Non-stationary Noise Research Articles

Sequential Fusion for Multi-rate Multi-sensor Nonlinear Dynamic Systems with Heavy-Tailed Noise and Missing Measurements

This paper focuses on sequential fusion estimation for multi-rate multi-sensor nonlinear dynamic systems with heavy-tailed noise and missing measurements. On the basis of Bayesian inference, a sequential Student’s t-based unscented Kalman filter (SSTUKF), together with its square-root form (SR-SSTUKF), is proposed by using the unscented transform to calculate Student’s t weighted integrals. Considering the nonstationary measurement noise and/or accumulated computation error, adaptive factors are introduced by the t-test to suppress uncertainties. Additionally, the complexity computation and convergence analysis of the SR-SSTUKF are presented. The validity and robustness of the proposed sequential fusion method are illustrated by an example of agile target tracking. Simulation results indicate that the SR-SSTUKF with adaptive factors can further enhance accuracy and yield reliable estimations.

On the probabilistic-statistical approach to the analysis of nonlocality parameters of plasma density

A sample of values of plasma density in a thermonuclear facility is studied. A methodology for processing experimental data that makes it possible to establish correspondence between this sample and a model of nonstationary noise is proposed. This model is formed as convolution of a stationary sequence and a memory function, and it makes it possible to simulate the competition between space and time nonlocalities. A physical interpretation of the nonlocality parameters is described.

A nonlinear filter based on GSK for relative navigation using relative orbital elements

Due to the sensitivity of the relative orbital elements model to the measurement noise, the non-stationary heavy-tailed noise(NSHT) induced by the time-varying environment during the relative navigation usually leads to filter divergence. To address this problem, a new nonlinear filter based on Gaussian-Student's-Multivariate K(GSK) mixture distribution is proposed in this paper. A Dirichlet stochastic mixture vector fusing Gaussian, Student's t, and Multivariate K distributions is introduced, thus proposing a GSK mixture distribution modeling measurement likelihood; then the Kullback-Leibler Divergence (KLD) of the true posteriori probability density function(PDF) and the approximate posteriori PDF are minimized by a variational Bayesian(VB) technique to solve for the state and parameter approximate a posteriori estimations, and finally a new nonlinear filter based on the GSK mixture distribution is derived for angles-only relative navigation in time-varying environments. Simulation outcomes indicate that the filter can realize state estimation in non-stationary states effectively with 45.16% higher estimation accuracy than the existing advanced filters.

Diffusion Augmented Complex Inverse Square Root for Adaptive Frequency Estimation over Distributed Networks

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark’s transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments.

Interacting multiple model adaptive robust Kalman filter for process and measurement modeling errors simultaneously

This paper proposes an effective Interactive Multiple Model Adaptive Robust Kalman Filter (IMMARKF) without time delay to handle situations where both process modeling errors and measurement modeling errors exist simultaneously. Building upon the robust Centered Error Entropy Kalman Filter (CEEKF) for outlier measurements and the Adaptive Kalman Filter (AKF) for process modeling errors, the IMMARKF method combines the Gaussian optimality of the KF, the adaptability of AKF, and the robustness of CEEKF using the interacting multiple model (IMM) principle to adapt reasonably to changing application environments, and can obtain estimation results in the absence of time delay. Target tracking simulations show that compared to existing methods, the proposed method can better adapt to non-stationary noise and application environments where process anomalies and measurement anomalies occur simultaneously.

Impact of Mask Type as Training Target for Speech Intelligibility and Quality in Cochlear-Implant Noise Reduction

The selection of a target when training deep neural networks for speech enhancement is an important consideration. Different masks have been shown to exhibit different performance characteristics depending on the application and the conditions. This paper presents a comprehensive comparison of several different masks for noise reduction in cochlear implants. The study incorporated three well-known masks, namely the Ideal Binary Mask (IBM), Ideal Ratio Mask (IRM) and the Fast Fourier Transform Mask (FFTM), as well as two newly proposed masks, based on existing masks, called the Quantized Mask (QM) and the Phase-Sensitive plus Ideal Ratio Mask (PSM+). These five masks are used to train networks to estimate masks for the purpose of separating speech from noisy mixtures. A vocoder was used to simulate the behavior of a cochlear implant. Short-time Objective Intelligibility (STOI) and Perceptual Evaluation of Speech Quality (PESQ) scores indicate that the two new masks proposed in this study (QM and PSM+) perform best for normal speech intelligibility and quality in the presence of stationary and non-stationary noise over a range of signal-to-noise ratios (SNRs). The Normalized Covariance Measure (NCM) and similarity scores indicate that they also perform best for speech intelligibility/gauging the similarity of vocoded speech. The Quantized Mask performs better than the Ideal Binary Mask due to its better resolution as it approximates the Wiener Gain Function. The PSM+ performs better than the three existing benchmark masks (IBM, IRM, and FFTM) as it incorporates both magnitude and phase information.

Adaptive nonlinear filtering algorithms for removal of non-stationary noise in electronystagmographic signals

Non-stationary physiological noise poses significant difficulties due to its time-varying and previously unknown characteristics. When processing electronystagmographic signals, linear filtering can distort diagnostically significant rapid changes caused by saccadic eye movements. In such cases, nonlinear filters based on robust estimators are more appropriate, whereas linear filtering effectively reduces white noise in parts of a signal with linear behaviour. Therefore, an adaptive signal processing approach that varies in nonlinearity from highly nonlinear robust estimation to linear averaging and combines their benefits appears promising. We have proposed a low-complexity adaptive method for switching filter sets and relevant filter parameter settings based on the estimated noise level and local signal behaviour. This method does not require time for filter parameter modification and does not need prior information on the signal model and noise variance. Based on this method, we have designed adaptive nonlinear filtering algorithms to exploit the advantages of both the nonlinear robust and linear averaging estimators. We have evaluated the filtering quality statistically using the minimum mean square error criteria and the maximum signal-to-noise ratio for a model signal with different levels of additive Gaussian noise. The proposed real-time adaptive filtering algorithms demonstrate a significant efficiency improvement compared to the commonly used filters. The proposed adaptive myriad algorithm achieves the highest efficiency by adjusting a sample myriad linearity parameter depending on the local estimate of a signal scale and changing the sliding window length and the coefficient affecting the linearity parameter.

Non-stationary mechanical sound source separation: An all-neural beamforming network driven by time–frequency convolution and self-attention

To tackle the challenging task of extracting target signal features amidst significant interference from complex, time-varying non-stationary noise in industrial scenarios, we propose a novel time-domain all-neural beamforming network tailored for non-stationary mechanical sound source separation, named TFANBNet. Leveraging time–frequency convolution and self-attention, TFANBNet promised robust performance in challenging acoustic environments. First, the proposed time–frequency convolution module employs parameterized complex-valued convolutional layers to simulate time–frequency transformations, thereby implicitly extracting time–frequency features. Then, the proposed adaptive attention transformer network enhances local attention interaction by integrating intermediate features, effectively enhancing long-range context modeling. Third, the beamforming module utilizes deep neural networks for beamforming weight estimation, replacing conventional noise covariance matrix computations, which have inherent performance limitations. Finally, the experimental results on the multi-channel spatial reverberation dataset synthesized from the MIMII dataset show that the proposed TFANBNet yields superior separation performance and generalization capabilities compared to the considered competitive methods.

Generalization of noise insulation afforded by common window designs with active noise control exposed to moving noise source

A window device that can provide noise insulation while maintaining natural ventilation is highly desirable and is especially sought after in heavily noise-polluted and hot-humid climates cities, such as Southeast Asian cities. However, a solution to provide such a window is non-trivial because the design principles guiding acoustics and ventilation are diametrically opposed. While louvre windows have traditionally been used in communal, healthcare, and some educational setting to provide a balance between acoustics and ventilation benefits, it is still sorely lacking to provide sufficient insertion loss without sacrificing ventilation entirely. A new plenum window design has recently garnered research and market interest to tackle the dichotomous problem. Additionally, the application of active noise control (ANC) in windows is gaining popularity and offers potential solutions to improve noise control without compromising ventilation. However, it remains unclear how different traditional and modern window designs compare in terms of their acoustic performance, especially when exposed to non-stationary noise sources such as urban traffic, a major noise pollutant. Thus, the present study seeks to provide a generalization of insertion loss provided by different window designs exposed to moving sources including a tangent study on ANC implementation via a time-domain approach.

Improved PID based Adaptive Controllers for Denoising Biomedical Signals

Biomedical signal processing is one of the most popular research domains. Very fine features in biomedical signals carry important information regarding patient’s health. So, it is necessary to have noise free biomedical signals for the correct diagnosis. The major trouble for biomedical equipment is Power Line Interference (PLI) which impairs the signals. An adaptive filter can be one of the possible solutions for the removal of non-stationary noise, but maintaining the system stability along with a high convergence rate is a critical issue. The adaptive algorithm works on the principle of minimization of error for optimized coefficients updating while PID controller attempts to minimize the error over time by adjusting the control variables. In this paper, these two different approaches are combined to get an efficient solution for adaptive PLI cancellation and two new algorithms namely PID-based Response Adjustment for Reducing Error (PID-RARE) and PID-based Coefficient Adjustment for Reducing Error (PID-CARE) are proposed. The integration of NSLMS adaptive algorithm with PID controller in the proposed algorithms are found to be an effective solution to adaptive PLI cancellation and have shown quite better performance in terms of SNRout, correlation coefficient, mean square error thereby providing more cleaner signal at lesser convergence rate.

Gravitational wave signal extraction against non-stationary instrumental noises with deep neural network

Sapce-borne gravitational wave antennas, such as LISA and LISA-like mission (Taiji and Tianqin), will offer novel perspectives for exploring our Universe while introduce new challenges, especially in data analysis. Aside from the known challenges like high parameter space dimension, superposition of large number of signals etc., gravitational wave detections in space would be more seriously affected by anomalies or non-stationarities in the science measurements. Considering the three types of foreseeable non-stationarities including data gaps, transients (glitches), and time-varying noise auto-correlations, which may come from routine maintenance or unexpected disturbances during science operations, we developed a deep learning model for accurate signal extractions confronted with such anomalous scenarios. Our model exhibits the same performance as the current state-of-the-art models do for the ideal and anomaly free scenario, while shows remarkable adaptability in extractions of coalescing massive black hole binary signal against all three types of non-stationarities and even their mixtures. This also provide new explorations into the robustness studies of deep learning models for data processing in space-borne gravitational wave missions.

Demonstration of machine learning-assisted low-latency noise regression in gravitational wave detectors

Abstract Low-latency noise regression algorithms are crucial for maximizing the science outcomes of the LIGO, Virgo, and KAGRA gravitational-wave detectors. This includes improvements in the detectability, source localization and pre-merger detectability of signals thereby enabling rapid multi-messenger follow-up. In this paper, we demonstrate the effectiveness of DeepClean, a convolutional neural network architecture that uses witness sensors to estimate and subtract non-linear and non-stationary noise from gravitational-wave strain data. Our study uses LIGO data from the third observing run with injected compact binary signals. As a demonstration, we use DeepClean to subtract the noise at 60 Hz due to the power mains and their sidebands arising from non-linear coupling with other instrumental noise sources. Our parameter estimation study on the injected signals shows that DeepClean does not do any harm to the underlying astrophysical signals in the data while it can enhance the signal-to-noise ratio of potential signals. We show that DeepClean can be used for low-latency noise regression to produce cleaned output data at latencies ~1–2 s. We also discuss various considerations that may be made while training DeepClean for low latency applications.

Sound source localization based on microphone array mounted on unmanned aerial vehicles

Abstract Microphone array installed on unmanned aerial vehicles (UAV) can be used for acoustic detection in scenes, such as detecting noise sources in factories or monitoring corona in power grids. However, using acoustic sensors on UAV has great challenges. The motor rotation of UAV and the non-stationary noise generated by propeller make it difficult for microphone array to obtain useful information for sound source localization. In order to reduce self-noise, an improved least mean square (LMS) adaptive filtering algorithm is proposed. Combining filtering algorithm and multiple signal classification (MUSIC) algorithm to locate the sound source, the noise spectrum characteristics of UAV in outdoor free flight mode are analyzed. The microphone array is used to collect data and realize sound source localization in low Signal-to-Noise Ratio (SNR) environment. The simulation and experimental results show that the algorithm improves the robustness of the sound source localization algorithm in low SNR environment, and realizes the real-time localization of the target sound source during the flight of UAV with microphone array.

Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.

An unsupervised machine learning algorithm approach using K-Means Clustering for optimizing Surface Wave Filtering in seismic reflection data

Surface waves often cause significant noise in seismic data, complicating the interpretation of subsurface structures. Traditional filtering methods, such as FK filtering, usually struggle with non-stationary noise and require extensive manual parameter tuning. This study explores the effectiveness of using K-means clustering, incorporating attributes such as amplitude, frequency, and phase to filter surface waves from seismic data. Synthetic seismic data were first generated to test the proposed method, ensuring its robustness before application to real field data. Attributes were extracted from each seismic trace, including instantaneous amplitude, frequency, and phase. These attributes were used as input parameters for the K-means clustering algorithm. The identified clusters corresponding to surface waves were then used to filter these waves from the seismic data. The K-Means clustering effectively differentiated surface waves from reflected waves in both synthetic and real seismic datasets. The method demonstrated that by including phase as an attribute, alongside amplitude and frequency, the accuracy of surface wave detection and filtering significantly improved. The synthetic data showed a clear separation of wave types, validating the method. When applied to real field data, the approach consistently removed surface waves, clarity of seismic reflections crucial for subsurface analysis.

Quantum decoherence dynamics in stochastically fluctuating environments.

We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.

Sample path moderate deviations for shot noise processes in the high intensity regime

We study the sample-path moderate deviation principle (MDP) for shot noise processes in the high intensity regime. The shot noise processes have a renewal arrival process, non-stationary noises (with arrival-time dependent distributions) and a general shot response function of the noises. The rate function in the MDP exhibits a memory phenomenon in this asymptotic regime, which is in contrast with that in the conventional time–space scaling regime. To prove the sample-path MDP, we first establish that this is equivalent to establishing the sample-path MDP of another process that is easier to study. We prove its finite-dimensional MDP and then establish the exponential tightness under the Skorohod J1 topology. This results in the sample-path MDP in D under the Skorohod J1 topology with a rate function that is derived from the rate function in the finite-dimensional MDP using the tools of reproducing kernel Hilbert space. In the proofs, because of the non-stationarity of shot noise process, we establish a new exponential maximal inequality and use it to prove exponential tightness and the aforementioned equivalence.

Characterization of the tail current of Channelrhodopsin-2 variants

Our study focused on specific ChR2 variants, particularly those with the Step function Opsins (SFO) mutation at the D156-C128 gate. These are widely used in optogenetics due to their heightened sensitivity to light and bi-stable prolonged activation. However, in some ChR2 variants, specifically D156 mutants, a tail current occurs when continuous light exposure is stopped. We specifically examined the D156H-T159S ChR2 variant, which demonstrated a tail current that was somewhat responsive to light and voltage, with a single-channel current of around 9fA, similar to wt-ChR2 as determined by stationary noise analysis. To further investigate, we used nonstationary noise analysis in cell-attached patching mode, which revealed that the tail current's single-channel current falls within the same range as the peak current, albeit with mild contamination from adaptation and desensitization. This finding strongly supports the notion that a portion of the ChR2 molecules open or re-open at the end of illumination, leading to further membrane depolarization.

Reconstruction of Binary Black Hole Harmonics in LIGO Using Deep Learning

Gravitational-wave signals from coalescing compact binaries in the LIGO and Virgo interferometers are primarily detected by the template-based matched filtering method. While this method is optimal for stationary and Gaussian data scenarios, its sensitivity is often affected by nonstationary noise transients in the detectors. Moreover, most of the current searches do not account for the effects of precession of black hole spins and higher-order waveform harmonics, focusing solely on the leading-order quadrupolar modes. This limitation impacts our search for interesting astrophysical sources, such as intermediate-mass black hole binaries and hierarchical mergers. Here we show, for the first time, that deep learning can be used for accurate waveform reconstruction of precessing binary black hole signals with higher-order modes. This approach can also be adapted into a rapid trigger generation algorithm to enhance online searches. Our model, tested on simulated injections in real LIGO noise from the third observing run (2019–2020) achieved a high degree of overlap with injected signals. This accuracy was consistent across a wide range of black hole masses and spin configurations chosen for this study. When applied to real gravitational-wave events, our model's reconstructions achieved between 85% and 98% overlap with those obtained by Coherent WaveBurst (unmodeled) and LALInference (modeled) analyses. These results suggest that deep learning is a potent tool for analyzing signals from a diverse catalog of compact binaries.

Attenuation of non-stationary random noise in ground penetrating radar data based on time-varying filtering

The attenuation of random noise is significant in the enhancement of the signal-to-noise ratio in ground penetrating radar (GPR) data. However, the non-stationary nature of random noise poses significant challenges to most conventional denoising methods. We propose a time-varying bandpass filter (TVBF) based on the local maxima multiple synchrosqueezing transform (LMMSST), referred to as TVBFLMMSST, for the attenuation of non-stationary random noise in GPR data. The LMMSST method is introduced to achieve highly compressed time–frequency representation (TFR). By integrating an instantaneous frequency trajectory detection algorithm, we design the TVBF to successfully separate useful signals from random noise. The efficacy of the TVBFLMMSST is validated through synthetic and field experiments, demonstrating its capability to effectively isolate components of useful signals and noise signals. Compared to classical denoising methods, TVBFLMMSST exhibits robust performance in attenuating random noise while preserving the amplitude of useful signals.