Search Results (73)

This study addresses the performance degradation of $\alpha$ and $\alpha$-$\beta$ filters in 6G Integrated Sensing and Communications (ISAC) scenarios, attributed to violations of linearity and steady-state assumptions. These filters are originally designed with time-invariant gains derived under such assumptions to ensure low computational complexity. However, deviations from ideal conditions—such as non-white, biased, or non-Gaussian process noise—necessitate corrective mechanisms. We propose a weighted process noise approach that accounts for increased uncertainty due to assumption violations while preserving the filters’ closed-form structure and computational efficiency. By integrating uncertainty into the conventional gain formulation, the proposed method achieves performance closer to the optimal filter. Numerical results demonstrate superior accuracy over conventional filters across various noise variances and scenarios, without requiring parameter tuning. Notably, performance improvements become more pronounced as the measurement interval decreases. Full article

Various fields within biological and psychological inquiry recognize the significance of exploring long-range temporal correlations to study phenomena. However, these fields face challenges during this transition, primarily stemming from the impracticality of acquiring the considerably longer time series demanded by canonical methods. The Bayesian Hurst–Kolmogorov (HK) method estimates the Hurst exponents of time series—quantifying the strength of long-range temporal correlations or “fractality”—more accurately than the canonical detrended fluctuation analysis (DFA), especially when the time series is short. Therefore, the systematic application of the HK method has been encouraged to assess the strength of long-range temporal correlations in empirical time series in behavioral sciences. However, the Bayesian foundation of the HK method fuels reservations about its performance when artifacts corrupt time series. Here, we compare the HK method’s and DFA’s performance in estimating the Hurst exponents of synthetic long-range correlated time series in the presence of additive white Gaussian noise, fractional Gaussian noise, short-range correlations, and various periodic and non-periodic trends. These artifacts can affect the accuracy and variability of the Hurst exponent and, therefore, the interpretation and generalizability of behavioral research findings. We show that the HK method outperforms DFA in most contexts—while both processes break down for anti-persistent time series, the HK method continues to provide reasonably accurate H values for persistent time series as short as $N=64$ samples. Not only can the HK method detect long-range temporal correlations accurately, show minimal dispersion around the central tendency, and not be affected by the time series length, but it is also more immune to artifacts than DFA. This information becomes particularly valuable in favor of choosing the HK method over DFA, especially when acquiring a longer time series proves challenging due to methodological constraints, such as in studies involving psychological phenomena that rely on self-reports. Moreover, it holds significance when the researcher foreknows that the empirical time series may be susceptible to contamination from these processes. Full article

The current self-calibration approaches based on sparse Bayesian learning (SBL) demonstrate robust performance under uniform white noise conditions. However, their efficacy degrades significantly in non-uniform noise environments due to acute sensitivity to noise power estimation inaccuracies. To address this limitation, this paper proposes an orientation estimation method based on variational Bayesian inference to combat non-uniform noise and gain/phase error. The gain and phase errors of the array are modeled separately for calibration purposes, with the objective of improving the accuracy of the fit during the iterative process. Subsequently, the noise of each element of the array is characterized via independent Gaussian distributions, and the correlation between the array gain deviation and the noise power is incorporated to enhance the robustness of this method when operating in non-uniform noise environments. Furthermore, the Cramér–Rao Lower Bound (CRLB) under non-uniform noise and gain-phase deviation is presented. Numerical simulations and experimental results are provided to validate the superiority of this proposed method. Full article

Aiming at the problem that the pseudo-velocity measurement noise of non-holonomic constraints (NHCs) in the integrated navigation of vehicle-mounted a global navigation satellite system/inertial navigation system (GNSS/INS) is time-varying and thick-tailed in complex road conditions (turning, sideslip, etc.) and cannot be accurately predicted, an adaptive estimation method for the initial value of NHC lateral velocity noise based on multiple linear regression is proposed. On the basis of this method, a Gaussian Student’s T distribution variational Bayesian filtering algorithm (Ga-St VBAKF) based on NHC pseudo-velocity measurement noise modeling is proposed through modeling and analysis of pseudo-velocity measurement noise. Firstly, in order to adaptively adjust the initial value of NHC lateral velocity noise, a vehicle turning detection algorithm is used to detect whether the vehicle is turning. Secondly, based on the vehicle motion state, the variational Bayesian method is used to adaptively estimate the statistical characteristics of the measurement noise in real time based on modeling of the lateral velocity noise as Gaussian white noise or Student’s T distribution thick-tail noise. The test results show that compared to the traditional Kalman filtering algorithm with fixed noise, the Ga-St VBAKF algorithm with noise adaptation reduces the maximum horizontal position error by 65.9% in the GNSS/NHC/OD/INS (where OD stands for odometer and INS stands for inertial measurement unit) system when the vehicle is in a turning state, and by 42.3% in the NHC/OD/INS system. This indicates that the algorithm can effectively suppress the divergence of positioning errors during turning and improve the performance of integrated navigation. Full article

Achieving both accurate and real-time monitoring heartbeat signals by non-invasive sensing techniques is challenging due to various noise interferences. In this paper, we propose an enhanced discrete wavelet transform (DWT) method that incorporates objective denoising quality assessment metrics to determine accurate thresholds and adaptive threshold functions. Our approach begins by denoising ECG signals from various databases, introducing several types of typical noise, including additive white Gaussian (AWG) noise, baseline wandering noise, electrode motion noise, and muscle artifacts. The results show that for Gaussian white noise denoising, the enhanced DWT can achieve 1–5 dB SNR improvement compared to the traditional DWT method, while for real noise denoising, our proposed method improves the SNR tens or even hundreds of times that of the state-of-the-art denoising techniques. Furthermore, we validate the effectiveness of the enhanced DWT method by visualizing and comparing the denoising results of heartbeat signals monitored by fiber-optic micro-vibration sensors against those obtained using other denoising methods. The improved DWT enhances the quality of heartbeat signals from non-invasive sensors, thereby increasing the accuracy of cardiovascular disease diagnosis. Full article

Modern imaging systems produce a great volume of image data. In many practical situations, it is necessary to compress them for faster transferring or more efficient storage. Then, a compression has to be applied. If images are noisy, lossless compression is almost useless, and lossy compression is characterized by a specific noise filtering effect that depends on the image, noise, and coder properties. Here, we considered a modern HEIF coder applied to grayscale (component) images of different complexity corrupted by additive white Gaussian noise. It has recently been shown that an optimal operation point (OOP) might exist in this case. Note that the OOP is a value of quality factor where the compressed image quality (according to a used quality metric) is the closest to the corresponding noise-free image. The lossy compression of noisy images leads to both noise reduction and distortions introduced into the information component, thus, a compromise should be found between the compressed image quality and compression ratio attained. The OOP is one possible compromise, if it exists, for a given noisy image. However, it has also recently been demonstrated that the compressed image quality can be significantly improved if post-filtering is applied under the condition that the quality factor is slightly larger than the one corresponding to the OOP. Therefore, we considered the efficiency of post-filtering where a block-matching 3-dimensional (BM3D) filter was applied. It was shown that the positive effect of such post-filtering could reach a few dB in terms of the PSNR and PSNR-HVS-M metrics. The largest benefits took place for simple structure images and a high intensity of noise. It was also demonstrated that the filter parameters have to be adapted to the properties of residual noise that become more non-Gaussian if the compression ratio increases. Practical recommendations on the use of compression parameters and post-filtering are given. Full article

In the field of direction of arrival (DOA) estimation, a common assumption is that array noise follows a uniform Gaussian white noise model. However, practical systems often encounter non-ideal noise conditions, such as non-uniform or colored noise, due to sensor characteristics and external environmental factors. Traditional DOA estimation techniques experience significant performance degradation in the presence of colored noise, necessitating the exploration of specialized DOA estimation methods for such environments. This study introduces a DOA estimation method for acoustic vector arrays based on a spectrum attention mechanism (SAM). By employing SAM as an adaptive filter and constructing a double-branch model combining a convolutional neural network (CNN) and long short-term memory (LSTM), the method extracts the spatial and temporal features of signals, and effectively reduces the frequency components of colored noise, enhancing DOA estimation accuracy in colored noise scenarios. At an SNR of −5 dB, it achieves an accuracy rate of 85% while maintaining a low RMSE of only 2.03°. Full article

Digital terrestrial television is now implemented in many countries worldwide and is now mature. Digital Video Broadcasting-Terrestrial, second generation (DVB-T2) is the European standard adopted or deployed by European and African countries which uses Orthogonal Frequency-Division Multiplexing (OFDM) modulation to achieve good throughput performance. However, its main particularity is the number of subcarriers operated for OFDM modulation which varies from 1024 to 32,768 subcarriers. Also, mobile reception is planned in DVB-T2 in addition to rooftop antenna and portable receptions planned in DVB-T. However, the main challenge of DVB-T2 for mobile reception is the presence of a carrier frequency offset (CFO) which degrades the system performance by inducing an Intercarrier Interference (ICI) on the DVB-T2 signal. This paper evaluates the system performance in the presence of the CFO when Gaussian noise and a TU6 channel are applied. Universal Filtered Multicarrier (UFMC) and non-uniform constellations (NUCs) have previously demonstrated good performance in comparison with OFDM and Quadrature Amplitude Modulation (QAM) in DVB-T2. The impact of CFO on the UFMC- and NUC-based DVB-T2 system is additionally investigated in this work. The results demonstrate that the penalties induced by CFO insertion in UFMC- and NUC-based DVB-T2 are highly reduced in comparison to those for the native DVB-T2. At a bit error rate (BER) of ${10}^{-3}$, the CFO penalties induced by the native DVB-T2 are $0.96$$\mathrm{d}$$\mathrm{B}$ and 4 $\mathrm{d}$$\mathrm{B}$, respectively, when only Additive White Gaussian Noise (AWGN) is used and when TU6 is additionally considered. The penalties are equal to $0.84$$\mathrm{d}$$\mathrm{B}$ and $0.2$$\mathrm{d}$$\mathrm{B}$ for UFMC/NUC-based DVB-T2. Full article

Digital image correlation (DIC) is a non-contact measurement technique used to evaluate surface deformation of objects. Typically, pointwise moving least squares (PMLS) fitting is applied to process the noisy data from DIC to obtain an accurate strain field. In this study, a self-adaptive pointwise moving least squares (SPMLS) method was developed to optimize the process of window size selection, thereby attaining superior accuracy in measurements. The premise of this method is that the noise in the displacement field follows white Gaussian noise. Under this assumption, it analyses the random errors and systematic errors of the PMLS method under different calculation window sizes. The optimal size of the calculation window is determined by minimizing the errors. Subsequently, the strain field is computed based on the optimized calculation window. The results were compared with a typical PMLS method. Whether calculating low-gradient strain fields or high-gradient strain fields, the computational accuracy of SPMLS is close to the optimal accuracy of PMLS. This study effectively addresses the inherent challenge of manually selecting window size in the PMLS method. Full article

In this work, we obtain non-Gaussian (NG) stochastic solutions to $\chi$-Wick-type stochastic ($\chi$-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the $\chi$-Wick product ($\chi$-Wk-product) and an $\chi$-Hermite transform ($\chi$-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers’ equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to $\chi$-Wk-TS Burgers’ equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution. Full article

Real-time monitoring of heartbeat signals using multimode fiber optic microvibration sensing technology is crucial for diagnosing cardiovascular diseases, but the heartbeat signals are very weak and susceptible to noise interference, leading to inaccurate diagnostic results. In this paper, a combined enhanced discrete wavelet transform (DWT) and non-local mean estimation (NLM) denoising method is proposed to remove noise from heartbeat signals, which adaptively determines the filtering parameters of the DWT-NLM composite method using objective noise reduction quality assessment metrics by denoising different ECG signals from multiple databases with the addition of additive Gaussian white noise (AGW) with different signal-to-noise ratios (SNRs). The noise reduction results are compared with those of NLM, enhanced DWT, and conventional DWT combined with NLM method. The results show that the output SNR of the proposed method is significantly higher than the other methods compared in the range of −5 to 25 dB input SNR. Further, the proposed method is employed for noise reduction of heartbeat signals measured by fiber optic microvibration sensing. It is worth mentioning that the proposed method does not need to obtain the exact noise level, but only the adaptive filtering parameters based on the autocorrelation nature of the denoised signal. This work greatly improves the signal quality of the multimode fiber microvibration sensing system and helps to improve the diagnostic accuracy. Full article

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an ${\mathcal{l}}_1-{\mathcal{l}}_1$ optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method. Full article

LoRa technology is being integrated into industrial applications as part of Industry 4.0 owing to its longer range and low power consumption. However, noise, interference, and the fading effect all have a negative impact on LoRa performance in an industrial environment, necessitating solutions to ensure reliable communication. This paper evaluates and compares LoRa’s performance in terms of packet error rate (PER) with and without forward error correction (FEC) in an industrial environment. The impact of integrating an infinite impulse response (IIR) or finite impulse response (FIR) filter into the LoRa architecture is also evaluated. Simulations are carried out in MATLAB at 868 MHz with a bandwidth of 125 kHz and two spreading factors of 7 and 12. Many-to-one and one-to-many communication modes are considered, as are line of sight (LOS) and non-line of Sight (NLOS) conditions. Simulation results show that, compared to an environment with additive white Gaussian noise (AWGN), LoRa technology suffers a significant degradation of its PER performance in industrial environments. Nevertheless, the use of forward error correction (FEC) contributes positively to offsetting this decline. Depending on the configuration and architecture examined, the gain in signal-to-noise ratio (SNR) using a 4/8 coding ratio ranges from 7 dB to 11 dB. Integrating IIR or FIR filters also boosts performance, with additional SNR gains ranging from 2 dB to 6 dB, depending on the simulation parameters. Full article

The remote and non-contact monitoring of human respiration and heartbeat based on radars is a safe and convenient practice. However, how to accurately estimate the heart rate is still an open issue, because the heartbeat information in radar signals is affected by respiratory harmonics. In this paper, a maximum likelihood estimation was introduced to extract the heart rate from high-pass-filtered radar heartbeat waveforms where the low-frequency respiratory and heartbeat components were attenuated. The closed-form asymptotic estimation variance of the maximum likelihood estimator was derived to describe its performance in white Gaussian noise with a high signal-to-noise ratio (SNR). The proposed method was verified using two publicly available datasets and demonstrated superior performance compared to other methods. The estimation method and the asymptotic estimation variance here described are also applicable for signal period estimation in other settings with similar conditions. Full article

With the increasing applications of UWB indoor positioning technologies in industrial areas, to further enhance the positioning precision, the UWB/IMU combination method (UICM) has been considered as one of the most effective solutions to reduce non-line-of-sight (NLOS) errors. However, most conversional UICMs suffer from a high probability of positioning failure due to uncontrollable and cumulative errors from inertial measuring units (IMU). Hence, to address this issue, we improved the extended Kalman filter (EKF) algorithm of an indoor positioning model based on UWB/IMU tight combination with a double-loop error self-correction. Compared with conventional UICMs, this improved model consists of new modules for fixing time desynchronization, optimizing the threshold setting for UWB ranging, data fusion in NLOS, and double-loop error estimation, sequentially. Further, systematic error controllability analysis proved that the proposed model could satisfy the controllability of UWB indoor positioning systems. To validate this improved UICM, inevitable obstacles and atmospheric interferences were regarded as Gaussian white noises to verify its environmental adaptability. Finally, the experimental results showed that this proposed model outperformed the state-of-the-art UWB-based positioning models with a maximum deviation of 0.232 m (reduced by 83.93% compared to a pure UWB model and 43.14% compared to the conventional UWB/IMU model) and standard deviation of 0.09981 m (reduced by 88.35% compared to a pure UWB model and 22.21% compared to the conventional UWB-IMU model). Full article