Adaptive Filter Weights Research Articles

Direct integration bias-compensated maximum correntropy criterion algorithm independent of measurement noise samples

In system identification, if the filter input and the desired signal are both interfered by noise, traditional adaptive filtering algorithms will not work effectively. The recently presented bias-compensated normalized maximum correntropy criterion (BC-NMCC) algorithm, which was developed based on the information theory learning (ITL) and Taylor expansion, can deal with this case. However, it needs to use measurement noise samples to update the adaptive filter weight vector, whose values are usually unavailable. To solve this problem, we propose a direct integration bias-compensated maximum correntropy criterion (DI-BC-MCC) algorithm under an unbiasedness criterion (UC). Specifically, we utilize a direct integral approach to calculate the expected values instead of using Taylor expansion. With this idea, the update equation of DI-BC-MCC does not involve measurement noise samples, unlike BC-NMCC. The derived compensation term can reduce the impact of input noise significantly, and DI-BC-MCC can perform well in impulsive noise environments. In addition, the steady-state performance of DI-BC-MCC is analyzed under some frequently used assumptions. Finally, simulations are provided to demonstrate the good performance of DI-BC-MCC and to verify the accuracy of the theoretical analysis.

Equalizer of Amplitude-Frequency Response of Acoustic Channels and its Adaptive Filter Based on Recursive Least Squares Algorithm with Diagonalized Correlation Matrix

The paper presents an equalizer of the amplitude-frequency response of the acoustic wave propagation channels in the rooms. The considered equalizer uses the so-called modified architecture based on the adaptive filter with the input signal filtering, which weights are calculated using the Recursive Least Squares (RLS) algorithm. The equalizer of the acoustic channels amplitude-frequency response usually requires the usage of the adaptive filters with the large number of weighs that means the large computational complexity of the adaptive filter. The adaptive filters based on the fast RLS algorithms are efficient in the terms of their complexity but often unstable if the number of adaptive filter weights is large. Therefore, the algorithms are poorly suited for usage in the amplitude-frequency response equalizers of the acoustic channels. Adaptive filters based on the RLS algorithm, which use the Matrix Inversion Lemma (MIL), are stable, but computationally complex. The equalizer presented in this paper uses a simplified adaptive filter based on the MIL RLS algorithm with a diagonalized correlation matrix of the filter input signal. In addition, in the filter, each of the square submatrices on the simplified correlation matrix diagonal is inverted using a computationally efficient version of the MIL that takes into account the symmetrical structure of the mentioned submatrices relatively their main diagonals. Computer simulation confirms the performance of the proposed equalizer and demonstrates its efficiency comparing to the unsimplified equalizer. The demo includes the graphs of the equalizer steady-state amplitude-frequency response, the acoustic channel amplitude-frequency responses before and after the equalization, and the power spectral density plots of the equalizer input signal and the signals passed through the equalizer and the acoustic medium. The equalizer can be used in the equipment for the high-quality voice and music reproduction in the conditions of the limited computing resources for the implementation of the equalizer.

Fast Heterogeneous Clutter Suppression Method Based on Improved Sparse Bayesian Learning

In order to deal with the problem space-time adaptive processing (STAP) performance degradation of an airborne phased array system caused by the serious shortage of independent and identical distributed (IID) training samples in the nonhomogeneous clutter environment, an improved direct data domain method based on sparse Bayesian learning is proposed in this paper, which only uses a single snapshot data of a cell under test (CUT) to suppress the clutter and has fast computational speed. Firstly, three hyper-parameters required to obtain the sparse solution are derived. Secondly, the comparative analysis of their iterative formulas is made, and the piecewise iteration of hyper-parameter that has an obvious influence on the computational complexity of obtaining sparse solution is presented. Lastly, with the approximate prior information of the target, the clutter sparse solution is given and its covariance matrix is effectively estimated to calculate the adaptive filter weight and realize the clutter suppression. Simulation results verify that the proposal can dramatically decrease the computational burden while keeping the superior heterogeneous clutter suppression performance.

Sparsity-Promoting Affine Projection Algorithm With Periodically-Updated Gain Matrix and Its Performance Analysis

Sparse system identification is often encountered in applications such as network and acoustic echo cancellation. This work applies the sparsity promoting method to the affine projection algorithm (APA) to develop a sparsity-promoting APA (SAPA). To reduce its computational complexity, the gain matrix of SAPA is periodically updated, which leads to a periodically updated gain matrix based SAPA (PSAPA). In addition, the steady-state and tracking performance of PSAPA is analyzed using an improved weighted energy conservation method, which takes account of the correlation between the adaptive filter weight vector and the noise vector. The results of performance analysis are also suited to other proportionate APAs (PAPAs). Simulation results verify the advantages of the proposed algorithms and show that the theoretical expressions on the steady-state and tracking performance can predict the stochastic behaviors well.

Removal of multiple artifacts from ECG signal using cascaded multistage adaptive noise cancellers

Although cascaded multistage adaptive noise cancellers have been employed before by researchers for multiple artifact removal from the ElectroCardioGram (ECG) signal, they all used the same adaptive algorithm in all the cascaded multi-stages for adjusting the adaptive filter weights. In this paper, we propose a cascaded 4-stage adaptive noise canceller for the removal of four artifacts present in the ECG signal, viz. baseline wander, motion artifacts, muscle artifacts, and 60 Hz Power Line Interference (PLI). We have investigated the performance of eight adaptive algorithms, viz. Least Mean Square (LMS), Least Mean Fourth (LMF), Least Mean Mixed-Norm (LMMN), Sign Regressor Least Mean Square (SRLMS), Sign Error Least Mean Square (SELMS), Sign-Sign Least Mean Square (SSLMS), Sign Regressor Least Mean Fourth (SRLMF), and Sign Regressor Least Mean Mixed-Norm (SRLMMN) in terms of Signal-to-Noise Ratio (SNR) improvement for removing the aforementioned four artifacts from the ECG signal. We employed the LMMN, LMF, LMMN, LMF algorithms in the proposed cascaded 4-stage adaptive noise canceller to remove the respective ECG artifacts as mentioned above. We succeeded in achieving an SNR improvement of 12.7319 dBs. The proposed cascaded 4-stage adaptive noise canceller employing the LMMN, LMF, LMMN, LMF algorithms outperforms those that employ the same algorithm in the four stages. One unique and powerful feature of our proposed cascaded 4-stage adaptive noise canceller is that it employs only those adaptive algorithms in the four stages, which are shown to be effective in removing the respective ECG artifacts as mentioned above. Such a scheme has not been investigated before in the literature.

Block-sparse sign algorithm and its performance analysis

System identification is often encountered in applications such as echo cancellation, active noise control, and channel equalization. If the unknown system is sparse, using sparsity-induced methods can improve the convergence performance. Recently, the l2,0-norm constraint was used to derive a block-sparse LMS (BS-LMS) algorithm to accelerate convergence for identifying multi-clustering sparse systems. In some cases, output of the unknown system is contaminated by impulsive noise, and BS-LMS performs poorly or even diverges when identifying such systems. To address this problem, this paper constructs a loss function by combining the absolute error and the l2,0-norm of adaptive filter weight vector, and then uses the subgradient descent method to develop a block-sparse sign algorithm (BS-SA). Its mean and mean-square performance is also analyzed based on the Gaussian-Bernoulli impulsive noise model under some frequently used assumptions. Finally, simulations are performed to test the robustness of BS-SA against impulsive noise and to evaluate the accuracy of theoretical expressions derived for statistical performance.

Cluster-sparsity-induced affine projection algorithm and its variable step-size version

The affine projection algorithm (APA) is widely used in various applications of adaptive filtering due to its decorrelating property. However, when the unknown system to be estimated is a cluster-sparse one, the APA cannot make full use of its cluster-sparsity characteristic to accelerate convergence rate. In this paper we propose a cluster-sparsity-induced APA (CSI-APA) to promote the performance of the adaptive filter for estimating cluster-sparse systems. When the number of elements in each cluster of the adaptive filter weights is set to one, the CSI-APA reduces to a sparsity-induced APA (SI-APA). Like other fixed step-size adaptive filtering algorithms, the proposed CSI-APA needs to make a trade-off between convergence rate and steady-state misalignment. To address this problem, the step-size of the CSI-APA is optimized by minimizing the mean-square deviation (MSD) at each iteration and a variable step-size CSI-APA (VSS-CSI-APA) is developed. Simulation results are provided to show the superior performance of the proposed algorithms.

Dynamic High-Pass Filtering and Multi-Spectral Attention for Image Super-Resolution.

Deep convolutional neural networks (CNNs) have pushed forward the frontier of super-resolution (SR) research. However, current CNN models exhibit a major flaw: they are biased towards learning low-frequency signals. This bias becomes more problematic for the image SR task which targets reconstructing all fine details and image textures. To tackle this challenge, we propose to improve the learning of high-frequency features both locally and globally and introduce two novel architectural units to existing SR models. Specifically, we propose a dynamic highpass filtering (HPF) module that locally applies adaptive filter weights for each spatial location and channel group to preserve high-frequency signals. We also propose a matrix multi-spectral channel attention (MMCA) module that predicts the attention map of features decomposed in the frequency domain. This module operates in a global context to adaptively recalibrate feature responses at different frequencies. Extensive qualitative and quantitative results demonstrate that our proposed modules achieve better accuracy and visual improvements against state-of-the-art methods on several benchmark datasets.

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Robust Detection Method of Arrival Time Difference Under Minimum Maximum Entropy Criterion

Accurate measurement of arrival time difference is one of the key technologies in many areas, such as the global positioning system. Due to the effects of environmental noises around receiver, the classic methods under least mean-square error rule are the lack of robustness. In this paper, a robust method of the time difference detection is addressed based on the minimum maximum entropy, referred to MMEATD. The maximum entropy function used in this method is a smooth approximation of the L1 norm. It has robustness to large outliers, but also is differentiable. Under the minimum maximum entropy criterion, the adaptive filter weight vector will be convergence, and its peak position indicates the arrival time difference. The computer simulation experiments show the estimation performance of this algorithm under different signal and noise ratio or different impulsive noise intension. Meanwhile, its estimation performance is compared with minimum mean square error algorithm. Results show that the proposed method has a good robustness under the impulsive noise environment.

Catching the high altitude invisible by satellite-based forward scatter PCL

This paper presents a feasibility study on using satellite signal for passive radar application. Our focus is on utilizing geostationary Earth orbit satellite signal with suitable properties, like Inmarsat. Then, a new method of detection for passive coherent location using adaptive filter weights variation model is presented. To evaluate the performance, three different scenarios including a low Earth orbit satellite, a space shuttle, and a high-altitude aircraft as the targets of interest are considered. In addition to being covert, it will be shown that using such passive radar system, we can benefit the forward scatter enhancement, which enables us to detect such high-altitude targets that are normally invisible to radar systems. At last, the performance of the proposed method is compared with that of traditional methods. The analysis reveals that the proposed method has higher detection performance compared to the traditional detection methods in passive radars.

Selective Normalized Subband Adaptive Filter With Subband Extension

We present a novel subband adaptive filtering (SAF) algorithm that selects a subset of subbands and uses them to update the adaptive filter weight. The normalized SAF (NSAF) algorithm has a tradeoff between the number of subbands and the convergence speed. As the number of subbands increases, the convergence speed gets faster. However, employing an increased number of subbands raises the computational complexity. To improve the convergence speed, we first extend the number of subbands and then develop a selective scheme exploiting an efficient subset of the extended subbands so as to remove redundancy in the computational complexity. We show that subbands with a larger ratio of the corresponding squared error to an input power should be selected to achieve a similar performance to that of the extended subband adaptive filter. Experimental results show that the proposed NSAF algorithm has better convergence performance compared with the conventional NSAF algorithm.

REDUCTION OF POWER LINE INTERFERENCES FROM ELECTROCARDIOGRAPHIC SIGNALS BY APPLYING ADAPTIVE FILTERING ON FIELD PROGRAMMABLE GATE ARRAY CIRCUITS

The paper presents an extended implementation of an adaptive filter structure for electrocardiographic (ECG) signals denoising which is implemented on Field Programmable Gate Array (FPGA) circuit. The proposed FPGA adaptive filter structure can be used to clean in real-time the ECG signals from power line interferences. In order to update the adaptive filter weights, the Least Mean Square (LMS) algorithm is used. The discrete forms of the filter structure and adaptive algorithm are presented and argued. The adaptive filter structure and the LMS algorithm were developed on the DE2 platform (Development and Education Board, version 2) which includes an Altera Cyclone II FPGA circuit. The obtained experimental results concludes that the FPGA implementation, designed to process the ECG signals in real-time, presents good performances in suppressing the power line interfering signals.

A Denoising Method Based on the Variable Step NLMP for the Pulsar Signal

In order to denoise the pulsar signal, a variable step NLMP algorithm was introduced under the-stable distribution. The algorithm introduced a step update factor. By adjusting parameters and error information, the algorithm can adjust the incremental direction of the adaptive filter weight vector accurately, and improve the convergence performance. Simulation results show that the variable step-size NLMP algorithm is better than the NLMP algorithm in the denoising effect in-stable distribution noise environments.

A Denoising Method Based on the Variable Step NLMP for the Pulsar Signal

In order to denoise the pulsar signal, a variable step NLMP algorithm was introduced under the-stable distribution. The algorithm introduced a step update factor. By adjusting parameters and error information, the algorithm can adjust the incremental direction of the adaptive filter weight vector accurately, and improve the convergence performance. Simulation results show that the variable step-size NLMP algorithm is better than the NLMP algorithm in the denoising effect in-stable distribution noise environments.

A Novel Method to Measure Array Manifolds of GNSS Adaptive Antennas

: We present a procedure for measuring the complete, in situ array manifold of a STAP-based adaptive antenna using only standard GNSS receiver measurements. Note that one needs in situ array manifolds in adaptive spatial processing as well as for estimation of the antenna induced biases in GNSS measurements. The proposed procedure is a straightforward extension of traditional outdoor GPS antenna calibration methods. The adaptive filter weights in the antenna electronics are carefully varied, and their effect on the GNSS receiver measurements are recorded. Using a system of equations derived in this paper, these receiver measurements are used to solve for the frequency response of each antenna element in each satellite direction. The accuracy of the proposed procedure is established using computer simulations. We also show that the measured array manifolds provide a very good estimate of the antenna induced biases in GNSS receiver measurements in the presence of interferers.

Active noise control with on-line estimation of non-Gaussian noise characteristics

Active noise control (ANC) is a methodology for attenuating noise based on adaptive signal processing algorithms. ANC is well assessed for the attenuation of Gaussian noise, but the rejection of non-Gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence. To overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise. This can be done either by modeling the impulsive noise with a non-Gaussian distribution such as the Symmetric α -stable ( S α S ) distribution or by applying an outlier detection method. With both approaches the accuracy in the noise description appears to be crucial for effective noise reduction. This paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time-varying noise distributions. The first one is based on the on-line estimation of an S α S model of the noise probabilistic description. The second relies on a simple on-line recursive procedure that reliably estimates amplitude thresholds for outlier detection. Both methods compare favorably with competitor approaches, while maintaining a sufficiently low algorithm complexity. Several examples are shown to demonstrate the algorithms' effectiveness.

An Innovations-Based Noise Cancelling Technique on Inverse Kepstrum Whitening Filter and Adaptive FIR Filter in Beamforming Structure

This paper presents an acoustic noise cancelling technique using an inverse kepstrum system as an innovations-based whitening application for an adaptive finite impulse response (FIR) filter in beamforming structure. The inverse kepstrum method uses an innovations-whitened form from one acoustic path transfer function between a reference microphone sensor and a noise source so that the rear-end reference signal will then be a whitened sequence to a cascaded adaptive FIR filter in the beamforming structure. By using an inverse kepstrum filter as a whitening filter with the use of a delay filter, the cascaded adaptive FIR filter estimates only the numerator of the polynomial part from the ratio of overall combined transfer functions. The test results have shown that the adaptive FIR filter is more effective in beamforming structure than an adaptive noise cancelling (ANC) structure in terms of signal distortion in the desired signal and noise reduction in noise with nonminimum phase components. In addition, the inverse kepstrum method shows almost the same convergence level in estimate of noise statistics with the use of a smaller amount of adaptive FIR filter weights than the kepstrum method, hence it could provide better computational simplicity in processing. Furthermore, the rear-end inverse kepstrum method in beamforming structure has shown less signal distortion in the desired signal than the front-end kepstrum method and the front-end inverse kepstrum method in beamforming structure.

Stochastic Analysis of the Normalized Subband Adaptive Filter Algorithm

This paper studies the statistical behavior of the normalized subband adaptive filtering (NSAF) algorithm. An accurate statistical model of the NSAF algorithm is obtained. In the derivation, we focus on Gaussian correlated input signals. By assuming that the analysis filter bank is paraunitary and taking into account the full band adaptation mechanism of the NSAF, expressions for the first and the second moments of the adaptive filter weights are derived without invoking the slow adaptation assumption. In the derivations, several hyperelliptic integrals appear. To tackle those integrals induced by Gaussian correlated inputs, we first give a solution by resorting to the adaptive Lobatto quadrature. By invoking the averaging principle, two other approximation methods, the chi-square method and the partial fraction expansion method, are presented to approximate the statistical model as well. Monte Carlo (MC) simulation results corroborate our predictions. The Lobatto quadrature method achieves a good agreement with the MC simulation results, even for a relatively large step size. Compared with the chi-square method and the partial fraction expansion method, the Lobatto quadrature method gives better performance in terms of predicting the mean square error when the length of the adaptive filters is small to medium. The chi-square approximation method and the partial fraction expansion method give a satisfactory performance with a relatively low computational complexity when the filter length is large.

Mitigation of Adaptive Antenna Induced Bias Errors in GNSS Receivers

Antenna arrays equipped with adaptive filtering allow global navigation satellite system (GNSS) receivers to operate in environments with harsh, sustained interference. However since these antennas utilize spatial and temporal filters, they have the potential to introduce significant bias errors into the code and carrier phase measurements made by GNSS receivers. For precision navigation applications, these biases must be mitigated. A novel bias estimation and correction technique is described in which additional logic is added to the receiver in order to provide runtime compensation for these antenna-induced biases. The technique is general in the sense that it can be applied to a wide variety of adaptive antenna and receiver implementations. It utilizes a computationally efficient bias estimation equation that incorporates stored antenna data, the adaptive filter weights, and the receiver discriminator function. After estimating the bias, the receiver can compensate for the bias errors either in the navigation processor or in the tracking loop of the GNSS receiver. Simulations demonstrate centimeter-level bias correction accuracy for a variety of signals using an adaptive antenna array in an environment with interference.