Absence Of Measurement Noise Research Articles

Analytical Approach to Design of Proportional-to-the-Absolute-Temperature Current Sources and Temperature Sensors Based on Heterojunction Bipolar Transistors

Embedded temperature sensors based on proportional-to-the-absolute-temperature (PTAT) current sources have the potential to lay the foundation for low-cost temperature-aware integrated circuit architectures if they meet the requirements of miniaturization, fabrication process match, and precise estimation in a wide range of temperatures. This paper addresses an analytical approach to the minimum-element PTAT circuit design capitalizing on the physics-based modeling of the heterojunction bipolar transistor (HBT) structures. It is shown that a PTAT circuit can be implemented on only two core HBT elements with good accuracy. Derived parametric relations allow a straightforward specification of the thermal gain at the design stage, which affects sensor sensitivity. Further derived current-to-temperature mapping expresses a temperature estimate based on the measured PTAT output current. Numerical examples indicate attainable estimation accuracy of 0.43% in case of a measurement instance taken in the absence of measurement noise.

Fine scale uncertainty in parameter estimation for elliptic equations

We study the problem of estimating the coefficients in an elliptic partial differential equation using noisy measurements of a solution to the equation. Although the unknown coefficients may vary on many scales, we aim only at estimating their slowly varying parts, thus reducing the complexity of the inverse problem. However, ignoring the fine-scale fluctuations altogether introduces uncertainty in the estimates, even in the absence of measurement noise. We propose a strategy for quantifying the uncertainty due to the fine-scale fluctuations in the coefficients by modeling their effect on the solution of the forward problem using the central limit theorem. When this is possible, the Bayesian estimation of the coefficients reduces to a weighted least-squares problem with a covariance matrix whose rank is low regardless of the number of measurements and does not depend on the details of the coefficient fluctuations.

Comparative Analysis of Some Modal Reconstruction Methods of the Shape of the Cornea from Corneal Elevation Data

A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity was performed, by using both standard radial polynomials and radial basis functions (RBFs). The hypothesis was that the correct approach in the case of highly irregular corneas should combine several bases. Standard approaches of reconstruction by Zernike and other types of radial polynomials were compared with the discrete least-squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the absence of measurement noise. For the reconstruction by polynomials, the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF was performed by using a regular grid of centers. The quality of fit was assessed by computing for each surface the mean square errors (MSEs) of the reconstruction by LSF, measured at the same nodes where the heights were collected. Another criterion of the fit quality used was the accuracy in recovery of the Zernike coefficients, especially in the case of incomplete data. The Zernike (and especially, the Bhatia-Wolf) polynomials constitute a reliable reconstruction method of a nonseverely aberrated surface with a small surface regularity index (SRI). However, they fail to capture small deformations of the anterior surface of a synthetic cornea. The most promising approach is a combined one that balances the robustness of the Zernike fit with the localization of the RBF.

Energy-based sensor network source localization via projection onto convex sets

This correspondence addresses the problem of locating an acoustic source using a sensor network in a distributed manner, i.e., without transmitting the full data set to a central point for processing. This problem has been traditionally addressed through the maximum-likelihood framework or nonlinear least squares. These methods, even though asymptotically optimal under certain conditions, pose a difficult global optimization problem. It is shown that the associated objective function may have multiple local optima and saddle points, and hence any local search method might stagnate at a suboptimal solution. In this correspondence, we formulate the problem as a convex feasibility problem and apply a distributed version of the projection-onto-convex-sets (POCS) method. We give a closed-form expression for the projection phase, which usually constitutes the heaviest computational aspect of POCS. Conditions are given under which, when the number of samples increases to infinity or in the absence of measurement noise, the convex feasibility problem has a unique solution at the true source location. In general, the method converges to a limit point or a limit cycle in the neighborhood of the true location. Simulation results show convergence to the global optimum with extremely fast convergence rates compared to the previous methods

Estimation of confidence intervals for radial emissivity and optimization of data treatment techniques in Abel inversion

A novel method is described for finding confidence intervals for radially resolved emissivity derived from Abel inversion. The essence of the method is that the measured lateral emission profile (here a profile is defined as a line-of-sight spatial map) is split into two components, namely (a) an estimated noise-free lateral emission profile that mimics the lateral emission profile in the absence of measurement noise and (b) a noise profile that estimates the magnitude of noise along the lateral profile. Through random-number generation, noise with a magnitude defined by the noise profile is then artificially added to the estimated noise-free lateral profile. If this noise-addition and subsequent Abel inversion is iterated for a sufficient number of cycles, a statistical distribution of the Abel-inverted radial profiles can be obtained and confidence intervals can thus be estimated. It was verified that an effective means for the estimation of the noise-free lateral profile involves approximation of the lateral emission profile through polynomial fitting. A noise profile can then be obtained by assuming that the residual between the experimental lateral profile and the fitted profile is due solely to noise. The validity of this methodology was verified with seven lateral test profiles. In addition, the parameters that are commonly used in data treatment by Abel inversion are optimized. It was found that 100–300 data points are sufficient for accurate Abel inversion using the Nestor-Olsen inversion algorithm; more data points provide only minimal improvement in the inversion. Also, it was found that most commonly observed lateral emission profiles can be satisfactorily approximated by polynomials with a degree of fifteen. Further, polynomial fitting can be used to partially filter out noise in the lateral profile. Depending on the shape of the lateral profile and the magnitude of the noise, the optimal polynomial order, in general, ranges from ten to fifteen. For higher-degree polynomials, the effectiveness of a polynomial as a noise filter decreases and severely degrades the quality of the Abel-inverted radial profile.

Correcting for sub-grid filtering effects in particle image velocimetry data

Particle image velocimetry methodology results in a spatial averaging of the real velocity field into a set of discrete measured velocities: one for each interrogation cell. In the absence of measurement noise, this filtering process results in a reduction of the measured turbulent kinetic energy and other second-order statistics of the velocity field. The reduction in this energy will naturally be dependent upon the amount of turbulent energy at lengthscales smaller than can be resolved by the interrogation cells that make up the measurement grid. This paper investigates the effects of sub-grid scale filtering on the second-order statistics of velocity. Several experiments are reported for which interrogation cell size to turbulent integral lengthscale ratios were varied. In addition, synthetic turbulent velocity fields with known spatial correlation functions are used to support experimental results and provide calibration for the estimation of the level of sub-grid filtering. It is suggested that to accurately capture most turbulent kinetic energy using PIV the interrogation cell should be at least of order ten times smaller than the integral lengthscale of the flow. A method is then provided to estimate the level of sub-grid filtering should the interrogation cell be larger than this limit up to around the size of the integral lengthscale. With interrogation cells larger than this lengthscale then sub-grid filtering is such that second-order statistics are reduced by over 50% and it should be considered unwise to rely on any second-order statistics from such a scenario, corrected or otherwise.

Empirical Modeling for Glucose Control in Critical Care and Diabetes

Empirical Volterra series models of glucose–insulin behavior were identified from input–output data provided by a physiologically-based nonlinear patient model. While completely identified nonlinear Volterra models provided accurate output prediction, clinical data limitations constrained the structure of the Volterra series to linear plus nonlinear diagonal coefficients. In the absence of measurement noise, the ability of this structurally constrained model to capture process dynamics was very good. The addition of Gaussian distributed measurement noise, having variance 10 mg2/dL2, significantly degraded coefficient estimates, but projection onto the Laguerre basis (with subsequent expansion to the Volterra space for analysis) provided excellent noise-filtering and model predictions requiring only 164 measurements to identify 121 Volterra coefficients. Linear and nonlinear model predictive control algorithms were developed from the identified Volterra models. In the absence of measurement noise, nonlinear control algorithms provided mild performance enhancement in rejecting a 50 g glucose challenge. With the addition of measurement noise matching the above noise characteristics, the benefits of nonlinear control were lost. The superiority of the nonlinear empirical model to capture open-loop data did not translate into closed-loop performance enhancement in the presence of measurement noise. Linear model predictive control, with the ability to filter noise effects by proper tuning, provided the best combination of performance and robustness to uncertainty (both measurement and model) in this nonlinear case study.

APPLICATION OF THE CONDITIONED REVERSE PATH METHOD

Conventional frequency response estimations often give results contaminated by the presence of non-linearities and the extraction of underlying linear system properties is thus difficult. To overcome this problem, the implementation of the Conditioned Reverse Path spectral method to the identification of single- and multi-degree-of-freedom (sdof and mdof) non-linear systems is considered, showing that conventional methods such as ‘H 1’ and ‘H 2’ lead to estimated frequency response functions which are often completely inadequate, even in absence of measurement noise. This spectral method allows to estimate the coefficients of the non-linearities away from the location of the applied excitations and also to identify the linear dynamic compliance matrix when the number of excitations is smaller than the number of response locations. This paper presents some guidelines to successfully apply this method to real non-linear systems; furthermore, the results from an experimental test over a sdof suspension system are shown.

Marked regularity models

We present a generalization of the regularity model, which is a stationary point process model describing how often and how regularly a random "event" occurs. The generalization allows the amplitude of each event to be a sample from a random process. First, we developed closed-form approximations of the power spectra of data segments; then we examined the accuracy of a procedure that estimates the regularity and mark process parameters by minimizing the error between measured spectra and the approximations. We found the following. In the absence of measurement noise, joint estimation of both mark and regularity parameters is accurate only if the ratio of the square of the mean of the marks to the variance of the marks (the SMNPR) is small. Marginal estimation of the regularity process parameters can be accurate if the mark process is taken into account by minimizing overall parameters; the accuracy then depends on both measurement noise and SMNPR. Error in the marginal estimation of the regularity process parameters will be inversely proportional to the SMNPR if the marks are ignored by minimizing only with respect to the regularity parameters, so ignoring the marks can cause a substantial degradation in accuracy when the SMNPR is small. We illustrate these findings with an acoustic scattering example in which simulated ultrasound measurements of tissue samples are characterized by their description in the parameter space.

Cumulant-based identification of noisy closed loop systems

SUMMARY Conventional parameter estimation approaches fail to identify linear systems operating in closed loop when both input and output measurements are contaminated by additive noise of unknown (cross)spectral characteristics. However, even in the absence of measurement noise, parameter estimation is involved owing to the additive system noise entering the loop. The present work introduces a novel criterion which is theoretically insensitive to a class of disturbances and yields the same parameter estimates that one obtains using mean squared error (MSE) minimization in the absence of noise. A strongly convergent sample-based approximation of the proposed criterion is introduced for consistent parameter estimation in practice. It is also shown that in the common case of ARMA modelling the resulting parameter estimates coincide with those obtained from a set of linear equations which can be solved using a time-recursive algorithm. Simulation results are presented to verify the performance of the proposed schemes in low-signal-to-noise-ratio environments.

Least squares range difference location

An array of n sensors at known locations receives the signal from an emitter whose location is desired. By measuring the time differences of arrival (TDOAs) between pairs of sensors, the range differences (RDs) are available and it becomes possible to compute the emitter location. Traditionally geometric solutions have been based on intersections of hyperbolic lines of position (LOPs). Each measured TDOA provides one hyperbolic LOP. In the absence of measurement noise, the RDs taken around any closed circuit of sensors add to zero. A bivector is introduced from exterior algebra such that when noise is present, the measured bivector of RDs is generally infeasible in that there does not correspond any actual emitter position exhibiting them. A circuital sum trivector is also introduced to represent the infeasibility; a null trivector implies a feasible RD bivector. A 2-step RD Emitter Location algorithm is proposed which exploits this implicit structure. Given the observed noisy RD bivector /spl Delta/, (1) calculate the nearest feasible RD bivector /spl Delta//spl circ/, and (2) calculate the nearest point to the (/sub 3//sup n/) planes of position, one for each of the triads of elements of /spl Delta//spl circ/. Both algorithmic steps are least squares (LS) and finite. Numerical comparisons in simulation show a substantial improvement in location error variances.