Observation Noise Research Articles

Application of optimized Kalman filtering in target tracking based on improved Gray Wolf algorithm

High precision is a very important index in target tracking. In order to improve the prediction accuracy of target tracking, an optimized Kalman filter approach based on improved Gray Wolf algorithm (IGWO-OKF) is proposed in this paper. Since the convergence speed of traditional Gray Wolf algorithm is slow, meanwhile, the number of gray wolves and the choice of the maximum number of iterations has a great influence on the algorithm, a nonlinear control parameter combination adjustment strategy is proposed. An improved Grey Wolf Optimization algorithm (IGWO) is formed by determining the best combination of adjustment parameters through the fastest iteration speed of the algorithm. The improved Grey Wolf Optimization algorithm (IGWO) is formed, and the process noise covariance matrix and observation noise covariance matrix in Kalman filter are optimized by IGWO. The proposed approach is applied into. The experiment results show that the proposed IGWO-OKF approach has low error, high accuracy and good prediction effect.

Multiple adaptive factors based interacting multiple model estimator

AbstractIn the field of optoelectronic tracking, precisely modeling the motion equations of the tracked target is often challenging, and in some cases, they may even be entirely unknown. This necessitates the use of a robust state estimator for accurate state estimation. Additionally, atmospheric turbulence, variations in illumination, and intricate observation backgrounds may introduce a significant increase in observation noise for the tracked target. To address these challenges, one approach is to introduce adaptive factors, such as the Mahalanobis method, into the robust state estimator to enhance estimation accuracy. However, further exploration has revealed that adaptive factors designed using different methods offer unique advantages in scenarios with varying levels of noise amplification. In this paper, different adaptive factors are further combined using an interacting multiple model approach, allowing the designed state estimator to exhibit stronger adaptability to noise amplification. The stability and effectiveness of this algorithm are validated through program simulations, double reflection mirror experiment, and drone trace prediction, demonstrating its applicability and reliability in diverse scenarios.

Data Assimilation of Ideally Expanded Supersonic Jet Using RANS Simulation for High-Resolution PIV Data

Data assimilation using particle image velocimetry (PIV) and Reynolds-averaged Navier–Stokes (RANS) simulation was performed for an ideally expanded supersonic jet flying at a Mach number of 2.0. The present study aims to efficiently reconstruct all the physical quantities in the aeroacoustic fields that match well with a realistic, experimentally obtained flow field. The two-dimensional, two-component PIV measurement was applied to the jet axis plane, and the time-averaged velocity field was obtained using single-pixel ensemble correlation. Two-dimensional axisymmetric RANS simulation using the Menter shear stress transport (SST) model was also performed, and the parameters of the SST model were optimized via data assimilation using the ensemble Kalman filter. The standard deviation of the observation noise σ, which is a parameter of the ensemble Kalman filter, is estimated by the previously proposed method (Nakamura et al., Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES. Int. J. Comp. Fluid. Dyn., 2022), and its effectiveness was investigated for the first time. This method effectively estimated the magnitude of σ at each generation without tuning the hyperparameters. The assimilated flow fields exhibited similar flow structures observed in PIV such as the potential core length or shear layer. Therefore, the present framework can be used to estimate time-averaged full flow fields that match well with experimentally observed flow fields, and has the potential to construct a database for the Navier-Stokes-based stability analysis that requires a full flow field.

How representative are air transport functional complex networks? A quantitative validation.

Functional networks have emerged as powerful instruments to characterize the propagation of information in complex systems, with applications ranging from neuroscience to climate and air transport. In spite of their success, reliable methods for validating the resulting structures are still missing, forcing the community to resort to expert knowledge or simplified models of the system's dynamics. We here propose the use of a real-world problem, involving the reconstruction of the structure of flights in the US air transport system from the activity of individual airports, as a way to explore the limits of such an approach. While the true connectivity is known and is, therefore, possible to provide a quantitative benchmark, this problem presents challenges commonly found in other fields, including the presence of non-stationarities and observational noise, and the limitedness of available time series. We explore the impact of elements like the specific functional metric employed, the way of detrending the time series, or the size of the reconstructed system and discuss how the conclusions here drawn could have implications for similar analyses in neuroscience.

Study on Damage Inference of Parker Trusses Based on Bayesian Principles

The assessment of the health condition and safety of engineering structures is currently a research focus in the field of civil engineering. The traditional deterministic model for damage recognition is limited by the fine reading of field inspections and the accuracy of experts, resulting in a low recognition rate. Structural damage identification methods that consider uncertainty have been developed due to modelling errors, observation noise, system time variability, and other factors that lead to uncertainty. This study focuses on the Parker truss structure, and a two-dimensional planar finite element model is established by setting various key parameters such as prior distribution, stiffness, modulus of elasticity, node distribution, and external loading. The model is updated using the Bayesian updating principle. This principle is then combined with the finite element model. Opensees software is used for programming, and the Monte Carlo random sampling technique is used for structural damage inference. The study results demonstrate that the method can accurately identify the damage level of Parker truss structures with high robustness. The method can be of reference significance and practical value for identifying damage in truss structures.

GNSS/5G Joint Position Based on Weighted Robust Iterative Kalman Filter

The Global Navigation Satellite System (GNSS) is widely used for its high accuracy, wide coverage, and strong real-time performance. However, limited by the navigation signal mechanism, satellite signals in urban canyons, bridges, tunnels, and other environments are seriously affected by non-line-of-sight and multipath effects, which greatly reduce positioning accuracy and positioning continuity. In order to meet the positioning requirements of human and vehicle navigation in complex environments, it was necessary to carry out this research on the integration of multiple signal sources. The Fifth Generation (5G) signal possesses key attributes, such as low latency, high bandwidth, and substantial capacity. Simultaneously, 5G Base Stations (BSs), serving as a fundamental mobile communication infrastructure, extend their coverage into areas traditionally challenging for GNSS technology, including indoor environments, tunnels, and urban canyons. Based on the actual needs, this paper proposes a system algorithm based on 5G and GNSS joint positioning, aiming at the situation that the User Equipment (UE) only establishes the connection with the 5G base station with the strongest signal. Considering the inherent nonlinear problem of user position and angle measurements in 5G observation, an angle cosine solution is proposed. Furthermore, enhancements to the Sage–Husa Adaptive Kalman Filter (SHAKF) algorithm are introduced to tackle issues related to observation weight distribution and adaptive updates of observation noise in multi-system joint positioning, particularly when there is a lack of prior information. This paper also introduces dual gross error detection adaptive correction of the forgetting factor based on innovation in the iterative Kalman filter to enhance accuracy and robustness. Finally, a series of simulation experiments and semi-physical experiments were conducted. The numerical results show that compared with the traditional method, the angle cosine method reduces the average number of iterations from 9.17 to 3 with higher accuracy, which greatly improves the efficiency of the algorithm. Meanwhile, compared with the standard Extended Kalman Filter (EKF), the proposed algorithm improved 48.66%, 35.17%, and 38.23% at 1σ/2σ/3σ, respectively.

Fast fitting of spectral lines with Gaussian and hyperfine structure models

The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task. We present a new computer program Spectrum Iterative Fitter (SPIF) for the fitting of spectra with Gaussians or with hyperfine line profiles. The aim is to show the computational efficiency of the program and to use it to examine the general accuracy of approximating spectra with simple models. We describe the implementation of the program. To characterise its performance, we examined spectra with isolated Gaussian components or a hyperfine structure, also using synthetic observations from numerical simulations of interstellar clouds. We examined the search for the globally optimal fit and the accuracy to which single-velocity-component and multi-component fits recover true values for parameters such as line areas, velocity dispersion, and optical depth. The program is shown to be fast, with fits of single Gaussian components reaching on graphics processing units speeds approaching one million spectra per second. This also makes it feasible to use Monte Carlo simulations or Markov chain Monte Carlo calculations for the error estimation. However, in the case of hyperfine structure lines, degeneracies affect the parameter estimation and can complicate the derivation of the error estimates. The use of many random initial values makes the fits more robust, both for locating the global $ minimum and for the selection of the optimal number of velocity components.

Intercomparison of multi-GNSS signals characteristics acquired by a low-cost receiver connected to various low-cost antennas

With the increasing number of low-cost GNSS antennas available on the market, there is a lack of comprehensive analysis and intercomparison of their performance. Moreover, multi-GNSS observation noises are not well recognized for low-cost receivers. This study characterizes the quality of GNSS signals acquired by low-cost GNSS receivers equipped with eight types of antennas in terms of signal acquisition, multipath error and receiver noise. The differences between various types of low-cost antennas are non-negligible, with helical antennas underperforming in every respect. Compared with a geodetic-grade station, GPS and Galileo signals acquired by low-cost receivers are typically weaker by 3–9 dB-Hz. While the L1, E1 and E5b signals are well-tracked, only 72% and 86% of L2 signals are acquired for GPS and GLONASS, respectively. The signal noise for pseudoranges varies from 0.12 m for Galileo E5b to over 0.30 m for GLONASS L1 and L2, whereas for carrier-phase observations it oscillates around 1 mm for both GPS and Galileo frequencies, but exceeds 3 mm for both GLONASS frequencies. Antenna phase center offsets (PCOs) vary significantly between frequencies and constellations, and do not agree between two antennas of the same type by up to 25 mm in the vertical component. After a field calibration a of low-cost antenna and consistent application of PCOs, the horizontal and vertical accuracy is improved to a few millimeter and a few centimeter level for the multi-GNSS processing with double-differenced and undifferenced approach, respectively. Last but not least, we demonstrate that PPP-AR is possible also with low-cost GNSS receivers and antennas, and improves the precision and convergence time. The results prove that selection of low-cost antenna for a low-cost GNSS receiver is of great importance in precise positioning applications.

Modified suppressed relative entropy fuzzy c-means clustering algorithm

The Fuzzy C-means (FCM) algorithm is one of the most widely used algorithms in unsupervised pattern recognition. As the intensity of observation noise increases, FCM tends to produce large center deviations and even overlap clustering problems. The relative entropy fuzzy C-means algorithm (REFCM) adds relative entropy as a regularization function to the fuzzy C-means algorithm, which has a good ability for noise detection and membership assignment to observed values. However, REFCM still tends to generate overlapping clusters as the size of the cluster increases and becomes imbalanced. Moreover, the convergence speed of this algorithm is slow. To solve this problem, modified suppressed relative entropy fuzzy c-means clustering (MSREFCM) is proposed. Specifically, the MSREFCM algorithm improves the convergence speed of the algorithm while maintaining the accuracy and anti-noise capability of the REFCM algorithm by adding a suppression strategy based on the intra-class average distance measurement. In addition, to further improve the clustering performance of MSREFCM for multidimensional imbalanced data, the center overlapping problem and the center offset problem of elliptical data are solved by replacing the Euclidean distance in REFCM with the Mahalanobis distance. Experiments on several synthetic and UCI datasets indicate that MSREFCM can improve the convergence speed and classification performance of the REFCM for spherical and ellipsoidal datasets with imbalanced sizes. In particular, for the Statlog dataset, the running time of MSREFCM is nearly one second less than that of REFCM, and the accuracy of MSREFCM is 0.034 higher than that of REFCM.

An energy-based pulsar period estimation method using Hilbert curve and double CNNs

In order to accurately estimate the period of X-ray pulsars to improve navigation performance, this paper proposes a pulsar period estimation method based on photon energy using reverse Hilbert coding and double Convolutional Neural Networks (CNNs) discrimination. This method uses photon energy information to perform epoch folding. It converts one-dimensional contour information into two-dimensional image signals through reverse Hilbert curve and recognizes contour image features through CNN models to determine the optimal period. According to the simulation results, the period estimation accuracy of this method is 0.5350 ns, which is 65.71% higher than the χ2 epoch folding method. The contour phase accuracy is 0.0004767, which is 41.93% higher than the χ2 epoch folding method. At the same time, the observation time and noise interference that may affect the accuracy of period estimation are also quantitatively analyzed. In addition, in order to simulate real navigation scenarios, this paper also conducts dynamic period estimation experiments on PSR B0531+21 pulsar in a specific period of time. The method proposed in this paper has the advantages of high precision, fast calculation speed, strong anti-interference ability and accurate dynamic period estimation, which can significantly improve the navigation performance of X-ray pulsars.

Stochastic gradient descent with random label noises: doubly stochastic models and inference stabilizer

Random label noise (or observational noise) widely exists in practical machine learning settings. While previous studies primarily focused on the effects of label noise to the performance of learning, our work intends to investigate the implicit regularization effects of label noise, under mini-batch sampling settings of stochastic gradient descent (SGD), with the assumption that label noise is unbiased. Specifically, we analyze the learning dynamics of SGD over the quadratic loss with unbiased label noise (ULN), where we model the dynamics of SGD as a stochastic differentiable equation with two diffusion terms (namely a doubly stochastic model). While the first diffusion term is caused by mini-batch sampling over the (label-noiseless) loss gradients, as in many other works on SGD (Zhu et al 2019 ICML 7654–63; Wu et al 2020 Int. Conf. on Machine Learning (PMLR) pp 10367–76), our model investigates the second noise term of SGD dynamics, which is caused by mini-batch sampling over the label noise, as an implicit regularizer. Our theoretical analysis finds such an implicit regularizer would favor some convergence points that could stabilize model outputs against perturbations of parameters (namely inference stability). Though similar phenomenon have been investigated by Blanc et al (2020 Conf. on Learning Theory (PMLR) pp 483–513), our work does not assume SGD as an Ornstein–Uhlenbeck-like process and achieves a more generalizable result with convergence of the approximation proved. To validate our analysis, we design two sets of empirical studies to analyze the implicit regularizer of SGD with unbiased random label noise for deep neural network training and linear regression. Our first experiment studies the noisy self-distillation tricks for deep learning, where student networks are trained using the outputs from well-trained teachers with additive unbiased random label noise. Our experiment shows that the implicit regularizer caused by the label noise tends to select models with improved inference stability. We also carry out experiments on SGD-based linear regression with ULN, where we plot the trajectories of parameters learned in every step and visualize the effects of implicit regularization. The results back up our theoretical findings.

A Mean-Field Game for a Forward-Backward Stochastic System with Partial Observation and Common Noise

A Mean-Field Game for a Forward-Backward Stochastic System with Partial Observation and Common Noise

Do Faculae Affect Autocorrelation Rotation Periods in Sun-like Stars?

Rotational periods derived from autocorrelation function (ACF) techniques on stars photometrically similar to the Sun in Kepler data have proven difficult to reliably determine. We investigate various instrumental and astrophysical factors affecting the accuracy of these measurements, including the effects of observational windows and noise, stellar activity and inclination, spectral passbands, and the separate normalization of contiguous segments. We validate that the flux variations due to faculae are very periodic, but starspots are the dominant source of bolometric and visible differential variability in Sun-like stars on rotational timescales. We quantify how much stronger the relative contribution of faculae would have to be to render Sun-like light curves periodic enough to reliably measure with autocorrelation methods. We also quantify how long starspot lifetimes need to be to render pure spot light curves periodic enough. In general, longer observational windows yield more accurate ACF measurements, even when faculae are not present. Due to the enhancement of the relative contribution of faculae, observing stars with intermediate inclinations, during activity minima, and/or through bluer passbands has the effect of strengthening the periodicity of the light curve. We search for other manifestations of faculae in broadband photometry of Sun-like stars and conclude that without absolute flux measurements or restriction to shorter-wavelength passbands, differential light curves are uninformative about faculae.

Acoustic Echo Cancellation Algorithm Based on Kalman Filtering of Skewed Observation Noise

Acoustic Echo Cancellation Algorithm Based on Kalman Filtering of Skewed Observation Noise

Investigating the Global Performance of the BDS-2 and BDS-3 Joint Real-Time Undifferenced and Uncombined Precise Point Positioning Using RTS Products from Different Analysis Centers

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively.

Wastewater-based reproduction numbers and projections of COVID-19 cases in three areas in Japan, November 2021 to December 2022.

BackgroundWastewater surveillance has expanded globally as a means to monitor spread of infectious diseases. An inherent challenge is substantial noise and bias in wastewater data because of the sampling and quantification process, limiting the applicability of wastewater surveillance as a monitoring tool.AimTo present an analytical framework for capturing the growth trend of circulating infections from wastewater data and conducting scenario analyses to guide policy decisions.MethodsWe developed a mathematical model for translating the observed SARS-CoV-2 viral load in wastewater into effective reproduction numbers. We used an extended Kalman filter to infer underlying transmissions by smoothing out observational noise. We also illustrated the impact of different countermeasures such as expanded vaccinations and non-pharmaceutical interventions on the projected number of cases using three study areas in Japan during 2021-22 as an example.ResultsObserved notified cases were matched with the range of cases estimated by our approach with wastewater data only, across different study areas and virus quantification methods, especially when the disease prevalence was high. Estimated reproduction numbers derived from wastewater data were consistent with notification-based reproduction numbers. Our projections showed that a 10-20% increase in vaccination coverage or a 10% reduction in contact rate may suffice to initiate a declining trend in study areas.ConclusionOur study demonstrates how wastewater data can be used to track reproduction numbers and perform scenario modelling to inform policy decisions. The proposed framework complements conventional clinical surveillance, especially when reliable and timely epidemiological data are not available.

Signal Recognition without State Space Expansion Based on Observations Containing a Singular Interference: The Case of Nonlinear Parameters of Basis Functions

This paper proposes a novel method for recognizing a set of signals with linearly and nonlinearly included parameters from a given ensemble of signals under essential a priori uncertainty. Due to this uncertainty, well-known statistical methods become inapplicable. Signals may be present in an additive mixture containing an observation noise and a singular interference; the distribution law of the noise is unknown, and only its correlation matrix is specified. The novel method is invariant to this interference, does not require traditional state-space expansion, and ensures the decomposition and parallelization of the computational procedure. The signals and interference are represented using conventional linear spectral decompositions with unknown coefficients and given basis functions. Random and methodological errors, as well as the resulting computational effect, are analyzed. An illustrative example is provided.

Social System Inference From Noisy Observations

This article studies social system inference from a single noisy trajectory of public evolving opinions, wherein observation noise leads to the statistical dependence of samples on time and coordinates. We first propose a cyber-social system that comprises individuals in a social network and a set of information sources in a cyber layer, whose opinion dynamics explicitly takes the asymmetric cognitive bias including confirmation bias and negativity bias and the process noise into account. Based on the proposed cyber-social model, we then study the sample complexity of least-square auto-regressive model estimation, which governs the length of a single observed trajectory that is sufficient for the identified model to achieve the prescribed levels of accuracy and confidence (PAC). Building on the identified social model, we then investigate social inference, with a particular focus on the weighted network topology and the model parameters of asymmetric cognitive bias. Finally, the theoretical results and the effectiveness of the proposed inference framework are validated by the U.S. Senate Member Ideology data.

Analysis of the ensemble Kalman–Bucy filter for correlated observation noise

Analysis of the ensemble Kalman–Bucy filter for correlated observation noise

Estimation of AMSU-A and MHS Antenna Emission from MetOp-A End-of-Life Deep Space View Test

A unique End-of-Life (EOL) Deep Space View Test (DSVT) was performed on 27 November 2021 for the Advanced Microwave Sounding Unit-A (AMSU-A) and the Microwave Humidity Sounder (MHS) onboard the first EUMETSAT MetOp-A satellite in the deorbiting process. The purpose of this test is to recalibrate the antenna sidelobe, to derive antenna emission, and to quantify the in-orbit asymmetric scan biases of AMSU-A and MHS to, ultimately, improve Near Real-Time (NRT) products for MetOp-B and -C and the entire Fundamental Climate Data Records (FCDR). In this study, MetOp-A AMSU-A and MHS EOL DSVT data on 27 November 2021 have been analyzed. The deep space scene antenna temperatures were first applied for the antenna pattern correction; then, the antenna reflector channel emissivity values were derived from the corrected temperatures. For the MHS, the observed scan-angle-dependent brightness temperatures (BTs) for all channels were well behaved after the antenna pattern correction, except for channel 1. The derived antenna reflector emissivity values from this test are 0.0016, 0.0036, 0.0036, and 0.0019 for channels 1, 3, 4, and 5, respectively. For AMSU-A, the deep space view counts were not homogeneous during the test period, exhibiting large variations in the along-track and cross-track directions, mainly due to the instrument temperature’s rapid change during the test period. The large relative noise in the deep space view observations negatively impacted the data quality and limits the value of this test. The large relative noise may contribute to the different emissivity values derived from the same frequency for channels 9 to 14. We also found unexpected scan-angle-dependent BT after antenna pattern correction for quasi-vertical (QV) channels 1 and 2 when compared to the emission model. Further investigation using a simulation confirmed that channels 1 and 2 are QV channels, as designed.