The influence of variations in ocular biometric and optical parameters on differences in refractive error.

PURPOSE: To present a paraxial method to estimate the influence of variations in ocular biometry on changes in refractive error (S) at a population level and apply this method to literature data. METHODS: Error propagation was applied to two methods of eye modelling, referred to as the simple method and the matrix method. The simple method defines S as the difference between the axial power and the whole-eye power, while the matrix method uses more accurate ray transfer matrices. These methods were applied to literature data, containing the mean ocular biometry data from the SyntEyes model, as well as populations of premature infants with or without retinopathy, full-term infants, school children and healthy and diabetic adults. RESULTS: Applying these equations to 1000 SyntEyes showed that changes in axial length provided the most important contribution to the variations in refractive error (57%-64%), followed by lens power/gradient index power (16%-31%) and the anterior corneal radius of curvature (10%-13%). All other components of the eye contributed <4%. For young children, the largest contributions were made by variations in axial length, lens and corneal power for the simple method (67%, 23% and 8%, respectively) and by variations in axial length, gradient lens power and anterior corneal curvature for the matrix method (55%, 21% and 14%, respectively). During myopisation, the influence of variations in axial length increased from 54.5% to 73.4%, while changes in corneal power decreased from 9.82% to 6.32%. Similarly, for the other data sets, the largest contribution was related to axial length. CONCLUSIONS: This analysis confirms that the changes in ocular refraction were mostly associated with variations in axial length, lens and corneal power. The relative contributions of the latter two varied, depending on the particular population.

Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data.

Integrative factorization methods for multi-omic data estimate factors explaining biological variation. Factors can be treated as covariates to predict an outcome and the factorization can be used to impute missing values. However, no available methods provide a comprehensive framework for statistical inference and uncertainty quantification for these tasks. A novel framework, Bayesian Simultaneous Factorization (BSF), is proposed to decompose multi-omics variation into joint and individual structures simultaneously within a probabilistic framework. BSF uses conjugate normal priors and the posterior mode of this model can be estimated by solving a structured nuclear norm-penalized objective that also achieves rank selection and motivates the choice of hyperparameters. BSF is then extended to simultaneously predict a continuous or binary phenotype while estimating latent factors, termed Bayesian Simultaneous Factorization and Prediction (BSFP). BSF and BSFP accommodate concurrent imputation, i.e., imputation during the model-fitting process, and full posterior inference for missing data, including "blockwise" missingness. It is shown via simulation that BSFP is competitive in recovering latent variation structure, and demonstrate the importance of accounting for uncertainty in the estimated factorization within the predictive model. The imputation performance of BSF is examined via simulation under missing-at-random and missing-not-at-random assumptions. Finally, BSFP is used to predict lung function based on the bronchoalveolar lavage metabolome and proteome from a study of HIV-associated obstructive lung disease, revealing multi-omic patterns related to lung function decline and a cluster of patients with obstructive lung disease driven by shared metabolomic and proteomic abundance patterns.

Simultaneous Measurement of Strain and Temperature Distributions Using Optical Fibers with Different GeO2 and B2O3 Doping.

Compensating for the effects of temperature is a crucial issue in structural health monitoring when using optical fiber sensors. This study focused on the change in sensitivity due to differences in GeO2 and B2O3 doping and then verified the accuracy when measuring the strain and temperature distributions simultaneously. Four types of optical fiber sensors were utilized to measure the strain and temperature in four-point bending tests, and the best combination of the sensors resulted in strain and temperature errors of 28.4 µÏµ and 1.52 °C, respectively. Based on the results obtained from the four-point bending tests, we discussed the error factors via an error propagation analysis. The results of the error propagation analysis agreed well with the experimental results, thus indicating the effectiveness of the analysis as a method for verifying accuracy and error factors.

Bayesian Regression Quantifies Uncertainty of Binding Parameters from Isothermal Titration Calorimetry More Accurately Than Error Propagation.

We compare several different methods to quantify the uncertainty of binding parameters estimated from isothermal titration calorimetry data: the asymptotic standard error from maximum likelihood estimation, error propagation based on a first-order Taylor series expansion, and the Bayesian credible interval. When the methods are applied to simulated experiments and to measurements of Mg(II) binding to EDTA, the asymptotic standard error underestimates the uncertainty in the free energy and enthalpy of binding. Error propagation overestimates the uncertainty for both quantities, except in the simulations, where it underestimates the uncertainty of enthalpy for confidence intervals less than 70%. In both datasets, Bayesian credible intervals are much closer to observed confidence intervals.

Error quantification in multi-parameter mapping facilitates robust estimation and enhanced group level sensitivity.

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of PD, R1, and MTsat maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the model-based signal-to-noise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental raw-image-based SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from PD to R1 and decreased from PD to MTsat by a factor of 3-4. Exploring the artefact-sensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisition-specific errors to down-weight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their single-repeat or averaged counterparts. The error and mSNR maps may better inform power-calculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the open-source hMRI toolbox.

Using Conventional Cameras as Sensors for Estimating Confidence Intervals for the Speed of Vessels from Single Images.

In this paper, we describe an image-based approach for estimating the speed of a moving vessel using the wakes that remain on the surface of water after the vessel has passed. The proposed method calculates the speed of the vessel using only one RGB image. In this study, we used the vanishing line of the mean water plane, the camera height concerning the level of the tide, and the intrinsic parameters of the camera to perform geometric rectification on the surface plane of the water. We detected the location of troughs on one of the wake arms and computed the distance between them in the rectified image to estimate the speed of the vessel as a so-called inverse ship wake problem. We used a radar that was designed to monitor ships to validate the proposed method. We used statistical studies to determine the reliability and error propagation of the estimated values throughout the calculation process. The experiments showed that the proposed method produced precise and accurate results that agreed with the actual radar data when using a simple capture device, such as a conventional camera.

Optimizing the Energy Efficiency of Unreliable Memories for Quantized Kalman Filtering.

This paper presents a quantized Kalman filter implemented using unreliable memories. We consider that both the quantization and the unreliable memories introduce errors in the computations, and we develop an error propagation model that takes into account these two sources of errors. In addition to providing updated Kalman filter equations, the proposed error model accurately predicts the covariance of the estimation error and gives a relation between the performance of the filter and its energy consumption, depending on the noise level in the memories. Then, since memories are responsible for a large part of the energy consumption of embedded systems, optimization methods are introduced to minimize the memory energy consumption under the desired estimation performance of the filter. The first method computes the optimal energy levels allocated to each memory bank individually, and the second one optimizes the energy allocation per groups of memory banks. Simulations show a close match between the theoretical analysis and experimental results. Furthermore, they demonstrate an important reduction in energy consumption of more than 50%.

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC.

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

Assessment of Position Repeatability Error in an Electromagnetic Tracking System for Surgical Navigation.

In this paper we present a study of the repeatability of an innovative electromagnetic tracking system (EMTS) for surgical navigation, developed to overcome the state of the art of current commercial systems, allowing for the placement of the magnetic field generator far from the operating table. Previous studies led to the development of a preliminary EMTS prototype. Several hardware improvements are described, which result in noise reduction in both signal generation and the measurement process, as shown by experimental tests. The analysis of experimental results has highlighted the presence of drift in voltage components, whose effect has been quantified and related to the variation of the sensor position. Repeatability in the sensor position measurement is evaluated by means of the propagation of the voltage repeatability error, and the results are compared with the performance of the Aurora system (which represents the state of the art for EMTS for surgical navigation), showing a repeatability error about ten times lower. Finally, the proposed improvements aim to overcome the limited operating distance between the field generator and electromagnetic (EM) sensors provided by commercial EM tracking systems for surgical applications and seem to provide a not negligible technological advantage.

Analytical Assessment of the Propagation of Colored Sensor Noise in Strapdown Inertial Navigation.

Knowledge of the propagation of sensor errors in strapdown inertial navigation is crucial for the design of inertial and integrated navigation systems. The propagation of initialization errors and deterministic sensor errors is well covered in the literature. If considered at all, the propagation of inertial sensor noise has typically been assessed for un-correlated (white) Gaussian noise. Real inertial sensor noise, however, is time-correlated (colored) and best described by a combination of different stochastic processes. In this paper, we demonstrate how a navigation system's response to colored noise input differs from the response to bias-like or white noise inputs. We present a method for assessing the navigation error from various inertial sensor noise processes without the need for time-consuming Monte Carlo simulations and demonstrate its application and validity with real sensor data. The proposed method is used to determine in which scenarios the sensor's real noise can be approximated by simple white Gaussian noise. The results indicate that neglecting colored sensor noise is justified for many applications, but should be checked individually for each sensor configuration and mission.

Optimization of b-value schemes for estimation of the diffusion coefficient and the perfusion fraction with segmented intravoxel incoherent motion model fitting.

PURPOSE: Intravoxel incoherent motion (IVIM) modeling for estimation of the diffusion coefficient (D) and perfusion fraction (f) is increasingly popular, but no consensus on standard protocols exists. This study provides a framework for optimization of b-value schemes for reduced estimation uncertainty of D and f from segmented model fitting. THEORY: Analytical expressions for uncertainties of D and f from segmented model fitting were derived as Cramer-Rao lower bounds (CRLBs). METHODS: Optimized b-value schemes were obtained for 3 to 12 acquisitions and in the limit of infinitely many acquisitions through constrained minimization of the CRLBs, with b-values constrained to be 0 or 200 to 800 s/mm2 . The optimized b-value scheme with eight acquisitions was compared with b-values linearly distributed in the allowed range using simulations and in vivo liver data from seven healthy volunteers. RESULTS: All optimized b-value schemes contained exactly three unique b-values regardless of the total number of acquisitions (0, 200, and 800 s/mm2 ) with repeated acquisitions distributed approximately as 1:2:2. Compared with linearly distributed b-values, the variability of estimates of D and f was reduced by approximately 30% as seen both in simulations and in repeated in vivo measurements. CONCLUSION: The uncertainty of IVIM D and f estimates can be reduced by the use of optimized b-value schemes.

Multispectral Sensor Calibration and Characterization for sUAS Remote Sensing.

This paper focuses on the calibration of multispectral sensors typically used for remote sensing. These systems are often provided with "factory" radiometric calibration and vignette correction parameters. These parameters, which are assumed to be accurate when the sensor is new, may change as the camera is utilized in real-world conditions. As a result, regular calibration and characterization of any sensor should be conducted. An end-user laboratory method for computing both the vignette correction and radiometric calibration function is discussed in this paper. As an exemplar, this method for radiance computation is compared to the method provided by MicaSense for their RedEdge series of sensors. The proposed method and the method provided by MicaSense for radiance computation are applied to a variety of images captured in the laboratory using a traceable source. In addition, a complete error propagation is conducted to quantify the error produced when images are converted from digital counts to radiance. The proposed methodology was shown to produce lower errors in radiance imagery. The average percent error in radiance was -10.98%, -0.43%, 3.59%, 32.81% and -17.08% using the MicaSense provided method and their "factory" parameters, while the proposed method produced errors of 3.44%, 2.93%, 2.93%, 3.70% and 0.72% for the blue, green, red, near infrared and red edge bands, respectively. To further quantify the error in terms commonly used in remote sensing applications, the error in radiance was propagated to a reflectance error and additionally used to compute errors in two widely used parameters for assessing vegetation health, NDVI and NDRE. For the NDVI example, the ground reference was computed to be 0.899 ± 0.006, while the provided MicaSense method produced a value of 0.876 ± 0.005 and the proposed method produced a value of 0.897 ± 0.007. For NDRE, the ground reference was 0.455 ± 0.028, MicaSense method produced 0.239 ± 0.026 and the proposed method produced 0.435 ± 0.038.

Uncertainties in Model-Based Diesel Particulate Filter Diagnostics Using a Soot Sensor.

Monitoring the filtration efficiency of the diesel particulate filter (DPF), is a legislative requirement for minimizing particulate matter (PM) emissions from diesel engines of passenger cars and heavy-duty vehicles. To reach this target, on-board diagnostics (OBD) in real-time operation are required. Such systems in passenger cars are often utilizing a soot sensor, models for PM emissions simulation and algorithms for diagnosis. Their performance is associated with a series of challenges related to the accuracy and effectiveness of involved models, algorithms and hardware. This paper analyzes the main influencing factors and their impact on the effectiveness of the OBD system. The followed method comprised an error propagation analysis to quantify the error of detection during a New European Driving Cycle (NEDC). The results of the study regarding the performance of the OBD model showed that the total error of diagnosis is ±28%. This performance can be improved by increasing the sensor accuracy and the soot model, which can make the model appropriate for even tighter legislation limits and other approaches such as on-board monitoring (OBM).

The Application of Social Characteristic and L1 Optimization in the Error Correction for Network Coding in Wireless Sensor Networks.

One of the remarkable challenges about Wireless Sensor Networks (WSN) is how to transfer the collected data efficiently due to energy limitation of sensor nodes. Network coding will increase network throughput of WSN dramatically due to the broadcast nature of WSN. However, the network coding usually propagates a single original error over the whole network. Due to the special property of error propagation in network coding, most of error correction methods cannot correct more than C/2 corrupted errors where C is the max flow min cut of the network. To maximize the effectiveness of network coding applied in WSN, a new error-correcting mechanism to confront the propagated error is urgently needed. Based on the social network characteristic inherent in WSN and L1 optimization, we propose a novel scheme which successfully corrects more than C/2 corrupted errors. What is more, even if the error occurs on all the links of the network, our scheme also can correct errors successfully. With introducing a secret channel and a specially designed matrix which can trap some errors, we improve John and Yi's model so that it can correct the propagated errors in network coding which usually pollute exactly 100% of the received messages. Taking advantage of the social characteristic inherent in WSN, we propose a new distributed approach that establishes reputation-based trust among sensor nodes in order to identify the informative upstream sensor nodes. With referred theory of social networks, the informative relay nodes are selected and marked with high trust value. The two methods of L1 optimization and utilizing social characteristic coordinate with each other, and can correct the propagated error whose fraction is even exactly 100% in WSN where network coding is performed. The effectiveness of the error correction scheme is validated through simulation experiments.

Error Budget for Geolocation of Spectroradiometer Point Observations from an Unmanned Aircraft System.

We investigate footprint geolocation uncertainties of a spectroradiometer mounted on an unmanned aircraft system (UAS). Two microelectromechanical systems-based inertial measurement units (IMUs) and global navigation satellite system (GNSS) receivers were used to determine the footprint location and extent of the spectroradiometer. Errors originating from the on-board GNSS/IMU sensors were propagated through an aerial data georeferencing model, taking into account a range of values for the spectroradiometer field of view (FOV), integration time, UAS flight speed, above ground level (AGL) flying height, and IMU grade. The spectroradiometer under nominal operating conditions (8 ∘ FOV, 10 m AGL height, 0.6 s integration time, and 3 m/s flying speed) resulted in footprint extent of 140 cm across-track and 320 cm along-track, and a geolocation uncertainty of 11 cm. Flying height and orientation measurement accuracy had the largest influence on the geolocation uncertainty, whereas the FOV, integration time, and flying speed had the biggest impact on the size of the footprint. Furthermore, with an increase in flying height, the rate of increase in geolocation uncertainty was found highest for a low-grade IMU. To increase the footprint geolocation accuracy, we recommend reducing flying height while increasing the FOV which compensates the footprint area loss and increases the signal strength. The disadvantage of a lower flying height and a larger FOV is a higher sensitivity of the footprint size to changing distance from the target. To assist in matching the footprint size to uncertainty ratio with an appropriate spatial scale, we list the expected ratio for a range of IMU grades, FOVs and AGL heights.

Hybrid Transverse Polar Navigation for High-Precision and Long-Term INSs.

Transverse navigation has been proposed to help inertial navigation systems (INSs) fill the gap of polar navigation ability. However, as the transverse system does not have the ability of navigate globally, a complicated switch between the transverse and the traditional algorithms is necessary when the system moves across the polar circles. To maintain the inner continuity and consistency of the core algorithm, a hybrid transverse polar navigation is proposed in this research based on a combination of Earth-fixed-frame mechanization and transverse-frame outputs. Furthermore, a thorough analysis of kinematic error characteristics, proper damping technology and corresponding long-term contributions of main error sources is conducted for the high-precision INSs. According to the analytical expressions of the long-term navigation errors in polar areas, the 24-h period symmetrical oscillation with a slowly divergent amplitude dominates the transverse horizontal position errors, and the first-order drift dominates the transverse azimuth error, which results from the gyro drift coefficients that occur in corresponding directions. Simulations are conducted to validate the theoretical analysis and the deduced analytical expressions. The results show that the proposed hybrid transverse navigation can ensure the same accuracy and oscillation characteristics in polar areas as the traditional algorithm in low and mid latitude regions.

Fast Alignment of SINS for Marching Vehicles Based on Multi-Vectors of Velocity Aided by GPS and Odometer.

In the strap-down inertial navigation system (SINS), the initial attitude matrix is acquired through alignment. Though there were multiple valid methods, alignment time and accuracy are still core issues, especially regarding the condition of the motion carrier. Inspired by the idea of constructing nonlinear vectors by velocity in a different coordinate frame, this paper proposes an innovative alignment method for a vehicle-mounted SINS in motion. In this method, the core issue of acquiring the attitude matrix is to calculate the matrix between the inertial frame and the initial body frame, which can be constructed through the nonlinear velocity vectors' information from the GPS and the odometer at different moments, which denominate the multi-vector attitude determination. The possibility of collinearity can easily be avoided by a turning movement. The characteristic of propagation of error is analyzed in detail, based on which an improved method is put forward to depress the effect of random noise. Compared with the existing alignment methods, this method does not use the measurement information of accelerometers. In order to demonstrate its performance, the method is compared with the two-position alignment method and the traditional two-stage alignment method. Simulation and vehicle-based experiment results show that the proposed alignment method can establish an attitude reference in 100 s with an azimuth error of less than 0.06°, and that the accuracy does not have a strong correlation with the accelerometer.

Propagation of measurement accuracy to biomass soft-sensor estimation and control quality.

In biopharmaceutical process development and manufacturing, the online measurement of biomass and derived specific turnover rates is a central task to physiologically monitor and control the process. However, hard-type sensors such as dielectric spectroscopy, broth fluorescence, or permittivity measurement harbor various disadvantages. Therefore, soft-sensors, which use measurements of the off-gas stream and substrate feed to reconcile turnover rates and provide an online estimate of the biomass formation, are smart alternatives. For the reconciliation procedure, mass and energy balances are used together with accuracy estimations of measured conversion rates, which were so far arbitrarily chosen and static over the entire process. In this contribution, we present a novel strategy within the soft-sensor framework (named adaptive soft-sensor) to propagate uncertainties from measurements to conversion rates and demonstrate the benefits: For industrially relevant conditions, hereby the error of the resulting estimated biomass formation rate and specific substrate consumption rate could be decreased by 43 and 64 %, respectively, compared to traditional soft-sensor approaches. Moreover, we present a generic workflow to determine the required raw signal accuracy to obtain predefined accuracies of soft-sensor estimations. Thereby, appropriate measurement devices and maintenance intervals can be selected. Furthermore, using this workflow, we demonstrate that the estimation accuracy of the soft-sensor can be additionally and substantially increased.

Methodological factors affecting joint moments estimation in clinical gait analysis: a systematic review.

Quantitative gait analysis can provide a description of joint kinematics and dynamics, and it is recognized as a clinically useful tool for functional assessment, diagnosis and intervention planning. Clinically interpretable parameters are estimated from quantitative measures (i.e. ground reaction forces, skin marker trajectories, etc.) through biomechanical modelling. In particular, the estimation of joint moments during motion is grounded on several modelling assumptions: (1) body segmental and joint kinematics is derived from the trajectories of markers and by modelling the human body as a kinematic chain; (2) joint resultant (net) loads are, usually, derived from force plate measurements through a model of segmental dynamics. Therefore, both measurement errors and modelling assumptions can affect the results, to an extent that also depends on the characteristics of the motor task analysed (i.e. gait speed). Errors affecting the trajectories of joint centres, the orientation of joint functional axes, the joint angular velocities, the accuracy of inertial parameters and force measurements (concurring to the definition of the dynamic model), can weigh differently in the estimation of clinically interpretable joint moments. Numerous studies addressed all these methodological aspects separately, but a critical analysis of how these aspects may affect the clinical interpretation of joint dynamics is still missing. This article aims at filling this gap through a systematic review of the literature, conducted on Web of Science, Scopus and PubMed. The final objective is hence to provide clear take-home messages to guide laboratories in the estimation of joint moments for the clinical practice.

Unaccounted uncertainty from qPCR efficiency estimates entails uncontrolled false positive rates.

BACKGROUND: Accurate adjustment for the amplification efficiency (AE) is an important part of real-time quantitative polymerase chain reaction (qPCR) experiments. The most commonly used correction strategy is to estimate the AE by dilution experiments and use this as a plug-in when efficiency correcting the Δ Δ C q . Currently, it is recommended to determine the AE with high precision as this plug-in approach does not account for the AE uncertainty, implicitly assuming an infinitely precise AE estimate. Determining the AE with such precision, however, requires tedious laboratory work and vast amounts of biological material. Violation of the assumption leads to overly optimistic standard errors of the Δ Δ C q , confidence intervals, and p-values which ultimately increase the type I error rate beyond the expected significance level. As qPCR is often used for validation it should be a high priority to account for the uncertainty of the AE estimate and thereby properly bounding the type I error rate and achieve the desired significance level. RESULTS: We suggest and benchmark different methods to obtain the standard error of the efficiency adjusted Δ Δ C q using the statistical delta method, Monte Carlo integration, or bootstrapping. Our suggested methods are founded in a linear mixed effects model (LMM) framework, but the problem and ideas apply in all qPCR experiments. The methods and impact of the AE uncertainty are illustrated in three qPCR applications and a simulation study. In addition, we validate findings suggesting that MGST1 is differentially expressed between high and low abundance culture initiating cells in multiple myeloma and that microRNA-127 is differentially expressed between testicular and nodal lymphomas. CONCLUSIONS: We conclude, that the commonly used efficiency corrected quantities disregard the uncertainty of the AE, which can drastically impact the standard error and lead to increased false positive rates. Our suggestions show that it is possible to easily perform statistical inference of Δ Δ C q , whilst properly accounting for the AE uncertainty and better controlling the false positive rate.