Estimation Error Research Articles

UWB distance estimation errors in (non-)line of sight situations within the context of 3D analysis of human movement

Abstract Integrated Ultrawideband (UWB) and Magnetic Inertial Measurement Unit (MIMU) sensors are becoming popular for indoor localization applications, as a higher accuracy can be achieved than with just MIMU sensors. These integrated sensors could extend stability and accuracy in the field of 3D analysis of human movement (3D AHM) if they can deliver position estimates with an accuracy close to 1 cm. Achieving this high accuracy of 1 cm remains challenging, with most studies reporting position estimation errors around 5 cm, often due to Non-Line of Sight (NLOS) conditions and systematic UWB sensor distance estimation errors. Studying the distance error characteristic of UWB in situations of 3D AHM is essential to deal with these errors. While research on UWB distance errors in Line of Sight (LOS) and NLOS situations exists, few studies focus on the NLOS errors caused by the human body and were not in the relevant scenarios of 3D AHM. Therefore, this article examines UWB sensor performance and distance error characteristics in LOS and NLOS situations typical for the 3D AHM. Both the LOS and NLOS situations were studied in the typical 3D AHM distance range of 0.2 m to 2 m. The NLOS situations were studied first with a human subject as NLOS causing object and then with simulated human body segments (PVC pipes filled with water) of varying diameters. In LOS situations, consistent systematic bias errors were observed, along with incidental errors at specific positions in the room. In NLOS scenarios caused by the human and simulated body segments, a consistent and reproducible overestimation of distances was found. The reproducibility of these errors based on relative node and object positions suggests that systematic mitigation methods could significantly reduce errors, enabling more accurate and reproducible 3D human movement analysis.

Contact State Recognition for Dual Peg-in-Hole Assembly of Tightly Coupled Dual Manipulator

Contact state recognition is a critical technology for enhancing the robustness of robotic assembly tasks. There have been many studies on contact state recognition for single-manipulator, single peg-in-hole assembly tasks. However, as the number of pegs and holes increases, the contact state becomes significantly more complex. Additionally, when a tightly coupled multi-manipulator is required, the estimation errors in the contact forces between pegs and holes make contact state recognition challenging. The current state recognition methods have not been tested in such tasks. This paper tested Support Vector Machine (SVM) and several neural network models on these tasks and analyzed the recognition accuracy, precision, recall, and F1 score. An ablation experiment was carried out to test the contributions of force, image, and position to the recognition performance. The experimental results show that SVM has better performance than the neural network models. However, when the size of the dataset is limited, SVM still faces generalization issues. By applying heuristic action, this paper proposes a two-stage recognition strategy that can improve the recognition success rate of the SVM.

Accurate and Reliable Food Nutrition Estimation Based on Uncertainty-Driven Deep Learning Model

Mobile Near-Infrared Spectroscopy (NIR) devices are increasingly being used to estimate food nutrients, offering substantial benefits to individuals with diabetes and obesity, who are particularly sensitive to food intake. However, most existing solutions prioritize accuracy, often neglecting to ensure reliability. This oversight can endanger individuals sensitive to specific foods, as it may lead to significant errors in nutrient estimation. To address these issues, we propose an accurate and reliable food nutrient prediction model. Our model introduces a loss function designed to minimize prediction errors by leveraging the relationships among food nutrients. Additionally, we developed a method that enables the model to autonomously estimate its own uncertainty based on the loss, reducing the risk to users. Comparative experiments demonstrate that our model achieves superior performance, with an R2 value of 0.98 and an RMSE of 0.40, reflecting a 5–15% improvement over other models. The autonomous result rejection mechanism showing a 40.6% improvement further enhances robustness, particularly in handling uncertain predictions. These findings highlight the potential of our approach for precise and trustworthy nutritional assessments in real-world applications.

Can tree hollow diameter be predicted? A study of native commercial trees in the eastern brazilian Amazon

The objective of this research was to test selected and validated generic and species-specific equations to estimate three different hollow diameter measurements in native commercial trees from a managed forest in the state of Pará, Brazil. A sample of 4,912 hollow trees, involving 29 species, was used to model the mean hollow diameter at tree level, and another composed of 3,867 hollow trees, belonging to 28 species, was used to model the mean hollow diameter of the first log of the commercial stem and the hollow diameter at the base of the tree. 30% of the two samples were previously randomly separated to validate the equations. The variables diameter at breast height (DBH), commercial height (hc), diameter of the log at the base of the tree (Db) and stem quality (SQ) were used in the modeling. In general, the models showed low adjusted coefficients of determination and the relevant standard errors of estimation. Despite this, validation indicated that the equations could generate accurate estimates. It has been found that it is more efficient, in terms of accuracy, to estimate the mean hollow diameter of the first log of the commercial stem, although it is more practical to estimate the hollow diameter at the base of the tree. Compared to generic equations, specific equations can generate more accurate estimates. Therefore, the hollow diameter in commercial trees can be estimated as a function of variables obtained from the forest inventory, and the best strategy is the use of species-specific equations to estimate the average hollow diameter in the initial portion of the commercial stem.

From lab to field with machine learning – Bridging the gap for movement analysis in real-world environments: A commentary

Biomechanical data collection was largely confined to controlled laboratory setups, relying on marker-based systems or force platforms. However, the emergence of wearable sensors and markerless motion capture has revolutionized this field, enabling data collection in real-world scenarios. This shift has also sparked interest in integrating machine learning (ML) into biomechanical workflows, promising to revolutionize data acquisition in field settings and refine data analysis (Halilaj et al., 2018). Figure 1 provides an overview of corresponding ML applications for key tasks in the biomechanical workflow. This commentary explores the transformative potential of ML in biomechanics, focusing on enhancing data collection and analysis in real-world environments. Pose estimation (a) is the process of automatically tracking and determining the body’s anatomical landmarks, body segments, or joint centre locations in video images using ML, enabling the quantification of human movement without marker and sensor attachments to the human body. Feature estimation (b) employs ML to predict complex biomechanical data, e.g. joint moments from more accessible data sources, including IMUs, pressure insoles, and RGB video cameras. Event detection (c) in time series data is the annotation of certain events that are used to extract useful and vital information or to remove unwanted and unnecessary data for further analysis. Clustering (d) involves grouping instances or individuals with similar biomechanical characteristics using unsupervised ML, thereby revealing underlying structures and subgroups within complex biomechanical data. Finally, automated classification (e) refers to the process of developing a predictive model that assigns input features of data samples to predefined categories or classes using supervised ML. Despite the advancements of ML in biomechanics, central challenges are faced. Estimation errors remain critically high depending on the task and application field, necessitating a careful reflection on data acquisition potentials. Furthermore, especially complex Deep Learning models, while showing promising performances, exhibit a lack of transparency in understanding their decision-making processes and the underlying patterns and rules learned from the data. This phenomenon, often termed as the black-box nature of these models, poses a considerable obstacle. In response, Explainable Artificial Intelligence (XAI), a field that encompasses different explainability approaches to shed light on the inner workings of complex, non-linear ML models, has gained increasing attention in recent years (Slijepcevic et al., 2023). A further central challenge is the availability of data and annotations, which describes the limited availability or insufficiency of relevant and comprehensive datasets, as well as task-specific annotations, for conducting thorough analyses and research in biomechanics. The lack of large-scale benchmark datasets available restricts the widespread adoption of ML-based approaches in biomechanics. Privacy concerns present significant ethical and legal issues, e.g. with identifiable video data. Additionally, model validation remains a critical problem, as many studies fail to validate their models on diverse datasets, often relying on limited data from a single laboratory. Furthermore, there is a risk that the fundamental mechanical understanding of biomechanical processes might be overshadowed by an over-reliance on ML techniques. In conclusion, the integration of ML into biomechanics presents a transformative opportunity for understanding human movement by enabling and improving data collection and analysis in real-world settings. Challenges in data accessibility and methodological transparency necessitate collaborative efforts for future advancements.

The Dynamic Event-Based Non-Fragile H∞ State Estimation for Discrete Nonlinear Systems with Dynamical Bias and Fading Measurement

The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused by unknown inputs is represented by a dynamic equation with bounded noise. Subsequently, the augmentation technique is employed and the dynamic event-triggered mechanism is introduced in the sensor-to-estimator channel to determine whether data should be transmitted or not, thereby conserving resources. Furthermore, an augmented state-dependent non-fragile state estimator is constructed considering gain perturbation of the estimator and fading measurements during network transmission. Sufficient conditions are provided based on Lyapunov stability and matrix analysis techniques to ensure exponential mean-square stability of the estimation error system while satisfying the H∞ disturbance fading level. The desired estimator gain matrix can be obtained by solving the linear matrix inequality (LMI). Finally, an example is presented to illustrate the effectiveness of the proposed method for designing estimators.

Properties of risk aversion estimated from portfolio weights

AbstractWhile risk tolerance is often elicited using questionnaire-based instruments, in this paper, we evaluate the merits of an inversion-based technique, wherein risk aversion parameters are inferred from an individual’s portfolio holdings and a sequence of realized returns. We obtain expressions for the finite sample and asymptotic variance of the estimated risk aversion parameter under the inversion approach with a single risky asset, demonstrating that confidence intervals for parameter estimates are relatively wide. Extending the analysis, we show that inferring risk aversion from multiple risky assets does not typically serve to reduce the estimated parameter variance, but rather propagates estimation error.

Adaptive control of bilateral teleoperators with convergent parameter estimation and guaranteed compliance

Although adaptive control has been studied for teleoperation systems in the past decades, the convergence of parameter estimation is generally difficult to claim in the existing methods, and thus only specific scenarios (e.g., free motion) and partial operation performance (e.g., synchronization) have been addressed. In this paper, we found that the convergence of parameter estimation is crucial for bilateral teleoperation systems to retain the guaranteed operation performances, including compliance in the tracking motion and transparency in the contact motion. Accordingly, this paper suggests an alternative adaptive control for bilateral teleoperation systems, where a new adaptive law with the estimation errors as leakage terms is developed to obtain finite-time convergence of the parameter estimation. This convergent property allows to compensate for the undesired dynamics (e.g., gravity) in the closed-loop system so as to achieve ideal compliance and transparency. The control system’s stability and performances under constant time delays are analyzed for three scenarios: free motion, tracking motion, and contact motion. The quantitative relationship between the joint velocities and the human torques in the tracking motion is also studied, and the transparency is addressed in the contact motion. Simulations and experiments on a Baxter robot all showcase the effectiveness and superiority of the developed approach.

Utility of the morphological scoring of costal cartilage ossification in age estimation of adult Egyptians using multidetector computed tomography

Abstract Age estimation of adults is a challenging procedure in forensic practice. Inspired by the previous work by Chinese scholars, we established population specific age estimation models from the osseous and calcified projections (OCP) of costal cartilages, using three-dimensional volume-rendering technique. A total of 168 clinical CT scans (2 mm slice thickness) were used to develop the sex-specific age prediction models from a sample of Egyptians, comprising 70 females and 98 males, with documented ages between 12 and 85 years. The sample was also used for validating the Chinese model. We reported the differences between the predictive accuracy of the Egyptian (population specific) and Chinese (non population specific) models. The most accurate age estimation model was stepwise linear regression with standard error of estimates (SEE) of 10.9 and 11.8 years in males and females, respectively. For the simple linear regression models, the most accurate formula included OCP of the right second costal cartilage in males and OCP of the left third costal cartilage in females with SEE of 11.2 and 12.2 years, respectively and mean absolute error (MAE) of 8.8 and 9.6 years, respectively. By comparison, the best accuracy rates produced by the Chinese vs. the Egyptian models in males and females within 5 years were 30.61% and 32.86% vs. 35.71% and 32.86%, respectively, whereas within 10 years, the accuracy rates increased up to 57.14% and 58.57% vs. 72.45% and 64.29%, respectively. Although the accuracy rates from the Chinese models were lower than those obtained from the Egyptian models, the MAE and least error values were comparable in both sexes. Notable accurate age estimation rates in the advanced age group ≥40 years were reached being 81.25% to 97.92% in males and 69.77% to 93.02% in females. OCP of the right first costal cartilage was the most accurate in cross-population application for males and females with MAE values of 10.7 and 11.03 years, respectively with balanced accuracy rates of age estimation using the 10-year interval and 40-year cutoff.

Force estimation for human–robot interaction using electromyogram signals from varied arm postures

In this paper, a system for force estimation based on surface electromyography signals measured from the eight channels of the Myo armband is presented. We evaluated nineteen regression models to continuously estimate force in three scenario cases to cover the natural movement in two degrees of freedom planer rehabilitation mobile robots. The best estimation model that could overcome the challenge in a variety of different scenarios was determined. Based on the experimental results, the Gaussian process regression model performed best, giving a root mean square error in the overall range of 1.18–1.77 N. Additionally, the results showed that the exponential algorithm outperformed other solutions, significantly reducing the force estimation error.

Statistically optimal firstorder algorithms: a proof via orthogonalization

Abstract We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$ (and possibly some labels ${\boldsymbol{y}}\in{\mathbb{R}}^{n}$) and would like to estimate a coefficient vector ${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by ${\boldsymbol{X}}$ or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix ${\boldsymbol{X}}$ is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as ‘Bayes AMP’). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to \infty $, $n/d\to \delta $, and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

Robust Matrix Completion with Heavy-Tailed Noise

This article studies noisy low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this article, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the Huber loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient descent with robust spectral initialization. We prove that under merely a bounded second-moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean errors of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our numerical studies. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Superconducting Self-Shielded and Zero-Boil-Off Magnetoencephalogram Systems: A Dry Phantom Evaluation.

Magnetoencephalography (MEG) systems are advanced neuroimaging tools used to measure the magnetic fields produced by neuronal activity in the human brain. However, they require significant amounts of liquid helium to keep the superconducting quantum interference device (SQUID) sensors in a stable superconducting state. Additionally, MEG systems must be installed in a magnetically shielded room to minimize interference from external magnetic fields. We have developed an advanced MEG system that incorporates a superconducting magnetic shield and a zero-boil-off system. This system overcomes the typical limitations of traditional MEG systems, such as the frequent need for liquid helium refills and the spatial constraints imposed by magnetically shielded rooms. To validate the system, we conducted an evaluation using signal source estimation. This involved a phantom with 50 current sources of known location and magnitude under active zero-boil-off conditions. Our evaluations focused on the precision of the magnetic field distribution and the quantification of estimation errors. We achieved a consistent magnetic field distribution that matched the source current, maintaining an estimation error margin within 3.5 mm, regardless of the frequency of the signal source current. These findings affirm the practicality and efficacy of the system.

Polynomial filter-based adaptive fault-tolerant control for a class of nonlinear systems with multiplicative faults

In this article, the problem of fault-tolerant control is investigated for polynomial nonlinear systems (PNSs) subject to multiplicative faults and measurement noise. Firstly, a matrix Taylor expansion technique is applied to transform the PNS into a linear parameter varying system. Then the polynomial filter is constructed to get estimations of states and unmatched disturbances, which reduces the effect of measurement noise. A novel adaptive fault-tolerant controller is proposed to compensate for multiplicative faults and unmatched disturbances. Furthermore, the condition of the parameter-dependent linear matrix inequality (PDLMI) is deduced, which guarantees the boundedness of tracking errors and estimation errors, and the sum of squares (SOS) decomposition technique is utilized to solve PDLMI. Finally, the simulation of a rotary steerable drilling tool system confirms the feasibility of the proposed adaptive fault-tolerant control framework.

Using a Triple Sensor Collocation Approach to Evaluate Small-Holder Irrigation Scheme Performances in Northern Ethiopia

This study uses a triple-sensor collocation approach to evaluate the performance of small-holder irrigation schemes in the Zamra catchment of Northern Ethiopia. Crop water productivity (CWP), as an integrator of biomass production and water use, was used to compare the overall efficiencies of three types of irrigation systems: traditional and modern diversions, and dam-based irrigation water supply. Farmer-reported data often rely on observations, which can introduce human estimation and measurement errors. As a result, the evaluation of irrigation scheme performance has frequently been insufficient to fully explain crop water productivity. To overcome the challenges of using one single estimation method, we used a triple-sensor collocation approach to evaluate the efficiency of three small-scale irrigation schemes, using water productivity as an indicator. It employed three independent methods: remotely sensed data, a model-based approach, and farmer in-situ estimates to assess crop yields and water consumption. To implement the triple collocation appraisal, we first applied three independent evaluation methods, i.e., remotely sensed, model-based, and farmer in-situ estimates of crop yields and water consumption, to assess the crop water productivities of the systems. Triple-sensor collocation allows for the appraisal and comparison of estimation errors of measurement sensor systems, and enables the ranking of the estimators by their quality to represent the de-facto unknown true value, in our case: crop yields, water use, and its ratio CWP, in small-holder irrigated agriculture. The study entailed four main components: (1) collecting in-situ information and data from small-holder farmers on crop yields and water use; (2) derivation of remote sensing-based CWP from the FAO WaPOR open database and time series; (3) evaluation of biomass, crop yields and water use (evapotranspiration) using the AquaCrop model, integrating climate, soil data, and irrigation management practices; (4) performing and analysis of a categorical triple collocation analysis of the independent estimator data and performance ranking of the three sensing and small-holder irrigation systems. Maize and vegetables were used as main crops during three consecutive irrigation seasons (2017/18, 2018/19, 2019/20). Civil war prevented further field surveying, in-situ research, and data collection. The results indicate that remote sensing products are performed best in the modern and dam irrigation schemes for maize. For vegetables, AquaCrop performed best in the dam irrigation scheme.

A TMSBL underwater acoustic channel estimation method based on dictionary learning denoising

The shallow sea underwater acoustic channel exhibits a significant sparse multipath structure. The temporally multiple sparse Bayesian learning (TMSBL) algorithm can effectively estimate this sparse multipath channel. However, the complexity of the algorithm is high, the signal-to-noise ratio (SNR) of shallow-sea underwater acoustic communication is low, and the estimation performance of the TMSBL algorithm is greatly affected by noise. To address this problem, an improved TMSBL underwater acoustic channel estimation method based on a dictionary learning noise reduction algorithm is proposed. Firstly, the K-Singular Value Decomposition (K-SVD) dictionary learning method is used to reduce the noise of the received pilot matrix, reducing the influence of noise on the signal. Then, the Generalized Orthogonal Matching Pursuit (GOMP) channel estimation method is combined to obtain a priori information such as the perceptual matrix and hyperparameter matrix for TMSBL channel estimation; and the noise variance is obtained by using the null subcarrier calculation instead of iteratively updating the noise variance in the TMSBL, to improve the estimation accuracy and reduce the algorithmic complexity. Finally, the TMSBL channel estimation method is used to estimate the underwater acoustic channels of different symbols jointly. The simulation results show that the normalized mean square error of the channel estimation of the improved TMSBL method is reduced by about 92.2% compared with the TMSBL algorithm, obtaining higher estimation accuracy; running time is reduced by about 45.6%, and there is also better performance in terms of the running speed, which provides a reference for underwater acoustic channel estimation.

Model-free detection and quantitative assessment of micro short circuits in lithium-ion battery packs based on incremental capacity and unsupervised clustering

Timely diagnosis of micro short circuit (MSC) faults is crucial for ensuring the safe operation of lithium-ion battery energy storage systems. Existing diagnostic methods face limitations such as high dependency on battery models, difficulty in determining accurate diagnostic thresholds, or low computational efficiency. This work presents a model-free approach for the detection and quantitative assessment of MSCs in lithium-ion battery packs, with incremental capacity (IC) and unsupervised clustering. First, the IC is extracted from charging voltage data to effectively characterize MSC faults in lithium-ion batteries. Next, principal component analysis is used to map the high-dimensional feature space onto a two-dimensional plane to facilitate fault detection and result visualization. Then, an unsupervised clustering algorithm is employed for anomaly detection to identify MSC cells within the battery pack. For the detected MSC cells, a method based on the maximum charging voltage difference between adjacent cycles is designed to estimate the MSC resistance, quantitatively assessing the severity and evolution stage of the MSC. Experimental results show that the accuracy of MSC detection is 99.17 % and the minimum relative error of short-circuit resistance estimation is 1.20 %, which demonstrates the effectiveness and feasibility of the proposed method.

Improved functional interval observer for mecanum‐wheels omnidirectional automated guided vehicle

AbstractThis article presents a study of interval estimation approach based on functional interval observers for mecanum‐wheels omnidirectional automated guided vehicle (MOAGV). In the context of MOAGV, the nonlinear system in discrete time incorporates model uncertainty and unknown bounded disturbances. A functional observer is developed by integrating terminal sliding mode and techniques, aiming to reduce the impact of lumped disturbances/uncertainties. Additionally, a novel observer structure is introduced to increase the degrees of freedom in the design process. Subsequently, the linear function bounds are obtained using the reachability analysis of the estimation error. Finally, the performance of the improved functional interval observer is demonstrated by numerical simulations.

Dual‐channel observer design for composite disturbances based on characteristic compensation

AbstractThis paper presents a non‐coupled structure of characteristic compensation dual‐channel observer (CCDCO) for handling systems subjected to composite disturbances. There exist an outer disturbance compensation channel (ODCC) and an inner disturbance compensation channel (IDCC) in the design strategy. Specifically, in the ODCC, the proposed frequency characteristic compensation observer (FCCO) extracts and removes the regular periodic components from the composite disturbances, where the estimation error preserves irregular characteristics. Thus, the estimation error of FCCO and irregular parts are treated as lumped terms estimated via compensation function observer (CFO) in the IDCC. As a solving skill for composite disturbances estimation, CCDCO has two important advantages over previous designs. First, the proposed non‐coupled structure explicitly distinguishes disturbance characteristics according to a priori information known or not. Second, by combining the benefits of the CFO and proposed FCCO, different types of disturbances can be estimated accordingly without coupling of each other. Simulation results on the robotic manipulator are provided to validate the effectiveness of the proposed method.

Online Estimation and Optimization of Utility-Based Shortfall Risk

Utility-based shortfall risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, in which samples from the underlying loss distribution are available one at a time. We cast the UBSR estimation problem as a root-finding problem and propose stochastic approximation-based estimation schemes. We derive nonasymptotic bounds on the estimation error in the number of samples. We also consider the problem of UBSR optimization within a parameterized class of random variables. We propose a stochastic gradient descent–based algorithm for UBSR optimization and derive nonasymptotic bounds on its convergence.