Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Enhancing the Instantaneous Dynamic Range of Electronic Warfare Receivers Using Statistical Signal Processing

Accurately processing multiple, time-coincident signals presents a challenge to Electronic Warfare (EW) receivers, especially if the signals are close in frequency and/or mismatched in amplitude. The metric that quantifies an EW receiver\u27s ability to measure time-coincident signals is the Instantaneous Dynamic Range (IDR), defined for a given frequency estimation accuracy, a given frequency separation and a given SNR as the maximum signal amplitude ratio that can be accommodated. Using a two sinusoid time-series model, this thesis analyzes IDR for ideal intercept and parametric digital EW receivers. In general, the number of signals contained in the EW receiver measurement interval is unknown. Thus, the non-parametric Discrete Fourier Transform (DFT) is employed in an EW intercept receiver with the associated amplitude dependent spectral leakage which limits IDR. A novel method to improve the DFT-based intercept receiver IDR by compensating for the high amplitude signal\u27s spectral leakage using computationally efficient 3 bin interpolation algorithms is proposed and analyzed. For a desired frequency estimation accuracy of 1.5 bins, the method achieves an IDR of 57 dB with little frequency separation dependence when the signals are separated by more than 2 bins with a low amplitude signal SNR of 10 dB. For situations where the number of signals contained in the measurement interval is known, the IDR of an Iterative Generalized Least Squares (IGLS) algorithm-based parametric receiver is analyzed. A real and complex signal IDR Cramer-Rao Bound (IDR-CRB) is derived for parametric receivers by extending results contained in Rife. For tight frequency estimate requirements (these requirements depend on the number of measurement samples), the IDR-CRB yields achievable bounds. For less stringent frequency estimate requirements, the IDR-CRB is unrealisti

Optimal maneuvering of seismic sensors for localization of subsurface targets

We consider the problem of detecting and locating buried land mines and subsurface objects by using a maneuvering array that receives scattered seismic surface waves. We demonstrate an adaptive system that moves an array of receivers according to an optimal positioning algorithm based on the theory of optimal experiments. The goal is to minimize the number of distinct measurements (array movements) needed to localize mines. The adaptive localization algorithm has been tested using experimental data collected in a laboratory facility at Georgia Tech. The performance of algorithm is exhibited for cases with one or two targets and in the presence of common types of clutter like rocks found in the soil. It has also been tested for the case where the propagation properties of the medium vary spatially. In almost all test cases the mines were located exactly using three or four array movements. It is envisioned that future systems could incorporate this new method into a portable mobile mine-location system

A pre-filtering maximum likelihood approach to multiple source direction estimation.

Imperial Users onl

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the sampling rate. Then, the signal can be perfectly reconstructed from its samples. Increasing evidence shows that the requirements imposed by Shannon's sampling theorem are too conservative for many naturally-occurring signals, which can be accurately characterized by sparse representations that require lower sampling rates closer to the signal's intrinsic information rates. Finite rate of innovation (FRI) is a new theory that allows to extract underlying sparse signal representations while operating at a reduced sampling rate. The goal of this PhD work is to advance reconstruction techniques for sparse signal representations from both theoretical and practical points of view. Specifically, the FRI framework is extended to deal with applications that involve temporal and spatial localization of events, including inverse source problems from radiating fields. We propose a novel reconstruction method using a model-fitting approach that is based on minimizing the fitting error subject to an underlying annihilation system given by the Prony's method. First, we showed that this is related to the problem known as structured low-rank matrix approximation as in structured total least squares problem. Then, we proposed to solve our problem under three different constraints using the iterative quadratic maximum likelihood algorithm. Our analysis and simulation results indicate that the proposed algorithms improve the robustness of the results with respect to common FRI reconstruction schemes. We have further developed the model-fitting approach to analyze spontaneous brain activity as measured by functional magnetic resonance imaging (fMRI). For this, we considered the noisy fMRI time course for every voxel as a convolution between an underlying activity inducing signal (i.e., a stream of Diracs) and the hemodynamic response function (HRF). We then validated this method using experimental fMRI data acquired during an event-related study. The results showed for the first time evidence for the practical usage of FRI for fMRI data analysis. We also addressed the problem of retrieving a sparse source distribution from the boundary measurements of a radiating field. First, based on Green's theorem, we proposed a sensing principle that allows to relate the boundary measurements to the source distribution. We focused on characterizing these sensing functions with particular attention for those that can be derived from holomorphic functions as they allow to control spatial decay of the sensing functions. With this selection, we developed an FRI-inspired non-iterative reconstruction algorithm. Finally, we developed an extension to the sensing principle (termed eigensensing) where we choose the spatial eigenfunctions of the Laplace operator as the sensing functions. With this extension, we showed that eigensensing principle allows to extract partial Fourier measurements of the source functions from boundary measurements. We considered photoacoustic tomography as a potential application of these theoretical developments

Intelligent joint channel parameter estimation techniques for mobile wireless positioning applications

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Mobile wireless positioning has recently received great attention. For mobile wireless communication networks, an inherently suitable approach is to obtain the parameters that are used for positioning estimates from the radio signal measurements between a mobile device and one or more xed base stations. However, obtaining accurate estimates of these location-dependent channel parameters is a challenging task. The focus of this thesis is on the estimation of these channel parameters for mobile wireless positioning applications. In particular, we investigate novel estimators that jointly estimate more than one type of channel parameters. We rst perform a comprehensive critical review on the most recent and popular joint channel parameter estimation techniques. Secondly, we improve a state-of-the-art technique, namely the Space Alternating Generalised Expectation maximisation (SAGE) algorithm by employing adaptive interference cancellation to improve the estimation accuracy of weaker paths. Thirdly, a novel intelligent channel parameter estimation technique using Evolution Strategy (ES) is proposed to overcome the drawbacks of the existing iterative maximum likelihood methods. Furthermore, given that in reality it is di cult to obtain the number of multipath in advance, we propose a two tier Hierarchically Organised ES to jointly estimate the number of multipath as well as the channel parameters. Finally, we extend the proposed ES method to further estimate the Doppler shift in mobile environments. Our proposed intelligent joint channel estimation techniques are shown to exhibit excellent performance even with low Signal to Noise Ratio (SNR) channel conditions as well as robust against uncertainties in initialisations.EPSRC and Cambridge Silicon Radi

Beyond the noise : high fidelity MR signal processing

This thesis describes a variety of methods developed to increase the sensitivity and resolution of liquid state nuclear magnetic resonance (NMR) experiments. NMR is known as one of the most versatile non-invasive analytical techniques yet often suffers from low sensitivity. The main contribution to this low sensitivity issue is a presence of noise and level of noise in the spectrum is expressed numerically as “signal-to-noise ratio”. NMR signal processing involves sensitivity and resolution enhancement achieved by noise reduction using mathematical algorithms. A singular value decomposition based reduced rank matrix method, composite property mapping, in particular is studied extensively in this thesis to present its advantages, limitations, and applications. In theory, when the sum of k noiseless sinusoidal decays is formatted into a specific matrix form (i.e., Toeplitz), the matrix is known to possess k linearly independent columns. This information becomes apparent only after a singular value decomposition of the matrix. Singular value decomposition factorises the large matrix into three smaller submatrices: right and left singular vector matrices, and one diagonal matrix containing singular values. Were k noiseless sinusoidal decays involved, there would be only k nonzero singular values appearing in the diagonal matrix in descending order providing the information of the amplitude of each sinusoidal decay. The number of non-zero singular values or the number of linearly independent columns is known as the rank of the matrix. With real NMR data none of the singular values equals zero and the matrix has full rank. The reduction of the rank of the matrix and thus the noise in the reconstructed NMR data can be achieved by replacing all the singular values except the first k values with zeroes. This noise reduction process becomes difficult when biomolecular NMR data is to be processed due to the number of resonances being unknown and the presence of a large solvent peak

Méthodes de codage et d'estimation adaptative appliquées aux communications sans fil

Les recherches et les contributions présentées portent sur des techniques de traitement du signal appliquées aux communications sans fil. Elles s’articulent autour des points suivants : (1) l’estimation adaptative de canaux de communication dans différents contextes applicatifs, (2) la correction de bruit impulsionnel et la réduction du niveau de PAPR (Peak to Average Power Ratio) dans un système multi-porteuse, (3) l’optimisation de schémas de transmission pour la diffusion sur des canaux gaussiens avec/sans contrainte de sécurité, (4) l’analyse, l’interprétation et l’amélioration des algorithmes de décodage itératif par le biais de l’optimisation, de la théorie des jeux et des outils statistiques. L’accent est plus particulièrement mis sur le dernier thème

Reduced Complexity Sequential Monte Carlo Algorithms for Blind Receivers

Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation. Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary. We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically. Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes. Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.Ph.D.Committee Chair: Douglas B. Williams; Committee Member: Brani Vidakovic; Committee Member: G. Tong zhou; Committee Member: Gordon Stuber; Committee Member: James H. McClella