equivalent to the classical fast transversal filter (FTF) algorithm. The FTF algorithm exploits the shift invariance that is present in the RLS adaptation of an FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson (1947) algorithm. In the subsampled-updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur-type algorithm that, once properly initialized, does not require inner products. The various convolutions that appear In the algorithm are done using the fast Fourier transform (FFT). The resulting algorithm is doubly fast since it exploits FTF and FFTs. The roundoff error propagation in the FSU SFTF algorithm is identical to that in the SFTF algorithm: a numerically stabilized version of the classical FTF algorithm. The roundoff error generation, on the other hand, seems somewhat smaller. For relatively long filters, the computational complexity of the new algorithm is smaller than that of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation.

Sparse adaptive filtering algorithms are utilized to exploit potential sparse structure information as well as to mitigate noises in many unknown sparse systems. Sparse recursive least square (RLS) algorithms have been attracted intensely attentions due to their low-complexity and easy- implementation. Basically, these algorithms are constructed by standard RLS algorithm and sparse penalty functions (e.g., l_1-norm). However, existing sparse RLS algorithms do not exploit the sparsity efficiently. In this paper, an improved adaptive filtering algorithm is proposed by incorporating a novel correntropy induced metric (CIM) constraint into RLS, which is termed as RLS- CIM algorithm. Specifically, we adopt a well-known Gaussian kernel in CIM and further devise a novel variable kernel width to control the sparse penalty in different transient-error scenarios. Numerical simulation results are given to corroborate the proposed algorithm via mean square deviation (MSD).

Envelope tracking has many important applications in electrical distribution systems for either flicker meters or flicker compensators. This paper presents a novel control technique for flicker mitigation. This technique is based on the instantaneous tracking of the measured voltage envelope. The ADAptive LINEar neuron (ADALINE) algorithm, and the Recursive Least Square (RLS) algorithm are introduced for the flicker envelope tracking. The ADALINE algorithm is characterized by a light computational demand, unlike that of existing techniques; the RLS algorithm outperforms the ADALINE algorithm by its fast convergence and robust tracking performance. Both the ADALINE and the RLS algorithms give accurate results even under rapid dynamic changes. The paper investigates the effects of different parameters on the performance of the ADALINE algorithm and that of the RLS algorithm. Extensive simulations of the proposed flicker tracking algorithms are conducted to evaluate their performance for the tracking and mitigation of voltage flicker. The ADALINE and the RLS algorithms are examined by tracking and mitigating the flicker produced by a resistance welder and an arc furnace in a simple distribution system simulated in the PSCAD/EMTDC package.

A fast transversal filtering algorithm for pole-zero modeling

Two continuous-time recursive least-squares (RLS) algorithms are derived in this work in a unified approach, one for the Gramm-Schmidt orthogonalization (GSO) of multiple signals and the other for the lattice filter with time-shifted data. The GSO algorithm is derived in the continuous-time domain directly in the sense of the exact minimization of integral-squared-error. Then, the lattice algorithm can be obtained by applying the developed GSO to the updates of the forward and backward predictions of time-shifted data. The two algorithms are highly modular and use the same kind of module. Unlike the discrete-time RLS algorithms, no extra parameters are required to link the modules, and each module performs independently a standard order-one continuous-time RLS weight update using its present local information of the inputs and the feedback of the output. >

A new adaptive algorithm is proposed by introducing some modifications to the recursive least squares (RLS) algorithm. Except for the noise variance, the proposed algorithm does not require any statistics or knowledge of the desired signal, thus, it is suitable for adaptive filtering for channel estimation in code division multiple access (CDMA) systems in cases where the standard RLS approach cannot be used. A theoretical analysis demonstrates the convergence of the proposed algorithm, and simulation results for CDMA channel estimation show that the proposed algorithm outperforms existing channel estimation schemes.

Recursive least squares (RLS)-based algorithms are a class of fast online training algorithms for feedforward multilayered neural networks (FMNNs). Though the standard RLS algorithm has an implicit weight decay term in its energy function, the weight decay effect decreases linearly as the number of learning epochs increases, thus rendering a diminishing weight decay effect as training progresses. In this paper, we derive two modified RLS algorithms to tackle this problem. In the first algorithm, namely, the true weight decay RLS (TWDRLS) algorithm, we consider a modified energy function whereby the weight decay effect remains constant, irrespective of the number of learning epochs. The second version, the input perturbation RLS (IPRLS) algorithm, is derived by requiring robustness in its prediction performance to input perturbations. Simulation results show that both algorithms improve the generalization capability of the trained network.

The problem of pole-zero cancellation in transfer function identification and application to adaptive stabilization

In this thesis, four methods specifically designed for sparse systems estimation are originally developed and presented, which were called here: Relaxations method, Successive Expansions method, l 1 -norm Minimization method and Automatic Adjustment of the Regularization Factor method. The four proposed methods are based on the Least Squares (LS) Estimation method and incorporate techniques related to convex optimization and to the theory of compressive sensing. The simulation results show that the proposed methods herein present superior performance than the ordinary LS estimation method and the Recursive Least Squares (RLS) with convex regularization method (l 1 -RLS), in many cases achieving the same optimal performance presented by the LS Oracle method. Furthermore, the proposed methods demand lower computational cost than the l 1 -RLS method.

This paper proposes a novel algorithm, called an order extended FTF (fast transversal filter) algorithm, which is suitable for adaptive arrays based on spatial and temporal signal processing such as decision feedback adaptive arrays. The proposed algorithm can be implemented with hardware whose complexity is proportional to the filter tap length, while the RLS (recursive least squares) algorithm requires hardware in proportion to the filter tap length. In spite of its low hardware complexity, the order extended FTF algorithm has an initial acquisition performance as fast as the RLS algorithm.

Lithium-ion power battery is the power source of many electronic control systems. The battery state of charge (SOC) and state of health (SOH) are very important to the safety and reliability of the electronic system. Therefore, high-precision estimation of battery SOC and SOH has become one of the current research hotspots in the battery field. In order to realize the state estimation of lithium-ion power battery, an equivalent circuit model of lithium-ion power battery is established. This article is based on the HPPC pulse experiment data and the second-order Thevenin equivalent circuit model. At different temperatures (0°C, 25°C, 45°C), the recursive least square (RLS) method is used to identify of parameters of the equivalent model circuit. The state equation and measurement equation of the double extended Kalman filter (DEKF) algorithm are used to estimate SOC and SOH. Finally, this article uses experimental data of the single cell to estimate the battery state. The accuracy and adaptability of the combination of least squares algorithm and dual extended Kalman filter are verified. This is of great significance for improving the safety, reliability and economic benefits of the battery system.

High-rate underwater acoustic (UWA) channels often demonstrate long, time-varying and sparse impulse responses. Classical and most used adaptive algorithms such as the recursive least-squares (RLS) algorithm and the normalized least-mean-square (NLMS) algorithm do not take sparseness into account when they try to match the channel. Thus, performance improvement of these algorithms is possible. Sparse adaptive algorithms developed for acoustic echo cancellation, such as the improved proportionate normalized least-mean-square (IPNLMS) algorithm and the improved proportionate affine projection algorithm (IPAPA), have shown better performance than the NLMS algorithm without any essential cost in computational complexity. In this work, we apply IPNLMS, IPAPA, RLS and NLMS in both channel estimation and decision feedback equalization (DFE) of a short-range, shallow water acoustic link. Our results confirm the superior performance of the sparse algorithms (IPAPA being the best) when the channel becomes sparse. In addition, it is shown that both IPAPA and IPNLMS have robust performance (similar to RLS) when the channel is non-sparse.

Digital‐domain self‐interference cancellation (SIC) technology effectively mitigates self‐interference by reconstructing the SI signal. Due to the high computational complexity of the traditional recursive least squares (RLS) algorithm in SIC, its real‐time engineering application capability is limited. To overcome this limitation, this paper proposes the application of the DCD‐RLS algorithm to SIC. The proposed method transforms the standard normal equations of the RLS algorithm into auxiliary normal equations and incorporates a bisection search strategy, thereby significantly reducing the computational complexity while maintaining optimal convergence performance. Simulation results demonstrate that the proposed algorithm not only achieves a significant reduction in computational complexity but also retains SIC performance, thus enhancing the implementation value of in‐band full‐duplex (IBFD) communication systems.We propose an RLS‐SIC algorithm based on dichotomous coordinate descent (DCD), that converts the RLS normal equations into auxiliary equations and uses a bisection search to greatly reduce computational complexity while preserving optimal convergence. Simulations show, the method maintains self‐interference cancellation performance with much lower complexity, improving the real‐time feasibility of in‐band full‐duplex communication systems.

Speech enhancement is a vital area of research, the performance of speech based human machine applications such as automatic speech recognition system, in car communication depends on the quality of speech communicated. Different methodologies have been used by various researchers to improve the quality of speech signal. In this paper an attempt is made to analyze the performance of Least Mean Square (LMS) and Recursive Least Squared (RLS) adaptive filter algorithm for speech enhancement application. The performance indices used for the evaluations is Mean Square Error (MSE), Signal to Noise Ration (SNR) and execution time. The detail analysis is done and experimentally the results are validated and certain modifications are suggested in the algorithm. The experimentation revels that LMS have fast convergence than RLS. The computational complexity of RLS is very high as compared to LMS.

In this paper an ell _1-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed ell _1-RTLS algorithm is an RLS like iteration using the ell _1 regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed ell _1-regularized RTLS for the sparse system identification setting.