scholarly journals Visual-inertial SLAM aided estimation of anchor poses and sensor error model parameters of UWB radio modules

2019 ◽  
Author(s):  
Philipp Lutz ◽  
Martin J. Schuster ◽  
Florian Steidle
Keyword(s):  
Error Model ◽  
Model Parameters ◽  
Sensor Error ◽  
Uwb Radio

scholarly journals Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

2017 ◽  
Vol 14 (18) ◽  
pp. 4295-4314 ◽  
Author(s):  
Dan Lu ◽  
Daniel Ricciuto ◽  
Anthony Walker ◽  
Cosmin Safta ◽  
William Munger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Likelihood Function ◽  
Terrestrial Ecosystem ◽  
Error Model ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Ecosystem Models ◽  
Bayesian Calibration

Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

scholarly journals Error Models for the Kinetic Evaluation of Chemical Degradation Data

Environments ◽  
2019 ◽  
Vol 6 (12) ◽  
pp. 124
Author(s):  
Johannes Ranke ◽  
Stefan Meinecke
Keyword(s):  
Error Model ◽  
Chemical Degradation ◽  
Model Parameters ◽  
Kinetic Evaluation ◽  
Error Structure ◽  
Error Models ◽  
Constant Variance ◽  
Degradation Data ◽  
True Value ◽  
Two Component

In the kinetic evaluation of chemical degradation data, degradation models are fitted to the data by varying degradation model parameters to obtain the best possible fit. Today, constant variance of the deviations of the observed data from the model is frequently assumed (error model “constant variance”). Allowing for a different variance for each observed variable (“variance by variable”) has been shown to be a useful refinement. On the other hand, experience gained in analytical chemistry shows that the absolute magnitude of the analytical error often increases with the magnitude of the observed value, which can be explained by an error component which is proportional to the true value. Therefore, kinetic evaluations of chemical degradation data using a two-component error model with a constant component (absolute error) and a component increasing with the observed values (relative error) are newly proposed here as a third possibility. In order to check which of the three error models is most adequate, they have been used in the evaluation of datasets obtained from pesticide evaluation dossiers published by the European Food Safety Authority (EFSA). For quantitative comparisons of the fits, the Akaike information criterion (AIC) was used, as the commonly used error level defined by the FOrum for the Coordination of pesticide fate models and their USe(FOCUS) is based on the assumption of constant variance. A set of fitting routines was developed within the mkin software package that allow for robust fitting of all three error models. Comparisons using parent only degradation datasets, as well as datasets with the formation and decline of transformation products showed that in many cases, the two-component error model proposed here provides the most adequate description of the error structure. While it was confirmed that the variance by variable error model often provides an improved representation of the error structure in kinetic fits with metabolites, it could be shown that in many cases, the two-component error model leads to a further improvement. In addition, it can be applied to parent only fits, potentially improving the accuracy of the fit towards the end of the decline curve, where concentration levels are lower.

Vision-based calibration/compensation technique for automatic stiffener bonder

2016 ◽  
Vol 231 (1) ◽  
pp. 167-180 ◽  
Author(s):  
Su Ye ◽  
Yutang Ye ◽  
Yu Xie ◽  
Ying Luo ◽  
Chunlei Du
Keyword(s):  
Error Compensation ◽  
Least Squares Method ◽  
Error Model ◽  
Compensation Method ◽  
Calibration Error ◽  
Model Parameters ◽  
Coordinate Systems ◽  
Printed Circuit ◽  
Pick And Place ◽  
Flexible Printed Circuit

This study developed a novel error compensation method aimed at eliminating placement error caused by hand–eye calibration and pick-and-place tool motions in automatic stiffener bonder for flexible printed circuit. Using the transformation of homogeneous coordinates to develop an error model of the system describing the coupling of errors among various coordinate systems, the least squares method is used to calculate the unknown model parameters. The experiment results demonstrate that this error compensation method reduced placement error by an order of magnitude. The mounting precision throughout the entire work area was ±0.046 mm at 3sigma, and for flexible printed circuit products with a specification limit of 0.1 mm, the process capability index of the automatic stiffener bonder in this study was 2.19. This represents that the system is capable of fully satisfying the precision requirements of flexible printed circuit stiffener bonding. The proposed system employing a vibrating feeder bowl and machine vision–aided target positioning is applicable to a variety of stiffeners, which enhances production flexibility. The proposed error model considers the complex coupling effect of the errors among multiple coordinate systems in hand–eye calibration, without the need of detecting and calculating the calibration error item by item, and takes into account the errors produced by the rotation and downward pressing motions of the pick-and-place tool.

Migratory Catch-Age Analysis

1990 ◽  
Vol 47 (12) ◽  
pp. 2315-2327 ◽  
Author(s):  
Terrance J. Quinn II ◽  
Richard B. Deriso ◽  
Philip R. Neal
Keyword(s):  
Auxiliary Information ◽  
Nonlinear Least Squares ◽  
Sensitivity Study ◽  
Error Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Migration Rates ◽  
Process Error ◽  
A New Technique ◽  
And Migration

We review techniques for estimating the abundance of migratory populations and develop a new technique based on catch-age data from geographic regions and our earlier technique, catch-age analysis with auxiliary information (Deriso et al. 1985, 1989). Data requirements are catch-age data over several years, some auxiliary information, and migration rates among regions. The model, containing parameters for year-class abundance, age selectivity, full-recruitment fishing mortality, and catchability, is fitted to data with a nonlinear least squares algorithm. We present a measurement error model and a process error model and favor the process error model because all model parameters can be jointly estimated. By application to data on Pacific halibut, the process error model converges readily and produces estimates with no significant bias. These estimates have relatively high precision compared to those from analyses which did not incorporate migration information. The error structure used in a model has a more significant impact on parameter estimates than migration rates. A sensitivity study of migration rates shows sensitivity of the order of the rates themselves.

scholarly journals Bayesian joint inference of hydrological and generalized error models with the enforcement of Total Laws

2017 ◽  
Author(s):  
Mario R. Hernández-López ◽  
Félix Francés
Keyword(s):  
Hydrological Modeling ◽  
Error Model ◽  
Joint Probability Distribution ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Hydrological Models ◽  
Inference Problem ◽  
Inference Models ◽  
Error Models ◽  
Joint Inference

Abstract. Over the years, the Standard Least Squares (SLS) has been the most commonly adopted criterion for the calibration of hydrological models, despite the fact that they generally do not fulfill the assumptions made by the SLS method: very often errors are autocorrelated, heteroscedastic, biased and/or non-Gaussian. Similarly to recent papers, which suggest more appropriate models for the errors in hydrological modeling, this paper addresses the challenging problem of jointly estimate hydrological and error model parameters (joint inference) in a Bayesian framework, trying to solve some of the problems found in previous related researches. This paper performs a Bayesian joint inference through the application of different inference models, as the known SLS or WLS and the new GL++ and GL++Bias error models. These inferences were carried out on two lumped hydrological models which were forced with daily hydrometeorological data from a basin of the MOPEX project. The main finding of this paper is that a joint inference, to be statistically correct, must take into account the joint probability distribution of the state variable to be predicted and its deviation from the observations (the errors). Consequently, the relationship between the marginal and conditional distributions of this joint distribution must be taken into account in the inference process. This relation is defined by two general statistical expressions called the Total Laws (TLs): the Total Expectation and the Total Variance Laws. Only simple error models, as SLS, do not explicitly need the TLs implementation. An important consequence of the TLs enforcement is the reduction of the degrees of freedom in the inference problem namely, the reduction of the parameter space dimension. This research demonstrates that non-fulfillment of TLs produces incorrect error and hydrological parameter estimates and unreliable predictive distributions. The target of a (joint) inference must be fulfilling the error model hypotheses rather than to achieve the better fitting to the observations. Consequently, for a given hydrological model, the resulting performance of the prediction, the reliability of its predictive uncertainty, as well as the robustness of the parameter estimates, will be exclusively conditioned by the degree in which errors fulfill the error model hypotheses.

Machine-Tool Error Observer Design With Application to Thermal Error Tracking

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Hua-Wei Ko ◽  
Patrick Bazzoli ◽  
J. Adam Nisbett ◽  
Douglas Bristow ◽  
Yujie Chen ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parameter Identification ◽  
Thermal Error ◽  
Error Model ◽  
Optimal Designs ◽  
Model Parameters ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Five Axis ◽  
Large Machine

Abstract A parameter identification procedure for identifying the parameters of a volumetric error model of a large machine tool requires hundreds of random volumetric error components in its workspace and thus takes hours of measurement time. It causes thermal errors of a large machine difficult to be tracked and compensated periodically. This paper demonstrates the application of the optimal observation design theories to volumetric error model parameter identification of a large five-axis machine. Optimal designs maximize the amount of information carried in the observations. In this paper, K-optimal designs are applied for the construction of machine-tool error observers by determining locations in the workspace at which 80 components of volumetric errors to be measured so that the model parameters can be identified in 5% of an 8-h shift. Many of optimal designs tend to localize observations at the boundary of the workspace. This leaves large volumes of the workspace inadequately represented, making the identified model inadequate. Therefore, the constrained optimization algorithms that force the distribution of observation points in the machine’s workspace are developed. Optimal designs reduce the number of observations in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic measurements. The design, implementation, and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 400-min period of operation are also reported. About 70–80% of machine-tool error can be explained using the proposed thermal error modeling methodology.

Particle Filter and Approximation Error Model for State Estimation in Hyperthermia

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Bernard Lamien ◽  
Helcio Rangel Barreto Orlande ◽  
Guillermo Enrique Eliçabe
Keyword(s):  
Particle Filter ◽  
State Estimation ◽  
Approximation Error ◽  
Error Model ◽  
Estimation Problem ◽  
Transient Temperature ◽  
Model Parameters ◽  
Hyperthermia Treatment ◽  
Measurement Models ◽  
Particle Filter Algorithm

This work deals with numerical simulation of a hyperthermia treatment of skin cancer as a state estimation problem, where uncertainties in the evolution and measurement models, as well as in the measured data, are accounted for. A reduced model is adopted, based on a coarse mesh for the solution of the partial differential equations that describe the physical problem, in order to expedite the solution of the state estimation problem with a particle filter algorithm within the Bayesian framework of statistics. The so-called approximation error model (AEM) is used in order to statistically compensate for model reduction effects. The Liu and West algorithm of the particle filter, together with the AEM, is shown to provide accurate estimates for the temperature and model parameters in a multilayered region containing a tumor loaded with nanoparticles. Simulated transient temperature measurements from one sensor are used in the analysis.

scholarly journals Impact of Model Complexity in the Monitoring of Machine Tools Condition Using Volumetric Errors

2020 ◽  
Vol 14 (3) ◽  
pp. 369-379
Author(s):  
Kanglin Xing ◽  
◽  
J. R. R. Mayer ◽  
Sofiane Achiche
Keyword(s):  
Machine Tool ◽  
Recognition Rate ◽  
Error Model ◽  
Model Complexity ◽  
Model Parameters ◽  
Machine Error ◽  
Error Models ◽  
Tool Condition ◽  
Volumetric Errors ◽  
Five Axis

The scale and master ball artefact (SAMBA) method allows estimating the inter- and intra-axis error parameters as well as volumetric errors (VEs) of a five-axis machine tool by using simple ball artefacts and the machine tool’s own touch-trigger probe. The SAMBA method can use two different machine error models named after the number of model parameters, i.e., the “13” and “84” machine error models, to estimate the VEs. In this study, we compare these two machine error models when using VE vector directions and values for monitoring the machine tool condition for three cases of machine malfunctions: 1) a C-axis encoder fault, 2) an induced X-axis linear positioning error, and 3) an induced straightness error simulated fault. The results show that the “13” machine error model produces more focused concentrated VE directions but smaller VE values when compared with the “84” machine error model; furthermore, although both models can recognize the three faults and are effective in monitoring the machine tool condition, the “13” machine error model achieves a better recognition rate of the machine condition. This paper provides guidelines for selecting machine error models for the SAMBA method when using VEs to monitor the machine tool condition.

Measurement-While-Drilling MWD Error Model Validation – Does the Model Reflect Reality?

2021 ◽  
Author(s):  
David Gutierrez ◽  
Chad Hanak
Keyword(s):  
Real Time ◽  
Service Providers ◽  
Error Model ◽  
Error Sources ◽  
Error Models ◽  
Sensor Error ◽  
Magnetic Model ◽  
Measurement While Drilling ◽  
Standard Deviations ◽  
Directional Sensor

Abstract It has been well documented that magnetic models and Measurement-while-Drilling (MWD) directional sensors are not free from error. It is for this reason that directional surveys are accompanied by an error model that is used to generate an ellipse of uncertainty (EOU). The directional surveys represent the highest probable position of the wellbore and the EOU is meant to encompass all of the possible wellbore positions to a defined uncertainty level. The wellbore position along with the individual errors are typically presumed to follow a Normal (Gaussian) Distribution. In order for this assumption to be accurate, 68.3% of magnetic model and directional sensor error should fall within plus or minus one standard deviation (1σ), 95.5% within two standard deviations (2σ), and 99.7% within three standard deviations (3σ) of the limits defined in the error model. It is the purpose of this study to evaluate the validity of these assumptions. The Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA) provides a set of MWD error models that are widely accepted as the industry standard for use in wellbore surveying. The error models are comprised of the known magnetic model and MWD directional sensor error sources and associated limits. It is the purpose of this paper to determine whether the limits defined in the ISCWSA MWD error models are representative of the magnitude of errors observed in practice. In addition to the ISCWSA defined error model terms, this research also includes an analysis of the sensor twist error term and the associated limits defined in the Fault Detection, Isolation, and Recovery (FDIR) error model. This study is comprised of 138 MWD runs that were selected based on the criteria that they were processed using FDIR with overlapping gyro surveying to ensure highly accurate and consistent estimated values. The error magnitudes and uncertainties estimated by FDIR were compiled and analyzed in comparison to the expected limits outlined in the error models. The results conclude that the limits defined in the ISCWSA error models are not always representative of what is observed in practice. For instance, in U.S. land the assumed magnitudes of several of the error sources are overly optimistic compared to the values observed in this study. This means that EOUs with which wells are planned may not be large enough in some scenarios which could cause the operator to assume unanticipated additional risk. The final portion of this analysis was undertaken to test the hypothesis that preventative measures such as additional non-magnetic spacing are generally being taken by operators and directional service providers to minimize additional injected error when survey corrections are not being implemented while drilling the well. This hypothesis was tested by dividing the 138 MWD runs into Historical (survey corrections were not utilized in real-time) and Real-Time (survey corrections were utilized in real-time) categories. The results indicate that there are no significant differences in the error estimates between the Historical and Real-Time categories. This result in combination with the determination that the majority of the error model error terms should be categorized as fat-tail distributed indicate that proper well spacing and economics calculated using separation factor alone are insufficient without the use of survey corrections in Real-Time.

scholarly journals An Angle Error Compensation Method Based on Harmonic Analysis for Integrated Joint Modules

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1715
Author(s):  
Yi Hu ◽  
Yuyi Zhan ◽  
Liang Han ◽  
Penghao Hu ◽  
Bing Ye ◽  
...  
Keyword(s):  
Harmonic Analysis ◽  
Coordinate Measuring Machine ◽  
Angle Measurement ◽  
Error Model ◽  
The Self ◽  
Model Parameters ◽  
Angle Error ◽  
Positioning Accuracy ◽  
Measuring Machine ◽  
High Repeatability

Nowadays, integrated joint modules are increasingly adopted in manipulators for their advantages of high integration, miniaturization and high repeatability positioning accuracy. The problem of generally low absolute positioning accuracy (namely angle measurement accuracy) must be solved before they can be introduced into the self-driven articulated arm coordinate measuring machine which is under study in our laboratory. In this study, the sources of joint module’s angle error were analyzed and the error model based on harmonic analysis was established. Two integrated joint modules were calibrated on the self-designed calibration platform and the model parameters were deduced, respectively. The angle error was then compensated in the experiments and the results demonstrated that the angle error of the joint modules was reduced by 82.03% on average. The established angle error model can be effectively applied into the self-driven articulated arm coordinated measuring machine.

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