Estimation Error Research Articles

Truthful and privacy-preserving generalized linear models

This paper explores estimating Generalized Linear Models (GLMs) when agents are strategic and privacy-conscious. We aim to design mechanisms that encourage truthful reporting, protect privacy, and ensure outputs are close to the true parameters. Initially, we address models with sub-Gaussian covariates and heavy-tailed responses with finite fourth moments, proposing a novel private, closed-form estimator. Our mechanism features: (1) o(1)-joint differential privacy with high probability; (2) o(1n)-approximate Bayes Nash equilibrium for (1−o(1))-fraction of agents; (3) o(1) error in parameter estimation; (4) individual rationality for (1−o(1)) of agents; (5) o(1) payment budget. We then extend our approach to linear regression with heavy-tailed data, using an ℓ4-norm shrinkage operator to propose a similar estimator and payment scheme.

A novel heart rate estimation framework with self-correcting face detection for neonatal intensive care unit

Remote photoplethysmography (rPPG) is a non-invasive method for monitoring heart rate (HR) and other vital signs by measuring subtle facial color changes caused by blood flow variations beneath the skin, typically captured through video-based imaging. Current rPPG technology, which is optimized for ideal conditions, faces significant challenges in real-world clinical settings such as Neonatal Intensive Care Units (NICUs). These challenges primarily arise from the limitations of automatic face detection algorithms embedded in HR estimation frameworks, which have difficulty accurately detecting the faces of newborns. Additionally, variations in lighting conditions can significantly affect the accuracy of HR estimation. The combination of these positional changes and fluctuations in lighting significantly impacts the accuracy of HR estimation. To address the challenges of inadequate face detection and HR estimation in newborns, we propose a novel HR estimation framework that incorporates a Self-Correcting face detection module. Our HR estimation framework introduces an innovative rPPG value reference module to mitigate the effects of lighting variations, significantly reducing HR estimation error. The Self-Correcting module improves face detection accuracy by enhancing robustness to occlusions and position changes while automating the process to minimize manual intervention. Our proposed framework demonstrates notable improvements in both face detection accuracy and HR estimation, outperforming existing methods for newborns in NICUs.

Geometric Extended State Observer on [formula omitted] with Fast Finite-Time Stability: Theory and Validation on a Multi-rotor Vehicle

This article presents an extended state observer for a vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a multi-rotor aerial vehicle with a fixed plane of rotors, modeled as an under-actuated system on the state-space TSE(3), the tangent bundle of the six-dimensional Lie group SE(3). This state-space representation globally represents rigid body motions without singularities. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant, and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from this extended state observer is also presented.

Estimation of battery state of charge based on changing window adaptive extended Kalman filtering

Adaptive extended Kalman filter (AEKF) is commonly used for lithium-ion battery state of charge (SOC) estimation. However, it overlooks the impact of changes in the distribution of error innovation sequence (EIS) on the noise covariance, resulting in inaccurate state of charge estimates. To address this issue, this paper introduces a novel approach called changing window adaptive extended Kalman filter (CW-AEKF) algorithm. This algorithm uses variance ratio and Levene test to identify the change in the distribution of error innovation sequence, and adaptively updates the optimal noise window length based on the judgment result to achieve accurate noise estimation. Subsequently, the proposed algorithm is combined with a temperature-corrected second-order RC equivalent circuit model for state of charge estimation. The results of dynamic stress test (DST) at different temperatures show that the changing window adaptive extended Kalman filter algorithm can obtain higher accuracy in state of charge estimation results than other algorithms, with state of charge estimation errors remaining within 1 %. Finally, the state of charge estimation of the changing window adaptive extended Kalman filter algorithm in publicly available datasets is analyzed. The results demonstrate that the proposed algorithm maintains strong generalization ability when facing various working conditions.

Respiratory system mechanics during noninvasive proportional assist ventilation: A model study

AbstractPurposeTo assess the accuracies of airway resistance (Raw) and compliance (Crs) calculations using the expiratory time constant (RCexp) method as well as the accuracy of Pmus estimation in obstructive lung models.MethodsA Respironics V60 ventilator was connected to an active lung simulator. The driving pressure was maintained at 5–10 cmH2O and positive end-expiration pressure (PEEP) was 5 cmH2O. Maximal Pmus, estimated based on equations of motion and respiratory mechanical properties, was calculated by the RCexp method to derive respiratory system compliance (Crs) and inspiratory (Rinsp) and expiratory (Rexp) resistance.ResultsDuring PAV, the assist proportion was adjusted to 55% and 40% with Pmus of 5 and 10 cmH2O, respectively. Pmus measurement errors were <20% of the preset values in most lung conditions. In the active lung model with PAV, an overestimation of Raw was found in the normal resistance condition, and Rinsp was underestimated in the severe obstructive model (P < 0.01). Crs was overestimated significantly except in the severe obstructive model at a Pmus of 10 cmH2O (all P < 0.01). Using the RCexp method, the target of ≤20% between the calculated and preset values in airway resistance was achieved in most obstructive models at a Pmus of 5 cmH2O.ConclusionsThe RCexp method might provide real-time assessments of respiratory mechanics (elastance and resistance) in the PAV mode. With low inspiratory effort, the estimation error was acceptable (<20%) in most obstructive lung models.

Sensorless Position Control in High-Speed Domain of PMSM Based on Improved Adaptive Sliding Mode Observer

To improve the speed buffering and position tracking accuracy of medium–high-speed permanent magnet synchronous motor (PMSM), a sensorless control method based on an improved sliding mode observer is proposed. By the mathematical model of the built-in PMSM, an improved adaptive super-twisting sliding mode observer is constructed. Based on the LSTA-SMO with a linear term of observation error, a sliding mode coefficient can be adjusted in real time according to the change in rotational speed. In view of the high harmonic content of the output back electromotive force, the adaptive adjustment strategy for the back electromotive force is adopted. In addition, in order to improve the estimation accuracy and resistance ability of the observer, the rotor position error was taken as the disturbance term, and the third-order extended state observer (ESO) was constructed to estimate the rotational speed and rotor position through the motor mechanical motion equation. The proposed method is validated in Matlab and compared with the conventional linear super twisted observer. The simulation results show that the proposed method enables the observer to operate stably in a wide velocity domain and reduces the velocity estimation error to 6.7 rpm and the position estimation accuracy error to 0.0005 rad at high speeds, which improves the anti-interference capability.

Optimizing GEDI Canopy Height Estimation and Analyzing Error Impact Factors Under Highly Complex Terrain and High-Density Vegetation Conditions

The Global Ecosystem Dynamics Investigation (GEDI) system provides essential data for estimating forest canopy height on a global scale. However, factors such as complex topography and dense canopy can significantly reduce the accuracy of GEDI canopy height estimations. We selected the South Taihang region of Henan Province, China, as our study area and proposed an optimization framework to improve GEDI canopy height estimation accuracy. This framework includes correcting geolocation errors in GEDI footprints, screening and analyzing features that affect estimation errors, and combining two regression models with feature selection methods. Our findings reveal a geolocation error of 4 to 6 m in GEDI footprints at the orbital scale, along with an overestimation of GEDI canopy height in the South Taihang region. Relative height (RH), waveform characteristics, topographic features, and canopy cover significantly influenced the estimation error. Some studies have suggested that GEDI canopy height estimates for areas with high canopy cover lead to underestimation, However, our study found that accuracy increased with higher canopy cover in complex terrain and dense vegetation. The model’s performance improved significantly after incorporating the canopy cover parameter into the optimization model. Overall, the R2 of the best-optimized model was improved from 0.06 to 0.61, the RMSE was decreased from 8.73 m to 2.23 m, and the rRMSE decreased from 65% to 17%, resulting in an accuracy improvement of 74.45%. In general, this study reveals the factors affecting the accuracy of GEDI canopy height estimation in areas with complex terrain and dense vegetation cover, on the premise of minimizing GEDI geolocation errors. Employing the proposed optimization framework significantly enhanced the accuracy of GEDI canopy height estimates. This study also highlighted the crucial role of canopy cover in improving the precision of GEDI canopy height estimation, providing an effective approach for forest monitoring in such regions and vegetation conditions. Future studies should further improve the classification of tree species and expand the diversity of sample tree species to test the accuracy of canopy height estimated by GEDI in different forest structures, consider the distortion of optical remote sensing images caused by rugged terrain, and further mine the information in GEDI waveforms so as to enhance the applicability of the optimization framework in more diverse forest environments.

Estimating the Distance Between Map Points May Be Related to Forms of Representing the Map´s Scale.

The way a map scale is represented plays a key role in comprehending it. In this research, we examined the relationships between the form of representation of the map's scale (numerical scale, linear graphic scale and circular graphic scale), the user's gender, and the distance between two map objects on user estimates of the distance between two objects on the map (i.e., a 5, 10, 15 and 20-min walk). We gave 183 college students 84 maps of three types: 28 numerical scale, 28 linear graphic scale, and 28 circular graphic scale. Each map presented varied distances to be estimated. We assessed the participants' accurate hits, errors, and their hits minus errors in these distance estimations. Participants had both more hits and more errors on circular scale maps than on linear or numerical scale maps, and the distances between objects and gender also significantly related to the estimated e distance. Both the type of scale and the distance between objects influenced the number of hits minus the number of errors.

Interferometric phase reconstruction with temporal decorrelation model constraints for time-series InSAR surface deformation monitoring

ABSTRACT The time series interferometric synthetic aperture radar (InSAR) (TSInSAR) is an effective technique for monitoring surface deformation with wide coverage and millimeter accuracy. There are two types of scatterers in the SAR field of view, including the permanent scatterer (PS) and the distributed scatterer (DS). Compared to PS with temporarily stable scattering behavior, the filtered interferometric phases are not consistent for DS susceptible to the decorrelation effect. To overcome the phase inconsistency degradation problem of the decorrelated DSs, the phase linking (PL) theory is introduced to recover the equivalent single-reference (ESR) phases from all interferometric combinations. However, the optimization performance of the PL theory is affected by the uncontrollable estimation error of coherence magnitude. Here, we present a novel enhanced PL (EPL) by incorporating with a priori temporal decorrelation model (TDM) to enhance the weight of the short-term interferograms and suppress the abrupt coherence jump with the long temporal baseline. Real experiment selects the Daguangbao landslide triggered by the ‘5.12’ Wenchuan Mw 7.9 earthquake as the study area to verify the algorithm’s effectiveness. Compared to traditional PL methods, the new EPL method can recover the interferometric phase fringe more clearly and obtain a smoother deformation velocity spatially with higher estimation accuracy.

Quantum interferences and gates with emitter-based coherent photon sources

Quantum emitters such as quantum dots, defects in diamond or in silicon have emerged as efficient single-photon sources that are progressively exploited in quantum technologies. In 2019, it was shown that the emitted single-photon states often include coherence with the vacuum component. Here we investigate how such photon-number coherence alters quantum interference experiments that are routinely implemented both for characterizing or exploiting the generated photons. We show that it strongly modifies intensity correlation measurements in a Hong–Ou–Mandel experiment and leads to errors in indistinguishability estimations. It also results in additional entanglement when performing partial measurements. We illustrate the impact on quantum protocols by evidencing modifications in heralding efficiency and fidelity of two-qubit gates.

Testing kinematic distances under a realistic Galactic potential. Investigating systematic errors in the kinematic distance method arising from a non-axisymmetric potential

Obtaining reliable distance estimates to gas clouds within the Milky Way is challenging in the absence of certain tracers. The kinematic distance approach has been used as an alternative, and it is derived from the assumption of circular trajectories around the Galactic centre. Consequently, significant errors are expected in regions where gas flow deviates from purely circular motions. We aim to quantify the systematic errors that arise from the kinematic distance method in the presence of a Galactic potential that is non-axisymmetric. We investigated how these errors differ in certain regions of the Galaxy and how they relate to the underlying dynamics. We performed 2D isothermal hydrodynamical simulation of the gas disk with the moving-mesh code Arepo adding the capability of using an external potential provided by the Agama library for galactic dynamics. We introduced a new analytic potential of the Milky Way, taking elements from existing models and adjusting parameters to match recent observational constraints. In line with results of previous studies, we report significant errors in the kinematic distance estimate for gas close to the Sun along sight lines towards the Galactic centre and anti-centre and associated with the Galactic bar. Kinematic distance errors are low within the spiral arms, as gas resides close to local potential minima and the resulting line-of-sight velocity is similar to what is expected for an axisymmetric potential. Interarm regions exhibit large deviations at any given Galactic radius, and this is caused by the gas being sped up or slowed down as it travels into or out of spiral arms. In addition, we identify ‘zones of avoidance’ in the $lv$-diagram, where the kinematic distance method is particularly unreliable and should only be used with caution and we find a power-law relation between the kinematic distance error and the deviation of the projected line-of-sight velocity from circular motion.

Pseudorandom high‐frequency injection synchronous reluctance motor sensorless control with parameter variation consideration

AbstractThe sensorless control of synchronous reluctance motor (SynRM) in the zero and low‐speed domain using the traditional high‐frequency injection method has the problems of audible noise caused by the high‐frequency injection and high‐frequency loss caused by the change of working conditions, which limits the practical application of SynRM in the industrial field. To solve the problem of high‐frequency noise and loss, a pseudo‐random high‐frequency injection method considering parameter variation is proposed in this paper. Firstly, the signal injection form was adjusted to expand the power spectral density of the high‐frequency current, and the current energy spike was suppressed to reduce high‐frequency noise. Secondly, the current demodulation was combined with the flux map model to complete the injection voltage amplitude adjustment, so that the response current was kept constant under multiple operating conditions to reduce the high‐frequency loss. At the same time, the flux map model is applied to the observer to reduce the rotor position estimation error caused by the cross‐coupling effect. Under the condition of satisfying the dynamic and steady performance requirements of sensorless control, the high‐frequency loss and sharp noise caused by the high‐frequency injection method are effectively suppressed. Finally, experiments were carried out on a 1.5 kW SynRM drive platform to verify the feasibility and effectiveness of the sensorless control scheme in this paper.

Robustness of Divergence Time Estimation Despite Gene Tree Estimation Error: A Case Study of Fireflies (Coleoptera: Lampyridae).

Genomic data has become ubiquitous in phylogenomic studies, including divergence time estimation, but provide new challenges. These challenges include, amongst others, biological gene tree discordance, methodological gene tree estimation error, and computational limitations on performing full Bayesian inference under complex models. In this study, we use a recently published firefly (Coleoptera: Lampyridae) anchored hybrid enrichment dataset (AHE; 436 loci for 88 Lampyridae species and 10 outgroup species) as a case study to explore gene tree estimation error and the robustness of divergence time estimation. First, we explored the amount of model violation using posterior predictive simulations because model violations are likely to bias phylogenetic inferences and produce gene tree estimation error. We specifically focused on missing data (either uniformly distributed or systematically) and the distribution of highly variable and conserved sites (either uniformly distributed or clustered). Our assessment of model adequacy showed that standard phylogenetic substitution models are not adequate for any of the 436 AHE loci. We tested if the model violations and alignment errors resulted indeed in gene tree estimation error by comparing the observed gene tree discordance to simulated gene tree discordance under the multispecies coalescent model. Thus, we show that the inferred gene tree discordance is not only due to biological mechanism but primarily due to inference errors. Lastly, we explored if divergence time estimation is robust despite the observed gene tree estimation error. We selected four subsets of the full AHE dataset, concatenated each subset and performed a Bayesian relaxed clock divergence estimation in RevBayes. The estimated divergence times overlapped for all nodes that are shared between the topologies. Thus, divergence time estimation is robust using any well selected data subset as long as the topology inference is robust.

Information Theory in a Darwinian Evolution Population Dynamics Model

Since Darwin, evolutionary population dynamics has captivated scientists and has applications beyond biology, such as in game theory where economists use it to explore evolution in new ways. This approach has renewed interest in dynamic evolutionary systems. In this paper, we propose an information-theoretic method to estimate trait parameters in a Darwinian model for species with single or multiple traits. Using Fisher information, we assess estimation errors and demonstrate the method through simulations.

Improved wind power assessments by bias adjusted reanalysed data with applications near Morocco's coast.

The wind energy requirements for high temporal and spatial observations, unavailable in many countries, are met by reanalysed wind data, which are increasingly used in wind power assessments. However, these data also include unrealistic features, making their validation compulsory. The validation analysis of ERA5 and MERRA-2 wind data, two of the most successful wind reanalyses, with observations near Morocco's coast, highlighted the existence of bias in both datasets, and other shortcomings. The study was conducted at eight selected sites in the period 2011-2020 using linear and probability density function based statistical tests. The local ERA5-BA and MERRA-2 BA velocity fields were created using Bias Adjustment (BA) Techniques. Only part of the observed and modelled datasets (training period) were used to identify the transfer function. The BA fields were verified against observations during the remaining period (verification period). They outperformed their respective non-adjusted fields and also the WFDE5 (the global bias-corrected ERA5 wind field) in the wind potential assessments, represented by capacity factor and low-wind day. At every location, the relative errors in the latter's estimates using ERA5-BA were lowered to less than 10 %, and the same was true for MERRA-2-BA. Thus, an observational dataset of reduced length can help overcome some reanalysed wind data limitations for wind power estimations. Additionally, this methodology can be applied to the correction of each reanalysis update.

-Penalized Multinomial Regression: Estimation, Inference, and Prediction, With an Application to Risk Factor Identification for Different Dementia Subtypes.

High-dimensional multinomial regression models are very useful in practice but have received less research attention than logistic regression models, especially from the perspective of statistical inference. In this work, we analyze the estimation and prediction error of the contrast-based -penalized multinomial regression model and extend the debiasing method to the multinomial case, providing a valid confidence interval for each coefficient and value of the individual hypothesis test. We also examine cases of model misspecification and non-identically distributed data to demonstrate the robustness of our method when some assumptions are violated. We apply the debiasing method to identify important predictors in the progression into dementia of different subtypes. Results from extensive simulations show the superiority of the debiasing method compared to other inference methods.

The Influence that the Complexity of the Three-Dimensional Eye Model Used to Generate Simulated Eye-tracking Data Has on the Gaze Estimation Errors Achieved Using the Data

Simulated eye-tracking data are an integral tool in the development of eye-tracking methods. Most of the simulated data used in eye-tracking-related research has been generated using low-complexity eye models that include a single spherical corneal surface. This study investigated the influence of eye-model complexity on the ability of simulated eye-tracking data to predict real-world outcomes. The experimental procedures of two pertinent comparative eye-tracking studies were replicated in a simulated environment using various eye-model complexities. The simulated outcomes were then evaluated against the findings of the comparative studies that were derived from real-world outcomes. The simulated outcomes of both comparative studies were significantly influenced by the eye-model complexity. Eye models that included an aspheric corneal surface best replicated experimental eye-tracking outcomes, while including a posterior corneal surface did not improve the ability of simulated data to replicate real-world outcomes. Using a wide-angle eye model that accurately replicates the peripheral optics of the eye did not improve simulated outcomes relative to a paraxial eye model.

Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data

The precise estimation of the state of charge (SOC) in lithium batteries is crucial for enhancing their operational lifespan. To address the issue of reduced accuracy in SOC estimation caused by the random missing values of lithium battery current measurements, a joint estimation method which combines recursive least squares with missing input data (MIDRLS) and the unscented Kalman filter (UKF) algorithm is proposed, called the MIDRLS-UKF algorithm. Firstly, the equivalent circuit model of a Thevenin battery is formulated. Then, the current imputation model is designed to interpolate the missing data, based on which the MIDRLS algorithm is derived by solving the unbiased estimation of the gradient of the objective function, thus realizing the online high-precision identification of the circuit model parameters. Furthermore, the proposed algorithm is combined with the UKF algorithm to facilitate the online precise estimation of SOC. The simulation results indicate a marked decrease in the SOC estimation error when employing the proposed joint algorithm, as opposed to the conventional forgetting factor recursive least squares (FFRLS) algorithm combined with the UKF joint estimation algorithm, which verifies the precision and effectiveness of the proposed joint algorithm.

Influence of the color of 3D-printed scan aids on the trueness of complete arch digital scans.

To determine the influence of using 3D-printed scan aids in varying colors on the trueness of digital scans. A master cast with five multi-unit analogues was scanned. The acquired dataset was exported to standard tessellation language (STL) file format to serve as the reference STL. 3D printing of the prototype in five distinct colors (beige [SABEIGE], grey [SAGREY], white [SAWHITE], red [SARED], and blue [SABLUE]) of polylactic acid filament was executed. The experimental STLs of each color group were aligned to the reference STL. RMS values were solely computed for the scan bodies. Based on the centers of the created best-fit and offset planes, scan bodies were converted into virtual cylinders. Cartesian coordinates of each cylinder were acquired. Subsequently, angular (AD) and linear deviation (LD) values were calculated. LD was further examined separately along the x, y, and z axes. Data were statistically analyzed. According to the results of one-way ANOVAs, significant differences were detected among color groups on AD, LD, RMS estimate error, ∆x, ∆y, and ∆z data. The lowest AD and LD values were exhibited by the SAGREY group in all implant sites. The SAGREY group was followed by the SABEIGE, SAWHITE, SARED, and SABLUE groups. The SAGREY outperformed the other groups in terms of trueness. Although the LD values of all color groups were below the threshold value (<100 µm), only the AD values of the SAGREY, SABEIGE, and SAWHITE groups were clinically acceptable (<0.5°).

Using a Stopping Rule to Optimize Cost-Quality Tradeoffs in a Large, Mixed-Mode Survey: A Simulation Study

Rising nonresponse and the increasing costs of conducting surveys are creating pressure on survey organizations to efficiently allocate resources. The challenge is to produce the highest quality data possible within a fixed budget. We use a stopping rule designed to minimize a function of cost and errors. The rule is based on the product of predicted costs and the predicted mean squared error of a survey estimate. We simulate the impact of implementing the stopping rule on the 2019 US Survey of Doctorate Recipients (SDR), which is a longitudinal survey conducted every two years in the US using web, mail, and CATI. We vary the types of models used to generate the input predictions (parametric regression vs. nonparametric tree models) and the timing of the implementation of the rule. We found that the modeling approach made less difference, while the timing of the implementation of the stopping rule made a large difference in outcomes. The rule is multivariate and optimizes outcomes for two variables. It performed better for one variable, leading to reduced costs and only small increases in errors. The other variable had larger error increases.