Vector quantization based Gaussian modeling for speaker verification

Gaussian mixture models (GMMs) have become an established means of modeling feature distributions in speaker recognition systems. It is useful for experimentation and practical implementation purposes to develop and test these models in an efficient manner particularly when computational resources are limited. A method of combining vector quantization (VQ) with single multi-dimensional Gaussians is proposed to rapidly generate a robust model approximation to the Gaussian mixture model. A fast method of testing these systems is also proposed and implemented. Results on the NIST 1996 Speaker Recognition Database suggest comparable and in some cases an improved verification performance to the traditional GMM based analysis scheme. In addition, previous research for the task of speaker identification indicated a similar system perfomance between the VQ Gaussian based technique and GMMs

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Gaussian process models for sensor-centric robot localisation

This paper presents an approach to building an observation likelihood function from a set of sparse, noisy training observations taken from known locations by a sensor with no obvious geometric model. The basic approach is to fit an interpolant to the training data, representing the expected observation, and to assume additive sensor noise. This paper takes a Bayesian view of the problem, maintaining a posterior over interpolants rather than simply the maximum-likelihood interpolant, giving a measure of uncertainty in the map at any point. This is done using a Gaussian process framework. To validate the approach experimentally, a model of an environment is built using observations from an omni-directional camera. After a model has been built from the training data, a particle filter is used to localise while traversing this environment

PySSM : a Python module for Bayesian inference of linear Gaussian state space models

PySSM is a Python package that has been developed for the analysis of time series using linear Gaussian state space models (SSM). PySSM is easy to use; models can be set up quickly and efficiently and a variety of different settings are available to the user. It also takes advantage of scientific libraries Numpy and Scipy and other high level features of the Python language. PySSM is also used as a platform for interfacing between optimised and parallelised Fortran routines. These Fortran routines heavily utilise Basic Linear Algebra (BLAS) and Linear Algebra Package (LAPACK) functions for maximum performance. PySSM contains classes for filtering, classical smoothing as well as simulation smoothing.

Probability analysis of machine angle stability with non-gaussian wind power input

The security of power transfer across a given transmission link is typically a steady state assessment. This paper develops tools to assess machine angle stability as affected by a combination of faults and uncertainty of wind power using probability analysis. The paper elaborates on the development of the theoretical assessment tool and demonstrates its efficacy using single machine infinite bus system.

Laser-radar data fusion with Gaussian Process Implicit Surfaces

This work considers the problem of building high-fidelity 3D representations of the environment from sensor data acquired by mobile robots. Multi-sensor data fusion allows for more complete and accurate representations, and for more reliable perception, especially when different sensing modalities are used. In this paper, we propose a thorough experimental analysis of the performance of 3D surface reconstruction from laser and mm-wave radar data using Gaussian Process Implicit Surfaces (GPIS), in a realistic field robotics scenario. We first analyse the performance of GPIS using raw laser data alone and raw radar data alone, respectively, with different choices of covariance matrices and different resolutions of the input data. We then evaluate and compare the performance of two different GPIS fusion approaches. The first, state-of-the-art approach directly fuses raw data from laser and radar. The alternative approach proposed in this paper first computes an initial estimate of the surface from each single source of data, and then fuses these two estimates. We show that this method outperforms the state of the art, especially in situations where the sensors react differently to the targets they perceive.

Traversability estimation for a planetary rover via experimental kernel learning in a Gaussian process framework

A critical requirement for safe autonomous navigation of a planetary rover is the ability to accurately estimate the traversability of the terrain. This work considers the problem of predicting the attitude and configuration angles of the platform from terrain representations that are often incomplete due to occlusions and sensor limitations. Using Gaussian Processes (GP) and exteroceptive data as training input, we can provide a continuous and complete representation of terrain traversability, with uncertainty in the output estimates. In this paper, we propose a novel method that focuses on exploiting the explicit correlation in vehicle attitude and configuration during operation by learning a kernel function from vehicle experience to perform GP regression. We provide an extensive experimental validation of the proposed method on a planetary rover. We show significant improvement in the accuracy of our estimation compared with results obtained using standard kernels (Squared Exponential and Neural Network), and compared to traversability estimation made over terrain models built using state-of-the-art GP techniques.

Fast re-parameterisation of Gaussian mixture models for robotics applications

Autonomous navigation and picture compilation tasks require robust feature descriptions or models. Given the non Gaussian nature of sensor observations, it will be shown that Gaussian mixture models provide a general probabilistic representation allowing analytical solutions to the update and prediction operations in the general Bayesian filtering problem. Each operation in the Bayesian filter for Gaussian mixture models multiplicatively increases the number of parameters in the representation leading to the need for a re-parameterisation step. A computationally efficient re-parameterisation step will be demonstrated resulting in a compact and accurate estimate of the true distribution.

Robust multiple-sensing-modality data fusion using Gaussian Process Implicit Surfaces

The ability to build high-fidelity 3D representations of the environment from sensor data is critical for autonomous robots. Multi-sensor data fusion allows for more complete and accurate representations. Furthermore, using distinct sensing modalities (i.e. sensors using a different physical process and/or operating at different electromagnetic frequencies) usually leads to more reliable perception, especially in challenging environments, as modalities may complement each other. However, they may react differently to certain materials or environmental conditions, leading to catastrophic fusion. In this paper, we propose a new method to reliably fuse data from multiple sensing modalities, including in situations where they detect different targets. We first compute distinct continuous surface representations for each sensing modality, with uncertainty, using Gaussian Process Implicit Surfaces (GPIS). Second, we perform a local consistency test between these representations, to separate consistent data (i.e. data corresponding to the detection of the same target by the sensors) from inconsistent data. The consistent data can then be fused together, using another GPIS process, and the rest of the data can be combined as appropriate. The approach is first validated using synthetic data. We then demonstrate its benefit using a mobile robot, equipped with a laser scanner and a radar, which operates in an outdoor environment in the presence of large clouds of airborne dust and smoke.

Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Hydraulic conductivity fields: Gaussian or not?

Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.

Autonomous vehicle path planning for persistence monitoring under uncertainty using Gaussian based Markov decision process

One of the main challenges facing online and offline path planners is the uncertainty in the magnitude and direction of the environmental energy because it is dynamic, changeable with time, and hard to forecast. This thesis develops an artificial intelligence for a mobile robot to learn from historical or forecasted data of environmental energy available in the area of interest which will help for a persistence monitoring under uncertainty using the developed algorithm.

An efficient DSE using conditional multivariate complex Gaussian distribution

This paper presents an efficient noniterative method for distribution state estimation using conditional multivariate complex Gaussian distribution (CMCGD). In the proposed method, the mean and standard deviation (SD) of the state variables is obtained in one step considering load uncertainties, measurement errors, and load correlations. In this method, first the bus voltages, branch currents, and injection currents are represented by MCGD using direct load flow and a linear transformation. Then, the mean and SD of bus voltages, or other states, are calculated using CMCGD and estimation of variance method. The mean and SD of pseudo measurements, as well as spatial correlations between pseudo measurements, are modeled based on the historical data for different levels of load duration curve. The proposed method can handle load uncertainties without using time-consuming approaches such as Monte Carlo. Simulation results of two case studies, six-bus, and a realistic 747-bus distribution network show the effectiveness of the proposed method in terms of speed, accuracy, and quality against the conventional approach.