Set-membership Affine Projection Algorithm Research Articles

Elicitation of fetal ECG from abdominal recordings using Blind Source Separation techniques and Robust Set Membership Affine Projection algorithm for signal quality enhancement

Background:The utilization of non-invasive techniques for fetal cardiac health surveillance is pivotal in evaluating fetal well-being throughout the gestational period. This process requires clean and interpretable fetal Electrocardiogram (fECG) signals. Method:The proposed work is the novel framework for the elicitation of fECG signals from abdominal ECG (aECG) recordings of the pregnant mother. The comprehensive approach encompasses pre-processing of the raw ECG signal, Blind Source Separation techniques (BSS), Decomposition techniques like Empirical Mode Decomposition (EMD), and its variants like Ensemble Empirical Mode Decomposition (EEMD), and Complete Ensemble Empirical Mode Decomposition with Additive Noise (CEEMDAN). The Robust Set Membership Affine Projection (RSMAP) Algorithm is deployed for the enhancement of the obtained fECG signal. Result:The results show significant improvements in the elicited fECG signal with a maximum Signal Noise Ratio (SNR) of 31.72 dB and correlation coefficient = 0.899, Maximum Heart Rate(MHR) obtained in the range of 108–142 bpm for all the records of abdominal ECG signals. The statistical test gave a p-value of 0.21 accepting the null hypothesis. The Abdominal and Direct Fetal Electrocardiogram Database (ABDFECGDB) from PhysioNet has been used for this analysis. Conclusion:The proposed framework demonstrates a robust and effective method for the elicitation and enhancement of fECG signals from the abdominal recordings.

Set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order

Nowadays, the use of adaptive filters plays an important role in multiple signal processing applications, such as active noise control, acoustic echo cancellers, system identifiers, channel equalizer, among others. Until date, many of the existing adaptive algorithms such as affine projection algorithms offer a high convergence speed. However, its computational cost is also high. Currently, several authors make extraordinary efforts to reduce its computational cost to be used in practical applications. In this paper, we propose a new set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order (SMAP-PC-VO). Specifically, we propose two techniques to create this algorithm; 1) the new algorithm uses an error bound, which is obtained by calcuting the percentage change of the error signal, to avoid the computation of the variance of additive noise, since in existing approaches this parameter determines the error bound. In practical applications, the computation of the variance of additive noise is infeasible since this signal is not available; 2) we propose a new method to dynamically modify the projection order in the new algorithm. As a consequence, its computational cost is reduced. To demonstrate its performance, the proposed algorithm was successfully tested in different environments for system identification and active noise control for headphone applications. The simulation results demonstrate that the proposed algorithm presents good convergence properties. In addition, the proposed algorithm exhibits a low overall computational complexity.

Improved simple set‐membership affine projection algorithm for sparse system modelling: Analysis and implementation

Recently, the improved simple set-membership affine projection (IS-SM-AP) algorithm has been proposed in order to exploit sparsity in system models. Although its update equation resembles that of the set-membership affine projection (SM-AP) algorithm, the IS-SM-AP algorithm has two fundamental advantages over the SM-AP algorithm: (i) it can exploit sparsity in system models and (ii) its computational complexity is lower. Up to now, the properties of this algorithm have been addressed only through numerical simulations, and no analytical study has been presented. To fill this gap, in this study, the authors analyse the steady-state mean squared error of the IS-SM-AP algorithm using the energy conservation method. Furthermore, some important implementation issues are addressed, and a time-varying parameter for the discard function is proposed. Finally, the authors present numerical results corroborating the theoretical analysis and the effectiveness of the proposed time-varying parameter.

Data Censoring with Set-Membership Affine Projection Algorithm

In this paper, the set-membership affine projection (SM-AP) algorithm is utilized to censor non-informative data in big data applications. To this end, the probability distribution of the additive noise signal and the excess of the mean-squared error (EMSE) in steady-state are employed in order to estimate the threshold parameter of the single threshold SM-AP (ST-SM-AP) algorithm aiming at attaining the desired update rate. Furthermore, by defining an acceptable range for the error signal, the double threshold SM-AP (DT-SM-AP) algorithm is proposed to detect very large errors due to the irrelevant data such as outliers. The DT-SM-AP algorithm can censor non-informative and irrelevant data in big data applications, and it can improve the misalignment and convergence rate of the learning process with high computational efficiency. The simulation and numerical results corroborate the superiority of the proposed algorithms over traditional algorithms.

Data selection with set-membership affine projection algorithm

In this paper, the set-membership affine projection (SM-AP) algorithm is utilized to censor non-informative data in big data applications. To this end, the probability distribution of the additive noise signal and the excess of mean-squared error (EMSE) in steady-state are employed in order to estimate the threshold parameter of the single threshold SM-AP (ST-SM-AP) algorithm aiming at attaining the desired update rate. Furthermore, by defining an acceptable range for the error signal, the double threshold SM-AP (DT-SM-AP) algorithm is proposed to detect very large errors due to the irrelevant data such as outliers. The DT-SM-AP algorithm can censor non-informative and irrelevant data in big data applications, and it can improve misalignment and convergence rate of the learning process with high computational efficiency. The simulation and numerical results corroborate the superiority of the proposed algorithms over traditional algorithms.

A Fast Converging Channel Estimation Algorithm for Wireless Sensor Networks

A set-membership affine projection algorithm is proposed that can estimate a complex-valued channel matrix using a set of complex-valued pilots in the presence of additive white Gaussian noise. It is shown that the algorithm converges faster than the well-known set-membership normalized least mean square algorithm (SM-NLMS) while it resolves the high steady-state error value and the complexity issues in the regular affine projection algorithm. The fast convergence of the proposed algorithm means that a shorter training sequence inside each data block is required, which in turn improves the effective bit rate. This fast convergence is more pronounced when the pilot vectors are highly correlated. We incorporated the set-membership filtering framework into our study to reduce the computational complexity of the algorithm and preserve energy in the WSNs. Other studies have shown the superiority of the adaptive filtering algorithms, and in particular the NLMS algorithm, over other alternatives in various signal processing areas in WSNs, therefore, our proposed algorithm is a powerful substitute for a variety of algorithms. In other words, the implementation of various signal processing algorithms for different purposes can be replaced with the implementation of the proposed multipurpose algorithm. In this paper, we combine the results of our previous studies and prove the convergence of the algorithm. Furthermore, the steady-state analysis in the output mean square error is presented for two cases of pilot signals, and in the conducted simulations, the MSE performance of the algorithm is compared with the regular affine projection algorithm and the SM-NLMS algorithm.

A Variable Step-Size Shrinkage Set-Membership Affine Projection Algorithm for Noisy Input

To solve the conflicting requirement of fast convergence and low steady-state misalignment, a variable step-size shrinkage set-membership affine projection algorithm is proposed, which is efficient for the correlated input signal and noisy input environments. The new variable step size is derived by minimizing the square of noise-free a posteriori error, and the shrinkage method is employed to estimate the second-order statistics of the noise-free a priori error vector. Moreover, the stability analysis of the algorithm is conducted. Simulations demonstrate the effectiveness of the proposed algorithm for various noisy input environments.

On the robustness of set-membership adaptive filtering algorithms

In this paper, we address the robustness, in the sense of l2-stability, of the set-membership normalized least-mean-square (SM-NLMS) and the set-membership affine projection (SM-AP) algorithms. For the SM-NLMS algorithm, we demonstrate that it is robust regardless of the choice of its parameters and that the SM-NLMS enhances the parameter estimation in most of the iterations in which an update occurs, two advantages over the classical NLMS algorithm. Moreover, we also prove that if the noise bound is known, then we can set the SM-NLMS so that it never degrades the estimate. As for the SM-AP algorithm, we demonstrate that its robustness depends on a judicious choice of one of its parameters: the constraint vector (CV). We prove the existence of CVs satisfying the robustness condition, but practical choices remain unknown. We also demonstrate that both the SM-AP and SM-NLMS algorithms do not diverge, even when their parameters are selected naively, provided the additional noise is bounded. Numerical results that corroborate our analyses are presented.

New Trinion and Quaternion Set-Membership Affine Projection Algorithms

This brief introduces new data-selective adaptive filtering algorithms for trinion and quaternion spaces T and H. The work advances the set-membership trinionand quaternion-valued normalized least mean square (SMTNLMS and SMQNLMS) and the set-membership trinionand quaternion-valued affine projection (SMTAP and SMQAP) algorithms. We derive set-membership trinion algorithms and then, as special cases, obtain trinion algorithms not employing the set-membership strategy. Prediction simulations based on recorded wind data are provided, showing the improved performance of the proposed algorithms in terms of reduced computational complexity. Then, the quaternion-based SMQAP and SMQNLMS algorithms are derived, and their improved performances are verified in an adaptive beamforming problem.

Robust Set-Membership Affine Projection Algorithm with Coefficient Vector Reuse

This paper proposes a robust set-membership affine projection algorithm with coefficient vector reuse (RSM-APA-CVR) for high background noise environment. In the proposed algorithm, the sum of the squared \(L_{2}\) norms of the differences between the updated weight vector and past weight vectors is minimized and a new robust error bound is designed. Simulation results in acoustic echo cancellation context show that the proposed algorithm has faster convergence rate and smaller steady-state misalignment as compared to the conventional RSM-APA.

Optimal constraint vectors for set-membership affine projection algorithms

There is a growing interest in adaptive filtering solutions whose learning processes are data selective, bringing about computational reduction and energy savings while improving estimation accuracy. The set-membership affine projection algorithms are a representative family of algorithms including data-selection mechanisms. The update process of these algorithms depends on the choice of a constraint vector (CV) which, up to now, is based on some heuristics. In this paper we propose an optimal CV and discuss some of its inherent properties. The resulting problem falls into a convex optimization framework, allowing some unexpected features to surface; for instance, the widely used simple choice CV is asymptotically optimal for statistically white stationary inputs. Simulations indicate the optimal CV outperforms the simple choice CV regarding update rates and steady-state mean squared errors for statistically colored inputs.

L 0 norm constraint set‐membership affine projection algorithm with coefficient vector reuse

Proposed is an L 0 norm constraint set-membership affine projection algorithm with coefficient vector reuse, which is derived by minimising a differentiable cost function that utilises the L 0 norm of the updated weight vector as well as the sum of the squared Euclidean norms of the differences between the updated weight vector and past weight vectors. In addition, a power estimate method is introduced to eliminate the effect of the fluctuation of the output error on the step size. Simulations on sparse system identifications demonstrate that the proposed algorithm achieves a lower steady-state misalignment than the existing algorithms in a high background noise environment.

A Set-Membership Affine Projection Algorithm-Based Adaptive-Controlled SMES Units for Wind Farms Output Power Smoothing

This paper presents a novel adaptive control scheme of the superconducting magnetic energy storage (SMES) units with the purpose of smoothing the wind farms' output power. The adaptive control scheme is based on the set-membership affine projection algorithm (SMAPA), which provides a faster convergence and less computational complexity than the normalized least-mean-square algorithm. In this study, two grid-connected fixed-speed wind farms are considered. The control strategy of the SMES units is based on a pulse width modulation (PWM) voltage source converter (VSC) and a dc-dc converter. The VSC and dc-dc converter is used to control the reactive and active power exchange with the power system, respectively. The SMAPA-based adaptive proportional-integral (PI) controllers are utilized to control both converters. For realistic responses, real wind speed data extracted from Hokkaido Island, Japan, and two-mass drive train model of the wind turbine generator system are used in the analyses. Also, a real 10 MVA SMES unit that was installed at a power plant in Kameyama, Japan, is connected to the point of common coupling of the wind farms. The validity of the proposed control scheme is verified by the simulation results, which are performed using PSCAD/EMTDC environment. With the SMAPA-based adaptive-controlled SMES units, the wind farms' output power can be smoothed easily avoiding huge effort for fine tuning the controllers' parameters.

Modified Adaptive Line Enhancer in Variable Noise Environments using Set-Membership Adaptive Algorithm

In most speech processing systems, speech signals degrade significantly in noisy environments. Therefore, noise cancellation methods are necessary to eliminate noise from the speech signal. This paper presents a development technique to improve the performance of a noise cancellation system called Adaptive Line Enhancer (ALE) in variable noise environments. The method is based on using a modified and simplified version of the set-membership Affine Projection algorithm (AP) adaptive filter. The modification introduced here is to make the adaptive algorithm, work with a dynamically variable step-size, as a substitute for the commonly used Least Mean Square (LMS) algorithm in ALE system. The performance of the developed ALE in variable noise is illustrated here, and the results are compared to similar ALE systems based on the classical adaptive algorithms, such as the Least-Mean-Square (LMS), the Normalized LMS (NLMS) and the Affine Projection (AP) algorithms. The developed adaptive line enhancer using the simplified affine projection algorithm showed a better performance than those based on LMS, NLMS and AP.

Robust Shrinkage Affine-Projection Sign Adaptive-Filtering Algorithms for Impulsive Noise Environments

Two robust affine projection sign (RAPS) algorithms, both of which minimize the mixed norm of $l_1$ and $l_2$ of the error signal, are proposed. The direction vector of the RAPS algorithms is obtained from the gradient of an $l_1$ norm-based objective function, while two related $l_2$ norm-based minimization problems are solved to obtain the line search of the two RAPS algorithms. The $l_1$ norm-based direction vector reduces the impact of impulsive noise, whereas the $l_2$ norm-based line search produces an unbiased solution in the proposed algorithms. In addition, one of the two RAPS algorithms shares the data selective adaptation used in the set-membership (SM) affine projection (SMAP) algorithm. The proposed algorithms are shown to offer a significant improvement in the convergence speed as well as a significant reduction in the steady-state misalignment relative to the pseudo affine projection sign (PAPS) algorithm. In addition, the proposed algorithms offer robust performance with respect to impulsive noise and improved tracking of the unknown system in comparison to that provided by the PAPS and Affine projection sign (APS) algorithms. These features of the proposed algorithms are demonstrated using simulation results in system-identification and echo-cancellation applications.

Steady-State MSE Performance of the Set-Membership Affine Projection Algorithm

The set-membership affine projection (SM-AP) algorithm has many desirable characteristics such as fast convergence speed, low power consumption due to data-selective updates, and low misadjustment. The main reason hindering the widespread use of the SM-AP algorithm is the lack of analytical results related to its steady-state performance. In order to bridge this gap, this paper presents an analysis of the steady-state mean square error (MSE) of a general form of the SM-AP algorithm. The proposed analysis results in closed-form expressions for the excess MSE and misadjustment of the SM-AP algorithm, which are also applicable to many other algorithms. This work also provides guidelines for the analysis of the whole family of SM-AP algorithms. The analysis relies on the energy conservation method and has the attractive feature of not assuming a specific model for the input signal. In addition, the choice of the upper bound for the error of the SM-AP algorithm is addressed for the first time. Simulation results corroborate the accuracy of the proposed analysis.

Robust Set-Membership Affine-Projection Adaptive-Filtering Algorithm

An improved set-membership affine-projection (AP) adaptive-filtering algorithm is proposed. The new algorithm uses two error bounds that are estimated during the learning phase and by this means significantly reduced steady-state misalignment is achieved as compared to those in the conventional AP and set-membership AP algorithms while achieving similar convergence speed and re-adaptation capability. In addition, the proposed algorithm offers robust performance with respect to the error bound, projection order, impulsive-noise interference, and in tracking abrupt changes in the underlying system. These features of the proposed algorithm are demonstrated through extensive simulation results in system-identification and echo-cancellation applications.

Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm

Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadjustment and computation complexity as many existing adaptive filtering algorithms. In this work analytical results related to the SM-AP algorithm are presented for the first time, providing tools to setup its parameters as well as some interpretation to its desirable features. The analysis results in expressions for the excess mean square error (MSE) in stationary environments and the transient behavior of the learning curves. Simulation results confirm the accuracy of the analysis and the good features of the SM-AP algorithms.

Set-membership affine projection algorithm

This letter presents a new data selective adaptive filtering algorithm, the set-membership affine projection (SM-AP) algorithm. The algorithm generalizes the idea of the set-membership NLMS (SM-NLMS) algorithm to include constraint sets constructed from the past input and desired signal pairs. The resulting algorithm can be seen as a set-membership version of the affine-projection (AP) algorithm with an optimized step size. Also, the SM-AP algorithm does not trade convergence speed with misadjustment and computational complexity as most adaptive filtering algorithms. Simulations show the good performance of the algorithm, especially for colored input signals, in terms of convergence, final misadjustment, and reduced computational complexity.