Statistical Characteristics Of Noise Research Articles

Q‐Learning Based Adaptive Kalman Filtering With Adaptive Window Length

ABSTRACTIn this article, we propose an adaptive Kalman filtering with adaptive window length based on Q‐learning for dynamic systems with unknown model information. The iteration step length of the Q‐function is quantitatively adjusted through the influence function. The adaptive Kalman filtering algorithm is used to set an appropriate weight matrix for the Q‐function to estimate unknown model parameters. One numerical example and a practice‐oriented case are given to illustrate the effectiveness of the proposed method. It is shown that this filtering can provide state estimates of best accuracy among all the compared methods when the model mismatch and noise statistical characteristics change.

Optimal acquisition time estimation method for CSEM with high-order pseudo-random signal

High-order pseudo-random signal is gradually being applied in controlled-source electromagnetic (CSEM) exploration. In contrast to the conventional single-frequency sweep mode, the high-order pseudo-random signal enables simultaneous transmission of multiple frequencies. However, estimating a fixed acquisition time based on observed noise levels often results in poor adaptability for high-order pseudo-random signal, which only require reception of one set of waveform. In this study, we presented an estimation method for acquisition time for CSEM with high-order pseudo-random signal using an improved logistic function. The improved logistic function was proposed to introduce a time-decay factor into the governing equation for the first time. By considering the transformation rule of noise statistical characteristics with time, the specific parameters of the function have been determined to better describe the dynamic evolution process of the signal quality. The effective frequencies were extracted at various acquisition times based on the noise evaluation number, and the resulting quantity of effective frequencies was used as the fitting target. Guidance for the fieldwork was determined based on the average time of the saturation period, in accordance with the properties of the function. The reliability of the improved logistic function was validated through a transmission current data simulation. The proposed method was demonstrated through the measured data from both strong and weak interference areas.

A novel adaptive unscented kalman filter algorithm for SOC estimation to reduce the sensitivity of attenuation coefficient

A new exponential adaptive strong tracking unscented Kalman filtering algorithm (ASTRUKF) is proposed to address the issues of slow tracking speed, untimely response of model parameter changes, and inaccurate noise statistical characteristics when estimating the State of Charge (SOC) of batteries at different temperatures, in order to reduce the sensitivity of attenuation coefficients. This algorithm improves upon the traditional method of calculating attenuation factor by incorporating the correlation between current and past residuals. It dynamically updates the Kalman gain and contribution rate using an exponential model, which increases the impact of current data. This algorithm also ensures the stability of the noise covariance matrix by stabilizing the attenuation factor within a fixed range. The contribution rate is utilized to estimate the statistical characteristics of detection noise, however it may exhibit bias. The ASTRUKF method exhibits a maximum estimation error of 10−8 at 0 °C and 10−12 at 15 and 25 °C. This value is well below the levels of the UKF and EKF algorithms. The ASTRUKF algorithm outperforms the UKF and EKF algorithms in terms of prediction accuracy at different temperatures. The ASTRUKF method is well-suited for estimating SOC and has excellent adaptability to temperature variations.

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.

Robust adaptive non‐linear alignment algorithm for SINS/DVL integrated navigation system based on variational Bayesian

AbstractThe problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods, we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter (KF) theory considering noise correlation. This method first extends credibility to the Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) based on the credibility theory. Further, an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation. A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm, further expanding its application scenarios, and the derivation process of the formula theory is provided. Finally, the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives, and a comparative analysis conducted on specific experimental data. The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods, indicating that the proposed algorithm has stable estimation performance and good real-time performance.

Underwater image classification based on image enhancement and information quality evaluation

Underwater target imaging is widely used in oceans, rivers and lakes detection fields, but due to the existence of water on light absorption scattering attenuation effect, the diffraction limit of imaging system, aberration distortion and underwater turbulence, underwater images has serious degradation, mainly manifested in noise, fuzzy and low resolution, etc. In recent years, some scholars have started from the image enhancement and restoration to improve the image degradation and improve the image clarity, but the effect still needs to be improved, and the resolution can not be improved, and some algorithms will even reduce the resolution.Resolution is an important parameter for the image evaluation, improving the image quality in the underwater imaging, especially in the human eye vision, which is largely determined by the improved resolution. Therefore, this paper starts from each aspects of image processing, studies, proposes and experiments a large number of image recovery algorithms. This paper analyzes various factors introducing noise in underwater imaging process, proposes block mixed filter image denoising method based on noise statistical characteristics, analyzes the necessity of evaluating image quality by using objective indicators, and gives the corresponding objective evaluation parameters according to the characteristics of the image recovery algorithm. According to the noise preprocessing method and the image quality evaluation method, the underwater image synthesis dataset is screened to improve the performance of the underwater object recognition model.

TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing: from synaptic plasticity to stochastic resonance.

We characterize TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing. We analyze different features that allow the devices to mimic biological synapses and present the models to reproduce analytically some of the data measured. In particular, we have measured the spike timing dependent plasticity behavior in our devices and later on we have modeled it. The spike timing dependent plasticity model was implemented as the learning rule of a spiking neural network that was trained to recognize the MNIST dataset. Variability is implemented and its influence on the network recognition accuracy is considered accounting for the number of neurons in the network and the number of training epochs. Finally, stochastic resonance is studied as another synaptic feature. It is shown that this effect is important and greatly depends on the noise statistical characteristics.

Self-Tuning Process Noise in Variational Bayesian Adaptive Kalman Filter for Target Tracking

Many practical systems, such as target tracking, navigation systems, autonomous vehicles, and other applications, are usually applied in dynamic conditions. Thus, the actual noise statistics characteristics of these systems are generally time varying and unknown, which will deteriorate the state estimation accuracy of the Kalman filter (KF) and even cause filter diverging. To address this issue, this paper proposes an adaptive process noise covariance (Qk)-based variational Bayesian adaptive Kalman filter (AQ-VBAKF) algorithm. Firstly, the adaptive factor is introduced to self-tune the process noise covariance; the adaptive factor is obtained based on the innovation sequences, which can adapt to the input measurement values. Then, the VB solution is applied to approximate the time variant and unknown measurement noise covariance. Therefore, this proposed algorithm can adjust the process noise covariance and the measurement noise covariance simultaneously based on the variable input signals, which can improve the self-adaptive ability of the state estimation filter in dynamic conditions. According to the dynamic target tracking test results, the proposed AQ-VBAKF outperforms several other existing filtering methods in estimation accuracy, robustness, and computational efficiency.

An Intelligent Cost-Reference Particle Filter with Resampling of Multi-Population Cooperation.

Although the cost-reference particle filter (CRPF) has a good advantage in solving the state estimation problem with unknown noise statistical characteristics, its estimation accuracy is still affected by the lack of particle diversity and sensitivity to the particles' initial value. In order to solve these problems of the CRPF, this paper proposed an intelligent cost-reference particle filter algorithm based on multi-population cooperation. A multi-population cooperative resampling strategy based on ring structure was designed. The particles were divided into multiple independent populations upon initialization, and each population generated particles with a different initial distribution. The particles in each population were divided into three different particle sets with high, medium and low weights by the golden section ratio according to the weight. The particle sets with high and medium weights were retained. Then, a cooperative strategy based on Gaussian mutation was designed to resample the low-weight particle set of each population. The high-weight particles of the previous population in the ring structure were randomly selected for Gaussian mutation to replace the low-weight particles in the current population. The low-weight particles of all populations were resampled in turn. The simulation results show that the intelligent CRPF based on multi-population cooperation proposed in this paper can reduce the sensitivity of the CRPF to the particles' initial value and improve the particle diversity in resampling. Compared with the general CRPF and intelligent CRPF with adaptive MH resampling (MH-CRPF), the RMSE and MAE of the proposed method are lower.

An Adaptive Fusion Attitude and Heading Measurement Method of MEMS/GNSS Based on Covariance Matching.

Aimed at the problem of filter divergence caused by unknown noise statistical characteristics or variable noise characteristics in an MEMS/GNSS integrated navigation system in a dynamic environment, on the basis of revealing the parameter adjustment logic of covariance matching adaptive technology, a fusion adaptive filtering scheme combining innovation-based adaptive estimation (IAE) and the adaptive fading Kalman filter (AFKF) is proposed. By setting two system tuning parameters, for the process noise covariance adaptation loop and the measurement noise covariance adaptation loop, covariance matching is sped up and achieves an effective suppression of filter divergence. The vehicle-mounted experimental results show that the mean square error of the combined attitude error obtained based on the fusion filtering method proposed in this paper is better than 0.5°, and the mean square error of the heading error is better than 1.5°. The results can provide technical support for the continuous extraction of low-cost attitude information from mobile platforms.

State of charge estimation for lithium-ion batteries based on fractional order multiscale algorithm

The accuracy of state of charge (SoC) plays a critical role in lithium-ion batteries management system, whereas it gradually reduces as ohmic internal resistance growing and maximum available capacity decreasing with battery aging, which is still an open and challenging problem in SoC estimation. To tackle this issue, a multi-scale estimation algorithm is proposed by incorporating fractional order adaptive extended Kalman filter and variable forgetting factor recursive least square (FOAEKF-VFFRLS). Firstly, in order to describe the physicochemical reactions inside battery accurately, a fractional order model of lithium-ion battery with its discrete form is introduced, and the resistor-capacitor (RC) values as well as the order of capacitors are obtained by employing ant colony algorithm (ACA). Secondly, for enhancing SoC estimation accuracy, a fractional order adaptive extended Kalman filter algorithm (FOAEKF) is proposed to continuously modify the noise statistical characteristics while utilizing observation data information. Thirdly, to predict ohmic internal resistance and maximum available capacity for battery, a variable forgetting factor recursive least square algorithm (VFFRLS) is established based on the fact that forgetting factor determined by individual data error would be suddenly changes in the case of inaccurate or perturbed data. Besides, to further improve the accuracy of SoC estimation, a multi-scale estimation approach is proposed in light of the slow variation of battery internal resistance and the fast change of SoC. Finally, through comparative experiments, it is proved that the proposed approach has comprehensive strengths. First, the minimum root mean square error (RMSE) of SoC estimation error is controlled within 0.52 %. Second, terminal voltage error is kept small while limiting SoC errors within narrow ranges. Third, favorable robustness in terms of SoC estimation is achieved despite SoC initial value is mis-initialized.

Discrete-time complementary filter for attitude estimation based on MARG sensor

The MARG sensor, which stands for the combination of a magnetometer, an accelerometer, and a gyroscope, is widely used for 3D attitude measurement. Among the mainstream solutions for MARG-based attitude estimation, the complementary filter (CF) is normally regarded as a simplified alternative to the Kalman filter (KF), mainly because CF can reduce the amount of calculations. A dual-vector discrete-time CF (DV-DTCF) and its tuning methods are introduced in this paper. Different from the quaternion-based attitude estimation algorithms, DV-DTCF has a linear measurement model, since it utilizes the gravity and geomagnetic vectors as its state variables instead of quaternions. This feature of DV-DTCF can avoid linearization error or the use of nonlinear algorithms, and can also greatly reduce its computational complexity. More interestingly, it is analytically revealed, and experimentally proven, that the proposed DV-DTCF is fully equivalent to a fixed-gain KF. This fascinating fact leads straightforwardly to the tuning methods of DV-DTCF via the corresponding fixed-gain KF and Riccati equation. These tuning methods of DV-DTCF are based on the statistic characteristics of MARG sensor noise, and that makes them solid and feasible. According to experimental results, DV-DTCF can achieve the same accuracy as that of commonly-used KF algorithms in MARG-based attitude estimation, but with much lower time consumption. Hence, the proposed DV-DTCF is especially suitable for applications that have strict limitations on computational costs.

Estimation of Longitudinal Force, Sideslip Angle and Yaw Rate for Four-Wheel Independent Actuated Autonomous Vehicles Based on PWA Tire Model.

This article introduces an efficient and high-precision estimation framework for four-wheel independently actuated (FWIA) autonomous vehicles based on a novel tire model and adaptive square-root cubature Kalman filter (SCKF) estimation strategy. Firstly, a reliable and concise tire model that considers the tire’s nonlinear mechanics characteristics under combined conditions through the piecewise affine (PWA) identification method is established to improve the accuracy of the lateral dynamics model of FWIA autonomous vehicles. On this basis, the longitudinal relaxation length of each tire is integrated into the lateral dynamics modeling of FWIA autonomous vehicle. A novel nonlinear state function, including the PWA tire model, is proposed in this paper. To reduce the impact of the uncertainty of noise statistics on the estimation accuracy, an adaptive SCKF estimation algorithm based on the maximum a posteriori (MAP) criterion is proposed in the estimation framework. Finally, the estimation accuracy and stability of the adaptive SCKF algorithm are verified by the co-simulation of CarSim and Simulink. The simulation results show that when the statistical characteristics of noise are unknown and the target state changes suddenly under critical maneuvers, the estimation framework proposed in this paper still maintains high accuracy and stability.

An improved initial alignment method based on adaptive robust CKF algorithm

When the misalignment angle is a large angle in the strapdown inertial navigation system (SINS), it is necessary to establish a nonlinear error model to estimate the error. Hence, an improved initial alignment method based on adaptive robust CKF algorithm is proposed in this paper. Firstly, based on the analysis results, SINS/GPS nonlinear error model is established. Secondly, in the view of observation gross errors and inaccurate noise statistical characteristics, adaptive robust CKF algorithm is designed. Finally, according to simulation analysis and experiment, adaptive robust CKF algorithm can augment the stability, improve filter estimation accuracy and convergence rate, which significantly improves the initial alignment ability of strapdown inertial navigation system at large azimuth misalignment angle.

A reliable estimation method for mining lithium-ion battery

Power battery SOC (state of charge, SOC) is one of the important decision-making factors of energy management. Accurate estimation plays an important role in optimizing vehicle energy management and improving the utilization of power battery energy. The key to accurate estimation of SOC is to determine circuit model parameters and estimation methods. The research object of this article is lithium manganese oxide battery for mining (LiMn2O4). The experiments of multiplying power, temperature and HPPC (hybrid pulse power characteristic, HPPC) are carried out. A self-tuning calculation method of dynamic system is proposed, and the dynamic self-tuning model based on second-order RC is established. At the same time, in view of the shortcoming that the UKF (Unscented Kalman Filter, UKF) algorithm cannot estimate the noise in real time, In order to improve the accuracy of battery SOC estimation, an adaptive square root unscented Kalman filter (ASR-UKF) algorithm is proposed, which can make the noise statistical characteristics follow the estimation results for adaptive adjustment. Finally, the constant current and dynamic conditions are tested. The results show that the maximum change rate of model parameters with magnification is 76%, and the maximum change rate with temperature is 73.7%. The analysis of dynamic characteristics is a key factor to improve the accuracy of SOC estimation; ASR-UKF Compared with the UKF algorithm, the error is reduced by 78% under constant current conditions and 85.7% under dynamic conditions. The reliability and real-time performance of the algorithm can be obtained by comparing the simulation data with the actual data. The conclusions of this paper can be used as a theoretical basis, which can be used for model analysis of lithium batteries for mining and estimation of internal state variables.

Efficient Residual Shrinkage CNN Denoiser Design for Intelligent Signal Processing: Modulation Recognition, Detection, and Decoding

The noises embedded in signals will degrade the signal processing quality. Traditional denoising algorithms might not work in practical systems since the statistical characteristics of noises might not be learned. To address this issue, we propose an efficient residual shrinkage convolutional neural network (RSCNN) aided denoiser based on the principle of the domain transformation, shrinking and inverse transforming operations conducted by the traditional denoiser. The proposed RSCNN is composed by the batch normalization layer, domain transformation layers, the shrinkage module and inverse transformation layers, wherein transformation layers consist of convolutional layers and the nonlinear activation function. Moreover, we propose a thresholds learning subnetwork to automatically determine the thresholds, so as to enhance noise suppressing performances. Furthermore, we compose the data set by preprocessing the received signals, and design the loss function according to different denoising requirements. To validate the efficiency and universality of the RSCNN aided denoiser, we apply the proposed RSCNN denoiser to three different application scenarios, including the modulation recognition, detection and decoding. After the offline training, at the online deployment stage, we utilize the RSCNN denoiser to reduce the noise power and improve the signal to noise ratios. Simulation results demonstrate that the proposed intelligent denoiser can efficiently improve the signal processing capabilities to achieve higher modulation recognition accuracy, better detection and decoding performances with lower complexity than benchmark schemes.

An Approximate Maximum Likelihood Estimator for Instantaneous Frequency Estimation of Multicomponent Nonstationary Signals

Nonstationary signals are widely observed in various applications. The instantaneous frequency (IF) is an important feature to capture the time-frequency (TF) characteristics of nonstationary signals, so the IF estimation problem has attracted increasing interests in the past three decades. In practice, the signal is usually composed of multiple components, and their IFs may intersect or are closely spaced with each other, which cannot be easily identified from the TF representation (TFR). In this case, the maximum likelihood estimator (MLE), which does not rely on the TFR, is commonly used. However, the MLE cannot deal with signals with time-varying amplitudes and suffers from a large computing load due to the multidimensional search within an indefinite parameter space. To address these problems, we propose an approximate MLE (AMLE). First, the IF is approximated by the Chebyshev interpolation polynomial and represented by several Chebyshev interpolation frequencies which are well bounded between zero and half of the sampling frequency, so that the multidimensional search can be performed within a bounded search space. Then, an approximate maximum likelihood function, which considers both the statistical characteristics of noise and the time-varying characteristics of amplitudes, is derived for amplitude-modulated and frequency-modulated signals. It is proven that the AMLE outperforms the MLE in the computing efficiency and estimation accuracy for nonstationary signals with more complicated IFs and amplitudes. Experimental hydroelectric rotor vibration and radar signals are tested, where the AMLE can accurately find those intersected and closely spaced IFs for their constituent components.

Magnetic Field Positioning Technology of Indoor Sports Bodies

Aiming at the problem of the failure of the global positioning system in the satellite denied environment, and facing the needs of the navigation and positioning in indoor space, the technology of indoor magnetic field vector positioning and navigation have been studied. Based on the geomagnetic matching technology, the wavelet analysis method is used to estimate the noise components and statistical characteristics of the magnetic field three-dimensional signal; combined with the Kalman filtering algorithm, through estimating and optimizing the magnetic field vector signal, an indoor magnetic positioning signal processing algorithm with wavelet analysis and Kalman fusion is established, realizing the optimization of the measurement accuracy of the geomagnetic signal and the accuracy of the fingerprint map. The experimental results indicate that the signal-to-noise ratio of the test sequence is increased by 3db, the root mean square error is reduced by about 30%, and the maximum positioning error reaches 1.34m, which can meet the requirements of indoor positioning.

Guaranteed Estimation of Solutions to the Cauchy Problem When the Restrictions on Unknown Initial Data Are Not Posed

The paper deals with Cauchy problems for first-order systems of linear ordinary differential equations with unknown data. It is assumed that the right-hand sides of equations belong to certain bounded sets in the space of square-integrable vector-functions, and the information about the initial conditions is absent. From indirect noisy observations of solutions to the Cauchy problems on a finite system of points and intervals, the guaranteed mean square estimates of linear functionals on unknown solutions of the problems under consideration are obtained. Under an assumption that the statistical characteristics of noise in observations are not known exactly, it is proved that such estimates can be expressed in terms of solutions to well-defined boundary value problems for linear systems of impulsive ordinary differential equations.