Estimation Error Research Articles

Sampled-data observer design for sensorless control of wind energy conversion system with PMSG

This paper presents a nonlinear observer for a variable-speed wind energy conversion system (WECS) utilizing a permanent magnet synchronous generator (PMSG). The study addresses the design of high-gain sampled-data observers based on the nonlinear WECS model, supported by formal convergence analysis. An essential aspect of this observer design is the incorporation of a time-varying gain, significantly enhancing system performance. Convergence of estimation errors is demonstrated using the input-to-state stability method. Simulation of the proposed observer is conducted using the MATLAB-Simulink tool. The obtained results are presented and analyzed to showcase the overall effectiveness of the proposed system.

Adaptive synergetic control for electronic throttle valve system

AbstractThis study has developed adaptive synergetic control (ASC) algorithm to control the angular position of moving plate in the electronic throttle valve (ETV) system. This control approach is inspired by synergetic control theory. The adaptive controller has addressed the problem of variation in systems parameters. The control design includes two elements: the control law and adaptive law. The adaptive law is developed based on Lyupunov stability analysis of the controlled system, and it is responsible for estimating the potential uncertainties in the system. The effectiveness of the proposed adaptive synergetic control has been verified by numerical simulation using MATLAB/Simulink. The results showed that the ASC algorithm could give good tracking performance in the presence of uncertainty perturbations. In addition, a comparison study has been made to compare the tracking performance of ASC and that based on conventional synergetic control (CSC) for the ETV system. The simulated results showed that the performance of ASC outperforms that based on CSC. Moreover, the results showed that the estimation errors between the actual and estimated uncertainties are bounded and there is no drift in the developed adaptive law of ASC.

Rapid Mass Conversion for Environmental Microplastics of Diverse Shapes.

Rivers have been recognized as the primary conveyors of microplastics to the oceans, and seaward transport flux of riverine microplastics is an issue of global attention. However, there is a significant discrepancy in how microplastic concentration is expressed in field occurrence investigations (number concentration) and in mass flux (mass concentration). Of urgent need is to establish efficient conversion models to correlate these two important paradigms. Here, we first established an abundant environmental microplastic dataset and then employed a deep neural residual network (ResNet50) to successfully separate microplastics into fiber, fragment, and pellet shapes with 92.67% accuracy. We also used the circularity (C) parameter to represent the surface shape alteration of pellet-shaped microplastics, which always have a more uneven surface than other shapes. Furthermore, we added thickness information to two-dimensional images, which has been ignored by most prior research because labor-intensive processes were required. Eventually, a set of accurate models for microplastic mass conversion was developed, with absolute estimation errors of 7.1, 3.1, 0.2, and 0.9% for pellet (0.50 ≤ C < 0.75), pellet (0.75 ≤ C ≤ 1.00), fiber, and fragment microplastics, respectively; environmental samples have validated that this set is significantly faster (saves ∼2 h/100 MPs) and less biased (7-fold lower estimation errors) compared to previous empirical models.

Distribution-informed and wavelength-flexible data-driven photoacoustic oximetry.

Photoacoustic imaging (PAI) promises to measure spatially resolved blood oxygen saturation but suffers from a lack of accurate and robust spectral unmixing methods to deliver on this promise. Accurate blood oxygenation estimation could have important clinical applications from cancer detection to quantifying inflammation. We address the inflexibility of existing data-driven methods for estimating blood oxygenation in PAI by introducing a recurrent neural network architecture. We created 25 simulated training dataset variations to assess neural network performance. We used a long short-term memory network to implement a wavelength-flexible network architecture and proposed the Jensen-Shannon divergence to predict the most suitable training dataset. The network architecture can flexibly handle the input wavelengths and outperforms linear unmixing and the previously proposed learned spectral decoloring method. Small changes in the training data significantly affect the accuracy of our method, but we find that the Jensen-Shannon divergence correlates with the estimation error and is thus suitable for predicting the most appropriate training datasets for any given application. A flexible data-driven network architecture combined with the Jensen-Shannon divergence to predict the best training data set provides a promising direction that might enable robust data-driven photoacoustic oximetry for clinical use cases.

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. Finally, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem. Funding: This work was supported by the Office of Naval Research [Grant N00014-22-1-2589] and Basic Energy Sciences [Grant DE-SC0023303]. The work of J. Lei was partially supported by the National Natural Science Foundation of China [Grants 72271187 and 62088101]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0068 .

An Interactive Transient Model Correction Active Sonar Target Tracking Method

Active sonar can usually only directly measure the distance and bearing information of underwater targets, and cannot directly obtain target velocity, acceleration and other information. Therefore, the amount of information is relatively small, making it difficult to support the construction of complex motion models. At the same time, the motion state of underwater maneuvering targets is changeable. In response to the problem of detecting and tracking underwater moving targets by active sonar, this paper proposes a target transient model correction (TMC) filtering tracking method. Based on the conventional Kalman filter (KF) estimation, residual covariance is used as a signal quantity. When there is a large change in it, a transient filter with constant gain is adopted to filter the measurement value. The filtered output is used to correct the KF gain matrix and the target motion state model, to avoid the problem of increasing or even diverging KF estimation errors caused by changes in process noise. Using this method can solve the problem of maintaining stability and filtering estimation accuracy of active sonar tracking of underwater maneuvering targets with less computational and engineering costs.

Ensemble forecasting: A foray of dynamics into the realm of statistics

AbstractUncertain quantities are often described through statistical samples. Can samples for numerical weather forecasts be generated dynamically? At a great expense, they can. With statistically constrained perturbations, a cloud of initial states is created and then integrated forward in time. By now, this technique has become ubiquitous in weather and climate research and operations. Ensembles are widely used, with demonstrated value. The atmosphere evolves in a multidimensional phase space. Does a cloud of ensemble solutions encompass the evolution of the real atmosphere? Theoretically, random perturbations in high‐dimensional spaces have negligible projection in any direction, including the error in the best estimate, therefore consistently degrading that. As the bulk of the perturbation variance lies in the null space of error, samples in multidimensional space do not contain reality. An evaluation suggests that initial and short‐range forecast error and ensemble perturbations are random draws from a high‐dimensional domain we call the subspace of possible error. Error in any initial condition is partly a result of stochastic observational and assimilation noise, while perturbations explore other, mostly independent directions from the subspace of possible error that may have resulted from other configurations of stochastic noise. What benefits may arise from the deterministic projection of such noise? Consistent with theoretical expectations, ensemble members consistently degrade the skill of the unperturbed forecast until medium range. The mean and all other products derived from ensembles suffer an 18‐hour loss in forecast Information. Since Information is a sufficient statistic, any rational user can benefit more from the unperturbed, than from an ensemble of weather forecasts. Furthermore, case‐dependent variations in the distribution or spread of ensembles have no impact on commonly used metrics. Can alternative, statistical applications provide comparable, or even higher‐quality probabilistic and other products, at the fraction of the cost of running an ensemble?

Computed tomographic age estimation from the iliac crest and ischial tuberosity in an Indian population using supervised machine learning approaches.

Within the pelvis the iliac crest and ischial tuberosity display delayed ossification and fusion, thus, presenting as reliable maturity indicators. Amongst the different iliac crest and ischial tuberosity age estimation methods, the modified Kreitner-Kellinghaus stages constitute one of the more promising methods. The present study was directed towards establishing the applicability of the modified Kreitner-Kellinghaus method using five supervised machine learning approaches. Clinical CT scans of consenting individuals were collected and scored using the modified Kreitner-Kellinghaus method for the iliac crest and ischial tuberosity, independently. Age was subsequently estimated using different machine learning models. Cumulative scores computed from both markers were additionally employed for age estimation using machine learning. For iliac crest age estimation, Random Forest and Gradient Boosting Regression furnished lowest mean absolute error (2.42 years) and root mean square error (3.06 years). For ischial tuberosity age estimation, Gradient Boosting Regression garnered the lowest computations of mean absolute error (2.60 years) and root mean square error (3.09 years). For cumulative score based age estimation, Support Vector Regression and Gradient Boosting Regression yielded lowest mean absolute error (2.48 years) and root mean square error (3.07 years). Obtained error computations indicate that the iliac crest is a more accurate age marker in comparison to the ischial tuberosity. Additionally, cumulative score-based approaches garnered similar/ marginally more precise results in comparison to the iliac crest with all five models. This marginal improvement is not sufficient to justify employing the relatively more complicated cumulative score-based approach for age estimation. Hence, whenever available, the iliac crest should be preferred over the ischial tuberosity/ cumulative score-based approaches for age estimation.

The effects of non-local observations on the adjoint estimation of local model parameters: An example of Manning’s n coefficient in a tidal model over the Bohai, Yellow, and East China Seas

Accurate parameter estimation is a key issue for enhancing the performance of hydrological models. With the rapid development of satellite technology, integrating satellite data and numerical modelling for parameter estimation has gained more prominence. The limited spatial coverage of altimeters necessitates areas without direct local observations to rely only on information from nearby non-local observations. However, the relation is far from clear between non-local observations and the estimation of local model parameters. In this study, a two-dimensional adjoint tidal model over the Bohai, Yellow, and East China Seas (BYECS) is developed, assimilating observations from TOPEX/Poseidon, Jason-1, and Jason-2 altimeters in conjunction with tide-gauge stations. In twin experiments, the feasibility and reliability of utilizing non-local observations are emphasized by varying synthetic observations. The experiments also reveal how the number and distance of non-local observations affect the ill-posedness of local parameter estimation. The estimation errors can be reduced by increasing observations within a ‘critical distance’, beyond which the accuracy does not improve further. Subsequently, the robustness of ‘critical distance’ is discussed under different prescribed parameter distributions, sizes of predefined optimized area, and random observational errors, indicating that the ‘critical distance’ is approximately 1.0°-2.0°. These results provide a positive reference for practical experiment. In BYECS, the order of Manning’s n coefficient ranges from 10-4 to 10-1, with an average value of 0.0246 in shallow waters. The spatial distribution reveals 9 high-value areas, primarily modulated by a concurrence of sandy sediment and weak tidal currents. This study offers valuable insights into refining the adjoint model for physical parameter estimation, particularly in anticipation of the expanded spatial coverage of SWOT. Compared to only assimilating T/P series altimeters, incorporating SWOT reduces discrepancies by over 38%. Additionally, the spatial Manning’s n coefficient provides guidance for enhancing tidal simulation in other models.

Structure tensor-based Gaussian kernel edge-adaptive depth map refinement with triangular point view in images

&lt;span lang="EN-US"&gt;Image reconstruction is the process of restoring the image resolution. In 3D image reconstruction, the objects in different viewpoints are processed with the triangular point view (TPV) method to estimate object geometry structure for 3D model. This work proposes a depth refinement methodology in preserving the geometric structure of objects using the structure tensor method with a Gaussian filter by transforming a series of 2D input images into a 3D model. The computation of depth map errors can be found by comparing the masked area/patch with the distribution of the original image's greyscale levels using the error pixel-based patch extraction algorithm. The presence of errors in the depth estimation could seriously deteriorate the quality of the 3D effect. The depth maps were iteratively refined based on histogram bins number to improve the accuracy of initial depth maps reconstructed from rigid objects. The existing datasets such as the dataset tanks and unit (DTU) and Middlebury datasets, were used to build the model out of the object scene structure. The results of this work have demonstrated that the proposed patch analysis outperformed the existing state of the art models depth refinement methods in terms of accuracy.&lt;/span&gt;

Selecting Invalid Instruments to Improve Mendelian Randomization with Two-Sample Summary Data.

Mendelian randomization (MR) is a widely-used method to estimate the causal relationship between a risk factor and disease. A fundamental part of any MR analysis is to choose appropriate genetic variants as instrumental variables. Genome-wide association studies often reveal that hundreds of genetic variants may be robustly associated with a risk factor, but in some situations investigators may have greater confidence in the instrument validity of only a smaller subset of variants. Nevertheless, the use of additional instruments may be optimal from the perspective of mean squared error even if they are slightly invalid; a small bias in estimation may be a price worth paying for a larger reduction in variance. For this purpose, we consider a method for "focused" instrument selection whereby genetic variants are selected to minimise the estimated asymptotic mean squared error of causal effect estimates. In a setting of many weak and locally invalid instruments, we propose a novel strategy to construct confidence intervals for post-selection focused estimators that guards against the worst case loss in asymptotic coverage. In empirical applications to: (i) validate lipid drug targets; and (ii) investigate vitamin D effects on a wide range of outcomes, our findings suggest that the optimal selection of instruments does not involve only a small number of biologically-justified instruments, but also many potentially invalid instruments.

A visual identification method of the growth posture of young peach fruits in orchards

A network model was proposed for identifying the growth posture of young peach fruits in orchards (YOLON) with the YOLOv5 network model in view of identifying the growth posture of young peach fruits in the natural growth state of orchards. First of all, Coordinate Attention (CA) was added based on the original backbone network due to the influence of peach young fruits on the near-color background to enhance the feature extraction ability of the image. Then, a small-target detection layer was added to the backbone network to optimize the detection effect of smaller young fruits. Finally, the rotating frame was selected to replace the original horizontal frame to detect the young fruits with directional attributes. Experiments showed that proposed YOLON in the visual recognition of the growth posture of multi-directional peach young fruits had the average accuracy rate of the recognition of peach young fruit and the estimation error of its growth angle of 93.04% and ±3.94°, respectively. It has a good recognition effect, which provides a reference for the visual recognition of the growth posture of other young fruits and vegetables.

Optimal design and allocation of stealthy attacks against remote state estimation for cyber-physical systems

This paper studies the design and allocation problem for stealthy attacks against remote state estimation for cyber-physical systems, where the data are transmitted through multiple wireless communication channels. With limited budget for the available energy at each step and total energy over the finite-time horizon, the aim of the stealthy attacker is to maximize the estimation error based on the collaboration between the attack matrices and schedule, which is formulated as the optimization problem with multi-variable coupling. Under the presented framework of stepwise optimization, the optimization problem is separated into two subproblems with the guarantee of optimality. First, for the optimal design of attack matrices, the analytical expression is derived by employing the proposed data isolation technique instead of the assumption utilized in the existing results that the output matrix is of full row rank. And then, for the optimal allocation of energy constrained attacks, the scheduling sequence is obtained by solving the transformed linear 0-1 programming. Finally, simulation results sustain the performance of the presented attack strategy.

Distributed State Estimation for Mixed Delays System Over Sensor Networks With Multichannel Random Attacks and Markov Switching Topology.

This article deals with the distributed state estimation for mixed delays system under unknown attacks. A new multichannel random attack model is established for the first time, where network attacks are considered to exist in three channels: the target-to-sensor channel, the senor-to-sensor channel, and the sensor-to-estimator channel. In the above model, transmitted packets are allowed to be attacked multiple times simultaneously, and when they are successfully attacked, the transmitted information is modified. Besides, the topology of the sensor network is considered to change dynamically according to the Markov chain. Based on the newly established distributed estimation model, the estimation error system is proven to be asymptotically mean-square stable under a given H∞ antidisturbance index by using a Lyapunov theory and a stochastic analysis technique; then, the estimator parameter matrices are solved utilizing a linearization method. Finally, several simulation examples are listed to testify the effectiveness of the designed algorithm.

A mean flow velocity estimation scheme based on flow field characteristics and distribution point optimization for carbon monitoring in coal-fired power plants: A numerical study

CO2 online monitoring provides a method to obtain carbon emissions by directly quantifying the flue gas flow rate and CO2 concentration. However, significant flow rate measurement errors arise due to the complexity of turbulence in large-diameter stacks. To address the issue, this study utilizes turbulence numerical simulation combined with mean velocity estimation error analysis to investigate the flow field of typical stacks in coal-fired power plants. The simulation results demonstrated that the evolution of turbulence exaggerates velocities. The flow field exhibits stable turbulence characteristics in a single-introduced stack, while in the double-introduced stack, the flow field dynamically evolves due to asymmetric collisions and abrupt expansions. Furthermore, the effects of load and temperature on the estimation error of flow velocity are established. The optimum monitoring height, the ideal chord angle and the stepped number of deployment points based on the log-linear method are determined. Within the single-introduced stack, a correction factor is introduced and a corresponding formula is established that links estimation errors with monitoring heights. This resulted in a dramatic reduction of the maximum estimation error from 14% to 0.3%. Finally, the systematic and simplified optimization scheme for estimating mean flow velocity is summarised, which provides a powerful reference for flow rate measurement for online CO2 monitoring in coal-fired power plants.

Exploring the Big Data Paradox for various estimands using vaccination data from the global COVID-19 Trends and Impact Survey (CTIS).

Selection bias poses a substantial challenge to valid statistical inference in nonprobability samples. This study compared estimates of the first-dose COVID-19 vaccination rates among Indian adults in 2021 from a large nonprobability sample, the COVID-19 Trends and Impact Survey (CTIS), and a small probability survey, the Center for Voting Options and Trends in Election Research (CVoter), against national benchmark data from the COVID Vaccine Intelligence Network. Notably, CTIS exhibits a larger estimation error on average (0.37) compared to CVoter (0.14). Additionally, we explored the accuracy (regarding mean squared error) of CTIS in estimating successive differences (over time) and subgroup differences (for females versus males) in mean vaccine uptakes. Compared to the overall vaccination rates, targeting these alternative estimands comparing differences or relative differences in two means increased the effective sample size. These results suggest that the Big Data Paradox can manifest in countries beyond the United States and may not apply equally to every estimand of interest.

Advancing state estimation for lithium-ion batteries with hysteresis through systematic extended Kalman filter tuning

Knowledge of remaining battery charge is fundamental to electric vehicle deployment. Accurate measurements of state-of-charge (SOC) cannot be obtained directly and estimation methods must be used instead. This requires both a good model of a battery and a well-designed state estimator. Here, hysteretic reduced-order battery models and adaptive extended Kalman filter estimators are shown to be highly effective, accurate predictors of SOC. A battery model parameterisation framework is proposed, which enhances standardised methods to capture hysteresis effects. The hysteretic model is parameterised for three independent NMC811 lithium-ion cells and is shown to reduce voltage RMS error by 50% across 18 h automotive drive-cycles. Parameterised models are used alongside an extended Kalman filter, which demonstrates the value of adaptive filter parameterisation schemes. When used alongside an extended Kalman filter, adaptive covariance matrices yield highly accurate SOC estimates, reducing SOC estimation error by 85%, compared to the industry standard battery model.

Image moment-based visual positioning and robust tracking control of ultra-redundant manipulator

Image moment features can describe more general target patterns and have good decoupling properties. However, the image moment features that control the camera’s rotation motion around the x-axis and y-axis mainly depend on the target image itself. In this paper, the ultra-redundant manipulator visual positioning and robust tracking control method based on the image moments are advocated.First, six image moment features used to control camera motion around the x-axis and around the y-axis are proposed. And then, a novel method is proposed to use to select image features. For tracking a moving target, a kalman filter combined with adaptive fuzzy sliding mode control method is proposed to achieve tracking control of moving targets, which can estimate changes in image features caused by the target’s motion on-line and compensate for estimation errors. Finally, the experimental system based on Labview-RealTime system and ultra-redundant manipulator is used to verify the real-time performance and practicability of the algorithm. Experimental results are presented to illustrate the validity of the image features and tracking method.

Assessing Multi‐Source Precipitation Estimates in Nepal: A Benchmark for Sub‐Seasonal Model Assessment

AbstractSub‐seasonal to seasonal (S2S) prediction provides an extended range of lead time for decision‐makers across multiple sectors. S2S forecast is crucial for a country that are susceptible to hydro‐meteorological disasters like Nepal. However, S2S forecast requires assessment with reliable datasets before its application. Since, Nepal lacks a dense station network, multi‐source precipitation estimates (MPEs) are the obvious alternatives. Therefore, using classical evaluation metrics and extreme precipitation indices, this study assessed eleven high‐resolution datasets against 159‐gauge stations over Nepal for the 2001–2020 period. These datasets are classified as gauge‐interpolated (APHRODITE), merged (TPMFD, MSWEP, CLDAS, and CHIRPS), satellite‐based (IMERGV7, IMERGV6, CMORPH, and PERSIANN), and reanalysis (ERA5‐L and HAR). Satellite datasets (except IMERGV7) failed to capture the spatial pattern of mean annual precipitation, while others broadly captured it. Most MPEs struggled to accurately estimate wet season precipitation compared to dry season. Furthermore, increasing estimation error from light to extreme precipitation and decreasing skill metrics from flat to complex terrain, demonstrate the intensity and terrain‐specific limitations of MPEs. In terms of precipitation extremes, APHRODITE exhibits the highest skill, followed by MSWEP, TPMFD, HAR, ERA5‐L, IMERGV7, CLDAS, IMERGV6, CHIRPS, CMORPH, and PERSIANN. IMERGV7 exhibits increased skill in detecting extreme precipitation and precipitation over orography against IMERGV6. APHRODITE and TPMFD datasets performed consistently well in all scales, including weekly anomaly, with an average anomaly correlation of 0.84 and 0.66 respectively. However, since APHRODITE is not widely available, TPMFD can serve as a benchmark dataset for evaluating high‐resolution S2S forecasts within the study region.

Optimisation of the Transmitter Layout in a VLP System Using an Aperture-Based Receiver

In this paper, we consider a visible light positioning (VLP) system, where an array of photo diodes combined with apertures is used as a directional receiver and a set of inexpensive and energy-efficient light-emitting diodes (LEDs) is used as transmitters. The paper focuses on the optimisation of the layout of the transmitter, i.e., the number and placement of the LEDs, to meet the wanted position estimation accuracy levels. To this end, we evaluate the Cramer–Rao bound (CRB), which is a lower bound on the mean-squared error (MSE) of the position estimate, to analyse the influence of the LEDs’ placement. In contrast to other works, where only the location of the LEDs was considered and/or the optimisation was carried out through simulations, in this work, the optimisation is carried out analytically and considers all the parameters involved in the VLP system as well as the illumination. Based on our results, we formulate simple rules of thumb with which we can determine the spacing between LEDs and the minimum number of LEDs, as well as their position on the ceiling, while also taking into account the requirements for the illumination.