GNSS Signal Detection Under Noise Uncertainty

High sensitivity detection techniques are required for indoor navigation using Global Navigation Satellite System (GNSS) receivers, and typically, a combination of coherent and non- coherent integration is used as the test statistic for detection. The coherent integration exploits the deterministic part of the signal and is limited due to the residual frequency error, navigation data bits and user dynamics, which are not known apriori. So, non- coherent integration, which involves squaring of the coherent integration output, is used to improve the detection sensitivity. Due to this squaring, it is robust against the artifacts introduced due to data bits and/or frequency error. However, it is susceptible to uncertainty in the noise variance, and this can lead to fundamental sensitivity limits in detecting weak signals. In this work, the performance of the conventional non-coherent integration-based GNSS signal detection is studied in the presence of noise uncertainty. It is shown that the performance of the current state of the art GNSS receivers is close to the theoretical SNR limit for reliable detection at moderate levels of noise uncertainty. Alternate robust post-coherent detectors are also analyzed, and are shown to alleviate the noise uncertainty problem. Monte-Carlo simulations are used to confirm the theoretical predictions.

Robust Formulations for Handling Uncertainty in Kernel Matrices

We study the problem of uncertainty in the entries of the Kernel matrix, arising in SVM formulation. Using Chance Constraint Programming and a novel large deviation inequality we derive a formulation which is robust to such noise. The resulting formulation applies when the noise is Gaussian, or has finite support. The formulation in general is non-convex, but in several cases of interest it reduces to a convex program. The problem of uncertainty in kernel matrix is motivated from the real world problem of classifying proteins when the structures are provided with some uncertainty. The formulation derived here naturally incorporates such uncertainty in a principled manner leading to significant improvements over the state of the art. 1.

Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.

A Method for Evaluation of Product Lifecycle Alternatives under Uncertainty

In each stage of product development, we need to take decisions, by evaluating multiple product alternatives based on multiple criteria. Classical evaluation methods like weighted objectives method assumes certainty about information available during product development. However, designers often must evaluate under uncertainty. Often the likely performance, cost or environmental impacts of a product proposal could be estimated only with certain confidence, which may vary from one proposal to another. In such situations, the classical approaches to evaluation can give misleading results. There is a need for a method that can aid in decision making by supporting quantitative comparison of alternatives to identify the most promising alternative, under uncertain information about the alternatives. A method called confidence weighted objectives method is developed to compare the whole life cycle of product proposals using multiple evaluation criteria under various levels of uncertainty with non crisp values. It estimates the overall worth of proposal and confidence on the estimate, enabling deferment of decision making when decisions cannot be made using current information available.

Uncertainty Quantification in Helicopter Performance Using Monte Carlo Simulations

The effect of structural and aerodynamic uncertainties on the performance predictions of a helicopter is investigated. An aerodynamic model based on blade element and momentum theory is used to predict the helicopter performance. The aeroelastic parameters, such as blade chord, rotor radius, two-dimensional lift-curve slope, blade profile drag coefficient, rotor angular velocity, blade pitch angle, and blade twist rate per radius of the rotor, are considered as random variables. The propagation of these uncertainties to the performance parameters, such as thrust coefficient and power coefficient, are studied using Monte Carlo Simulations. The simulations are performed with 100,000 samples of structural and aerodynamic uncertain variables with a coefficient of variation ranging from 1 to 5%. The scatter in power predictions in hover, axial climb, and forward flight for the untwisted and linearly twisted blades is studied. It is found that about 20-25% excess power can be required by the helicopter relative to the determination predictions due to uncertainties.

Representation of evidence: An approach to uncertainty handling in knowledge-based systems

Many knowledge based systems (KBS) transform a situation information into an appropriate decision using an in built knowledge base. As the knowledge in real world situation is often uncertain, the degree of truth of a proposition provides a measure of uncertainty in the underlying knowledge. This uncertainty can be evaluated by collecting `evidence' about the truth or falsehood of the proposition from multiple sources. In this paper we propose a simple framework for representing uncertainty in using the notion of an evidence space.

Uncertainty visualization using HDR volume rendering

In this paper, we explore a novel idea of using high dynamic range (HDR) technology for uncertainty visualization. We focus on scalar volumetric data sets where every data point is associated with scalar uncertainty. We design a transfer function that maps each data point to a color in HDR space. The luminance component of the color is exploited to capture uncertainty. We modify existing tone mapping techniques and suitably integrate them with volume ray casting to obtain a low dynamic range (LDR) image. The resulting image is displayed on a conventional 8-bits-per-channel display device. The usage of HDR mapping reveals fine details in uncertainty distribution and enables the users to interactively study the data in the context of corresponding uncertainty information. We demonstrate the utility of our method and evaluate the results using data sets from ocean modeling.