Statistical Properties Of Noise Research Articles

Normal-skew mixture-based robust probability hypothesis density filter under unknown statistical properties of noise

In multi-target tracking (MTT), the statistical properties of noise in real-world scenarios are often unknown. When noise modeling does not align with the actual noise, it can lead to inaccurate estimations of the number and locations of targets. To address this issue, we model the noise as a normal-skewed mixture (NSM) distribution (NSMD), comprising a linear combination of a normal distribution (ND) and a Gaussian scale distribution (GSD). By varying the parameters of the NSMD, it can fit arbitrary normal and/or heavy-tailed, and/or skewed nonsmooth noise. To enable the NSMD to adaptively fit noise with unknown statistical properties, we introduce a hierarchical model and a variational Bayesian (VB) approach to adjust the shape of the NSMD. The marginal likelihood function is then derived for filtering updates. Based on the NSMD and the marginal likelihood function, we propose a robust NSM-based probabilistic hypothesis density (NSM-PHD) filter to achieve improved MTT accuracy when noise statistical characteristics are unknown. Simulation results demonstrate that the NSM-PHD effectively enhances MTT accuracy under conditions of unknown noise statistical properties.

State Parameter Fusion Estimation for Intelligent Vehicles Based on IMM-MCCKF

The prerequisite for intelligent vehicles to achieve autonomous driving and active safety functions is acquiring accurate vehicle state parameters. Traditional Kalman filters often underperform in non-Gaussian noise environments due to their reliance on Gaussian assumptions. This paper presents the IMM-MCCKF filter, which integrates the interacting multiple model theory (IMM) and the maximum correntropy cubature Kalman filter method (MCCKF), for estimating the state parameters of intelligent vehicles. The IMM-MCCKF successfully suppresses non-Gaussian noise by optimizing a nonlinear cost function using the maximum correntropy criteria, allowing it to capture and analyze signal data outliers accurately. The filter designs various state and measurement noise submodels to adapt to the environment dynamically, thus reducing the impact of unknown noise statistical properties. Accurately measuring the velocity of a vehicle and the angle at which its center of mass drifts sideways is of utmost importance for its ability to maneuver, maintain stability, and ensure safety. These parameters are critical for implementing advanced control systems in intelligent vehicles. The study begins by constructing a nonlinear Dugoff tire model and a three-degrees-of-freedom (3DOF) vehicle model. Subsequently, utilizing low-cost vehicle sensor signals, joint simulations are conducted on the CarSim-Simulink platform to estimate vehicle state parameters. The results demonstrate that in terms of estimation accuracy and robustness in non-Gaussian noise scenarios, the proposed IMM-MCCKF filter consistently outperforms the MCCKF and CKF algorithms.

Evaluation of neural network models and quality forecasting based on process time‐series data

AbstractComplex industrial process modelling is critically important within the context of industrial intelligence. In recent years, soft sensor techniques based on neural networks have become increasingly popular for modelling nonlinear industrial processes. This paper proposes an integrated framework of neural network modelling and evaluation for nonlinear dynamic processes. This framework achieves an integrated solution for modelling, prediction, evaluation, and network structure parameter selection. It can be applied to noisy sensors and dense data in the time domain. The framework's proposed evaluation mechanism employs two novel evaluation metrics, the variational auto‐encoder (VAE)‐based Kullback–Leibler (KL) divergence metric and the maximum likelihood estimation‐based J metric, which both evaluate the model by mining the statistical properties of the residuals. The framework models the dynamic process with a model order based‐gated recurrent units (MOb‐GRU) neural network and a modified transformer model. Numerical experiments demonstrate that the evaluation mechanism functions properly in scenarios with multiple signal‐to‐noise ratios and multiple noise statistical properties and that the framework produces accurate modelling results.

FREQ-Seq2: a method for precise high-throughput combinatorial quantification of allele frequencies.

The accurate determination of allele frequencies is crucially important across a wide range of problems in genetics, such as developing population genetic models, making inferences from genome-wide association studies, determining genetic risk for diseases, as well as other scientific and medical applications. Furthermore, understanding how allele frequencies change over time in populations is central to ascertaining their evolutionary dynamics. We present a precise, efficient, and economical method (FREQ-Seq2) for quantifying the relative frequencies of different alleles at loci of interest in mixed population samples. Through the creative use of paired barcode sequences, we exponentially increased the throughput of the original FREQ-Seq method from 48 to 2,304 samples. FREQ-Seq2 can be targeted to specific genomic regions of interest, which are amplified using universal barcoded adapters to generate Illumina sequencing libraries. Our enhanced method, available as a kit along with open-source software for analyzing sequenced libraries, enables the detection and removal of errors that are undetectable in the original FREQ-Seq method as well as other conventional methods for allele frequency quantification. Finally, we validated the performance of our sequencing-based approach with a highly multiplexed set of control samples as well as a competitive evolution experiment in Escherichia coli and compare the latter to estimates derived from manual colony counting. Our analyses demonstrate that FREQ-Seq2 is flexible, inexpensive, and produces large amounts of data with low error, low noise, and desirable statistical properties. In summary, FREQ-Seq2 is a powerful method for quantifying allele frequency that provides a versatile approach for profiling mixed populations.

Sparse Signal Recovery through Long Short-Term Memory Networks for Compressive Sensing-Based Speech Enhancement

This paper presents a novel speech enhancement approach based on compressive sensing (CS) which uses long short-term memory (LSTM) networks for the simultaneous recovery and enhancement of the compressed speech signals. The advantage of this algorithm is that it does not require an iterative process to recover the compressed signals, which makes the recovery process fast and straight forward. Furthermore, the proposed approach does not require prior knowledge of signal and noise statistical properties for sensing matrix optimization because the used LSTM can directly extract and learn the required information from the training data. The proposed technique is evaluated against white, babble, and f-16 noises. To validate the effectiveness of the proposed approach, perceptual evaluation of speech quality (PESQ), short-time objective intelligibility (STOI), and signal-to-distortion ratio (SDR) were compared to other variants of OMP-based CS algorithms The experimental outcomes show that the proposed approach achieves the maximum improvements of 50.06%, 43.65%, and 374.16% for PESQ, STOI, and SDR respectively, over the different variants of OMP-based CS algorithms.

Quantum State Tomography in Nonequilibrium Environments

We generalize an approach to studying the quantum state tomography (QST) of open systems in terms of the dynamical map in Kraus representation within the framework of dynamic generation of informationally complete positive operator-valued measures. As applications, we use the generalized approach to theoretically study the QST of qubit systems in the presence of nonequilibrium environments which exhibit nonstationary and non-Markovian random telegraph noise statistical properties. We derive the time-dependent measurement operators for the quantum state reconstruction of the single qubit and two-qubit systems in terms of the polarization operator basis. It is shown that the behavior of the time-dependent measurement operators is closely associated with the dynamical map of the qubit systems.

Distributed Event-Triggered Nonlinear Fusion Estimation under Resource Constraints

This paper studies the event-triggered distributed fusion estimation problems for a class of nonlinear networked multi-sensor fusion systems without noise statistical properties. In practice, the sensor-to-remote estimator channel and the smart sensor-to-fusion center channel of the communication network will be faced with some resource constraint problems. To meet the finite communication resources during the information transmission, an event-triggered strategy and a dimensionality reduction strategy are introduced in a unified network framework to reduce communication traffic. Since the reduction of communication information will inevitably degenerate the estimation performance, two kinds of compensation strategies in terms of a unified model are proposed to restructure the untransmitted information. Then, the local/fusion estimators are designed based on the compensation information. Moreover, the linearization errors caused by the Taylor expansion are modeled by the state-dependent matrices with uncertain parameters when establishing estimation error systems, and then different robust recursive optimization problems are established to determine the estimator gains and the fusion criteria. Meanwhile, the stability conditions are also presented such that the square errors of the designed nonlinear estimators are asymptotically bounded. Finally, a vehicle localization system is employed to demonstrate the effectiveness and advantages of the proposed methods.

Noise Measurements and Noise Statistical Properties Investigations in a Stimulated Raman Scattering Microscope Based on Three Femtoseconds Laser Sources

To induce a Raman-active transition in a material, stimulated Raman scattering (SRS) spectroscopy/microscopy implementations typically rely on two pulsed laser sources. One of their limitations is that not all of the regions of Raman spectra can be investigated, so only some applications can be exploited. In this paper, the noise characterizations of a stimulated Raman scattering spectroscopy/microscopy implementation, based on the insertion of a third pulsed laser source, are provided. The merit of this system is that it is able to explore the large variety of SRS applications. In order to characterize our system, an investigation of different kinds of noises due to the laser sources and electronics sources was carried out. Firstly, the relative intensity noises of three femtosecond laser sources were measured. Secondly, noise characterizations of the detection system were carried out and our findings prove that our SRS microscope is shot noise-limited, demonstrating that the third laser source introduction is well suited and satisfies our purpose. Finally, the statistical properties of the overall image noises are analyzed and discussed.

Disentanglement Dynamics in Nonequilibrium Environments.

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

SPB-Net: A Deep Network for SAR Imaging and Despeckling With Downsampled Data

Synthetic aperture radar (SAR) typically faces both large-scale data and speckle noise problems, which, respectively, induce enormous strains on transmission and storage and interfere with the analysis and interpretation of SAR images. To tackle these, we present a real-time processing deep network, called SPB-Net, to implement imaging and speckle suppression simultaneously. First, a novel imaging-despeckling observation model with the nonlogarithmic additive speckle noise is established. Subsequently, guided by the statistical properties of noise and sparse and detail-preserved requirements in SAR imaging and despeckling, we formulate an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> along with two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> regularizations as the fidelity, sparse, and image detail-preserved constraints, respectively. Convolution layers are employed to improve the feature representation capability in the latter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> term as well. Based on this, we construct a corresponding convex optimization problem. Then, the complex-valued split Bregman method, focusing on the complex-variable convex problem, is unfolded into a parameter-learnable and architecture-fixed SPB-Net to solve the proposed problem effectively and efficiently. Experimental results with the downsampled Radarsat-1 raw data demonstrate the validity in imaging and speckle suppression and the real-time processing capability of the proposed SPB-Net.

Statistical image-based material decomposition for triple-energy computed tomography using total variation regularization.

Triple-energy computed tomography (TECT) can obtain x-ray attenuation measurements at three energy spectra, thereby allowing identification of different material compositions with same or very similar attenuation coefficients. This ability is known as material decomposition, which can decompose TECT images into different basis material image. However, the basis material image would be severely degraded when material decomposition is directly performed on the noisy TECT measurements using a matrix inversion method. To achieve high quality basis material image, we present a statistical image-based material decomposition method for TECT, which uses the penalized weighted least-squares (PWLS) criteria with total variation (TV) regularization (PWLS-TV). The weighted least-squares term involves the noise statistical properties of the material decomposition process, and the TV regularization penalizes differences between local neighboring pixels in a decomposed image, thereby contributing to improving the quality of the basis material image. Subsequently, an alternating optimization method is used to minimize the objective function. The performance of PWLS-TV is quantitatively evaluated using digital and mouse thorax phantoms. The experimental results show that PWLS-TV material decomposition method can greatly improve the quality of decomposed basis material image compared to the quality of images obtained using the competing methods in terms of suppressing noise and preserving edge and fine structure details. The PWLS-TV method can simultaneously perform noise reduction and material decomposition in one iterative step, and it results in a considerable improvement of basis material image quality.

A Novel Adaptive H-Infinity Cubature Kalman Filter Algorithm Based on Sage-Husa Estimator for Unmanned Underwater Vehicle

In the navigation of unmanned underwater vehicle (UUV), a filtering algorithm suitable for the working conditions is required. Due to the disturbance from the environment and maneuverability, outliers and noise with time-varying statistical properties always exist, which greatly affect the positioning accuracy and stability of the navigation system. In this paper, we present a novel nonlinear state estimation algorithm named AH∞CKF based on the combination of H∞CKF and Sage-Husa estimator. The recently developed H∞CKF provides nonlinear filtering good robustness, and Sage-Husa estimator could timely modify the statistical properties of noise. The novel algorithm is superior to H∞CKF in accuracy by combining Sage-Husa estimator with the H∞CKF while ensuring robustness. The effectiveness of the novel AH∞CKF is verified by lake experiment and simulation.

The filtering method of MEMS gyro signal based on sparse decomposition

Traditional denoising methods for Micro-electromechanical Systems (MEMS) gyro signal are required to obtain a priori noise statistical properties, which result in poor denoising performance in MEMS gyro utilized in Micro-Inertial Measurement While Drilling (MWD), due to the unknown and complex noise characteristics in MWD. According to this problem, a kind of gyro signal denoising method based on sparse decomposition without a requirement of the priori noise characteristics, utilizing a newly designed atom dictionary, is proposed. Firstly, the MEMS gyro output differential equation is established on the basis of the physical mechanism of the MEMS gyro, then the real MEMS gyro output signal characteristics are analyzed according to the solution of the differential equation. Secondly, the characteristic wave atom most similar to the gyro output signal is designed. Finally, the gyro signal sparse decomposition denoising experiments based on the designed atom dictionary are conducted, compared with the wavelet threshold method and Kalman filter. The experiment results show that the proposed denoising method based on sparse decomposition utilizing the newly designed atom dictionary outperforms wavelet threshold method and Kalman filter in MEMS gyro signal processing of MWD, especially when the noise statistical properties of gyro signal are completely unknown.

Gravitational wave denoising of binary black hole mergers with deep learning

Gravitational wave detection requires an in-depth understanding of the physical properties of gravitational wave signals, and the noise from which they are extracted. Understanding the statistical properties of noise is a complex endeavor, particularly in realistic detection scenarios. In this article we demonstrate that deep learning can handle the non-Gaussian and non-stationary nature of gravitational wave data, and showcase its application to denoise the gravitational wave signals generated by the binary black hole mergers GW150914, GW170104, GW170608 and GW170814 from advanced LIGO noise. To exhibit the accuracy of this methodology, we compute the overlap between the time-series signals produced by our denoising algorithm, and the numerical relativity templates that are expected to describe these gravitational wave sources, finding overlaps O≳0.99. We also show that our deep learning algorithm is capable of removing noise anomalies from numerical relativity signals that we inject in real advanced LIGO data. We discuss the implications of these results for the characterization of gravitational wave signals.

Identification of induction motor parameters with measurement errors

This paper proposes an algorithm for estimating parameters of asynchronous traction motors in the presence of measurement errors. The presence of measurement errors of voltage and current leads to biased estimates of motor parameters. Algorithmic approach to eliminating the influence of noise is used most often as it increases the accuracy of estimates without precision current and voltage meters. Known modifications of algorithms based on the method of total least squares suggest filtering the derivatives of noise, which increases the complexity of the algorithm and also changes the statistical properties of noise. The proposed algorithm is a generalization of the total least-squares technique and does not require knowledge of the laws governing the distribution of measurement errors. The results of modeling show that the parameter estimation is highly accurate than the ordinary least square. The proposed algorithm can be used to create precision control systems, as well as to diagnose faults in electric motors by K parameters.

An improved packing equivalent circuit modeling method with the cell‐to‐cell consistency state evaluation of the internal connected lithium‐ion batteries

AbstractThe existing equivalent modeling methods reported in literature focuses mainly on the battery cells and do not take the packing consistency state into consideration, which exists on the internal connected cells of the lithium‐ion battery pack. An improved equivalent circuit model is constructed and reported in this manuscript for the first time, which can be used to characterize the working characteristics of the packing lithium‐ion batteries. A new equilibrium concept named as state of balance is proposed as well as the calculation process, which is realized by considering the real‐time detected internal battery cell voltages. In addition, this new equilibrium concept aims to obtain more information on the real‐time consistency characterization of the battery pack. The improved adaptive equivalent circuit model is investigated by using the improved splice modeling method, in which the statistical noise properties are corrected and the additional parallel resistance‐capacitance circuit is introduced. The parameter correction treatment is carried out by comparing the estimated and experimental detected closed circuit voltages. Furthermore, the tracking error is found to be 0.005 V and accounts for 0.119% of the nominal battery voltage. By taking the packing consistency state and temperature correction into consideration, the accurate working characteristic expression is realized in the improved equivalent circuit modeling process. Finally, the model proposed in this manuscript presents a great number of advantages compared to other methods reported so far, like has the high accuracy, and the ability to protect the security of the lithium‐ion battery pack in the power supply application.

Cooperative Localisation of AUVs based on Huber-based Robust Algorithm and Adaptive Noise Estimation

In this paper, adaptive noise estimation is used along with a previously proposed Huber-based robust algorithm for cooperative localisation of Autonomous Underwater Vehicles (AUVs). The Huber-based robust cooperative localisation algorithm named Huber-based Iterative Divided Difference Filtering (HIDDF), proposed in our previous work, effectively achieved a robust result against abnormal measurement noise, enhanced the stability of the filtering algorithm and improved the performance of cooperative localisation state estimation. However, its performance could be significantly further improved if it could estimate the system's noise statistical properties online in real time and then adaptively adjust the filtering gain matrix accordingly. In this paper, a novel adaptive noise estimation algorithm is proposed based on a covariance matching method. The proposed algorithm is suitable for adaptively estimating Gaussian and non-Gaussian measurement as well as process noise. The efficacy of the proposed algorithm has been verified through simulation results. In order to further verify the effectiveness of the proposed algorithm in practical systems, lake tests were conducted. Then, based on offline test data, the performance of the cooperative positioning algorithm under dual-pilot and single-pilot schemes was simulated. The advantages and feasibility of the algorithm are analysed and compared through performance comparison. Cooperative localisation accuracy of the previously proposed Huber-based robust algorithm has been enhanced significantly when used with the proposed adaptive noise estimation algorithm.

Research on navigation for underwater unmanned vehicle based on dynamic gray filtering method

According to the problem of large platform noise and external disturbance influence and the data may have outliers for UUV navigation, a dynamic grey filtering method based on fractional order operator is proposed. This method does not require prior knowledge and noise statistical properties of UUV system while establishing a dynamic grey model based on fractional operator according to navigation data. The deviation between the grey prediction value and the next navigation sample value is calculated and the data is fused according to the deviation to realize the real-time filtering. The simulation results show that the method is effective and feasible.

Estimation of Canopy Height Using an Airborne Ku-Band Frequency-Modulated Continuous Waveform Profiling Radar

An airborne Ku -band frequency-modulated continuous waveform (FMCW) profiling radar terms as Tomoradar provides a distance-resolved measure of microwave radiation backscattered from the canopy surface and the underlying ground. The Tomoradar waveform data are acquired in the southern Boreal Forest Zone with Scots pine, Norway spruce, and birch as major species in Finland. A weighted filtering algorithm based on statistical properties of noise is designed to process the original waveform. In addition, another algorithm of estimating canopy height for the processed waveform is developed by extracting the canopy top and ground position. A higher-precision reference data from a Velodyne VLP-16 laser scanner and a digital terrain model are introduced to validate the accuracy of extracted canopy height. According to the processed results from 127 765 copolarization measurements in 32 stripes of Tomoradar field test, the mean error of canopy height varies from −0.04 to 1.53 m, and the root-mean-square error approximates 1 m. Moreover, the estimated canopy heights highly correlate with the reference data in view of that the correlation coefficients maintain from 0.86 to 0.99 with an average value of 0.96. All these results demonstrate that Tomoradar presents an important approach in estimating the canopy height with several meters footprint and is feasible of being a validation instrument for satellite LiDAR with large footprint in the forest inventory.

Adaptive maneuvering target tracking with 2-HFSWR multisensor surveillance system

The high frequency surface wave radar (HFSWR) with detection capability of hundreds of kilometers plays an important role in marine surveillance [1]–[8]. Nevertheless, HFSWR has low azimuth measurement accuracy, which causes great deviation of target location and tracking [9]. Meanwhile, the miniaturization of radar arrays leads to the limitation of antenna length, which further causes severe decline of azimuth accuracy. Moreover, the interference from external environment also decreases the azimuth accuracy, making the accurate tracking of vessels difficult. In recent years, the 2-HFSWR multisensor surveillance system has become a hot spot, because it only requires parameters of distance and velocity without using the azimuth measurement when tracking vessels. The 2-HFSWR multisensor surveillance system consists of two independent radars implementing the target location and tracking task by detecting the radial distance and velocity, respectively. The 2-HFSWR multisensor surveillance system can ensure the detection accuracy without azimuth measurement, which is advantageous to the miniaturization of HFSWR. However, there are still certain complicated cases to be solved for continuous tracking of vessels, for example sudden change in motion state, an inaccurate model, and unknown priori statistical properties of noise.