Observational error | EPFL Graph Search

Observational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement uncertainty. Science and experiments When either randomness or uncertainty modele

Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

Stéphane Guerrier, Mehran Khaghani, Jan Skaloud

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called “Allan variance slope method” which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing “automatic” approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their modelimplied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper, for the first time, formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments (GMWM) as an optimal choice. In addition to analytical proofs, experiment-driven Monte Carlo simulations demonstrated the superior performance of this estimator. Further analysis of error signal from a gyroscope was also provided to further motivate performing such analyses, as real-world observed error signals may show significant deviation from manufacturer-provided error models.

2020

SENSITIVITY ANALYSIS OF A PATIENT SPECIFIC FINITE ELEMENT MODEL FOR SHOULDER ARTHOPLASTY

Gerard Guell Bartrina

Background Glenohumeral osteoarthritis is common degenerative disease within the elderly population, which causes pain and reduced mobility. In advanced cases, total shoulder arthroplasty (TSA) is usually performed. Although TSA is an established procedure, prosthesis failure rate is still quite significant. A new prosthesis model is being investigated at the Laboratory of Biomechanical Orthopedics with the intent to reduce this failure rate. For such investigation, a finite element patient-specific model is being used. Due to their current research applications and future clinical applications, accuracy of patient-specific models needs to be ensured. This project studies to sensitivity of the FE patient specific model to uncertainties related to the model construction process Methods The present work studies the effect of mesh characteristics, the CT systematic error, material law and homogeneity in the FE model outputs. To reduce uncertainties due to mesh characteristics, a mesh convergence study is performed. The effect of CT systematic error, material law and homogeneity is studied through a factorial analysis. Results Variations in the systematic error, material law and homogeneity choice caused a difference in strain outputs in the bone to differ up to a value of two. On the other hand, stress and strain values in the cement underwent no significant variations. Homogeneous models followed the same patterns. However, the output values yielded by homogeneous models were smaller than those yielded by heterogeneous models. Conclusion Variations in the material law have much larger influence in the results than variations in the homogeneity or the CT systematic error. The cement layer attaching the glenoid implant to the scapula is not affected significantly by the material law or homogeneity of the bone. Homogeneous bone models tend to underestimate peak strain values, and thus, they should be avoided when studying critical performance conditions.

2017

A Framework for Inertial Sensor Calibration Using Complex Stochastic Error Models

Stéphane Guerrier, Jan Skaloud, Yannick Stebler

Modeling and estimation of gyroscope and accelerometer errors is generally a very challenging task, especially for low-cost inertial MEMS sensors whose systematic errors have complex spectral structures. Consequently, identifying correct error-state parameters in a INS/GNSS Kalman filter / smoother becomes difficult when several processes are superimposed. In such situations, the classical identification approach via Allan Variance (AV) analyses fails due to the difficulty of separating the error-processes in the spectral domain. For this purpose we propose applying a recently developed estimation method, called the Generalized Method of Wavelet Moments (GMWM), that is excepted from such inconveniences. This method uses indirect interference on the parameters using the wavelet variances associated to the observed process. In this article, the GMWM estimator is applied in the context of modeling the behavior of low-cost inertial sensors. Its capability to estimate the parameters of models such as mixtures of GM processes for which no other estimation method succeeds is first demonstrated through simulation studies. The GMWM estimator is also applied on signals issued from a MEMS-based inertial measurement unit, using sums of GM processes as stochastic models. Finally, the benefits of using such models is highlighted by analyzing the quality of the determined trajectory provided by the INS/GNSS Kalman filter, in which artificial GNSS gaps were introduced. During these epochs, inertial navigation operates in coasting mode while GNSS-supported trajectory acts as a reference. As the overall performance of inertial navigation is strongly dependent on the errors corrupting its observations, the benefits of using the more appropriate error models (with respect to simpler ones estimated using classical AV graphical identification technique) are demonstrated by a significant improvement in the trajectory accuracy.