This dissertation deals with the design of satellite-based navigation receivers. The term Global Navigation Satellite Systems (GNSS) refers to those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the american GPS is probably the most popular, the european contribution (Galileo) will be operative soon. Other global and regional systems exist, all with the same objective: aid user's positioning. Initially, the thesis provides the state-of-the-art in GNSS: navigation signals structure and receiver architecture. The design of a GNSS receiver consists of a number of functional blocks. From the antenna to the fi nal position calculation, the design poses challenges in many research areas. Although the Radio Frequency chain of the receiver is commented in the thesis, the main objective of the dissertation is on the signal processing algorithms applied after signal digitation. These ...

System designers across all disciplines of technology face the need to develop machines capable of independently processing and analyzing data and predicting future data. This is the fundamental problem of interest in “estimation theory,” wherein probabilistic analyses are used to isolate relationships between variables, and in “statistical inference,” wherein those variables are used to make inferences about real-world quantities. In practice, all estimators are designed based on limited statistical generalizations about the behavior of the observed and latent variables of interest; however, these models are rarely fully representative of reality. In such cases, there exists a “model misspecification,” and the resulting estimators will produce results that differ from those of the properly specified estimators. Evaluating the performance of a given estimator may sometimes be done by direct comparison of estimator outputs to known ground truth. However, in many cases, there ...

Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information, it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type of modeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection accuracy. Bayesian methods approximate the sparsity by probability distributions which are iteratively modified. We show one approach to making the Bayesian method the Relevance Vector ...

This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied. The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing. The nonlinear state estimation problem is ...

This work deals with the problem of calculating the Cramer-Rao lower bounds (CRLBs) for bistatic radar channels. To this purpose we exploited the relation between the Ambiguity Function (AF) and the CRLB. The bistatic CRLBs are analyzed and compared to the monostatic counterparts as a function of the bistatic geometric parameters. In the bistatic case both geometry factors and transmitted waveforms play an important role in the shape of the AF, and therefore in the estimation accuracy of the target range and velocity. In particular, the CRLBs depend on the target direction of arrival, the bistatic baseline length, and the distance between the target and the receiver. The CRLBs are then used to select the optimum bistatic channel (or set of channels) for the tracking of a radar target moving along a trajectory in a multistatic scenario and for design ...

are involved until the development of Sequential Monte Carlo techniques which are also known as the particle filters. In particle filtering, the problem is expressed in terms of state-space equations where the linearity and Gaussianity requirements of the Kalman filtering are generalized. Therefore, we need information about the functional form of the state variations. In this thesis, we bring a general solution for the cases where these variations are unknown and the process distributions cannot be expressed by any closed form probability density function. Here, we propose a novel modeling scheme which is as unified as possible to cover all these problems. Therefore we study the performance analysis of our unifying particle filtering methodology on non-stationary Alpha Stable process modeling. It is well known that the probability density functions of these processes cannot be expressed in closed form, except for ...

The ability to reliably and cheaply localize mobile terminals will allow users to understand and utilize the what, where and when of the surrounding physical world. Therefore, mobile terminal location information will open novel application opportunities in many areas. The mobile terminal positioning problem is categorized into three different types according to the availability of (1) initial accurate location information and (2) motion measurement data. Location estimation refers to the mobile positioning problem when both the initial location and motion measurement data are not available. If both are available, the positioning problem is referred to as position tracking. When only motion measurements are available the problem is known as global localization. These positioning problems were solved within the Bayesian filtering framework in order to work under a common theoretical context. Filter derivation and implementation algorithms are provided with emphasis on ...

Magnetic Resonance Spectroscopy (MRS) is a technique used in fundamental research and in clinical environments. During recent years, clinical application of MRS gained importance, especially as a non-invasive tool for diagnosis and therapy monitoring of brain and prostate tumours. The most important asset of MRS is its ability to determine the concentration of chemical substances non-invasively. To extract relevant signal parameters, MRS data have to be quantified. This usually doesn¢t prove to be straightforward since in vivo MRS signals are characterized by poor signal-to-noise ratios, overlapping peaks, acquisition related artefacts and the presence of disturbing components (e.g. residual water in proton spectra). The work presented in this thesis aims to improve the quantification in different applications of MRS in vivo. To obtain the signal parameters related to MRS data, different approaches were suggested in the past. Black-box methods, don¢t require ...

This PhD thesis considers the problem of locating some target nodes in different wireless infrastructures such as wireless cellular radio networks and wireless sensor networks. To be as realistic as possible, mixed line-of-sight and non-line-of-sight (LOS/NLOS) localization environment is introduced. Both the conventional non-cooperative localization and the new emerging cooperative localization have been studied thoroughly. Owing to the random nature of the measurements, probabilistic methods are more advanced as compared to the old-fashioned geometric methods. The gist behind the probabilistic methods is to infer the unknown positions of the target nodes in an estimation process, given a set of noisy position related measurements, a probabilistic measurement model, and a few known reference positions. In contrast to the majority of the existing methods, harsh but practical constraints are taken into account: neither offline calibration nor non-line-of-sight state identification is equipped in ...

This thesis comprises two parts. The first part deals with single carrier and multiple-carrier based frequency estimation. The second part is concerned with the application of ultrasound using the proposed estimators and introduces a novel efficient implementation of a subspace tracking technique. In the first part, the problem of single frequency estimation is initially examined, and a hybrid single tone estimator is proposed, comprising both coarse and refined estimates. The coarse estimate of the unknown frequency is obtained using the unweighted linear prediction method, and is used to remove the frequency dependence of the signal-to-noise ratio (SNR) threshold. The SNR threshold is then further reduced via a combination of using an averaging filter and an outlier removal scheme. Finally, a refined frequency estimate is formed using a weighted phase average technique. The hybrid estimator outperforms other recently developed estimators and ...

This dissertation presents the outcome of investigations which envisaged to develop improved state and ‘combined state and parameter’ estimation algorithms for nonlinear signal models (during the contingent situations) where the complete knowledge of process and/or measurement noise covariance are not available. Variants of “adaptive nonlinear estimators” capable of providing satisfactory estimation results in the face of unknown noise covariance have been proposed in this dissertation. The proposed adaptive nonlinear estimators incorporate adaptation algorithms with which they can implicitly or explicitly, estimate unknown noise covariances along with estimation of states and parameters. Adaptation algorithms have been mathematically derived following different methods of adaptation which include Maximum Likelihood Estimation (MLE), Covariance Matching method and Maximum a Posteriori (MAP) method. The adaptive nonlinear estimators which have been proposed in this dissertation are formulated with the help of a general framework for adaptive nonlinear ...

The respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling in which the heart rate accelerates during inhalation and decelerates during exhalation. Its quantification has been suggested as a tool to assess different diseases and conditions. However, whilst the potential of the RSA estimation as a diagnostic tool is shown in research works, its use in clinical practice and mobile applications is rather limited. This can be attributed to the lack of understanding of the mechanisms generating the RSA. To try to explain the RSA, studies are done using noninvasive signals, namely, respiration and heart rate variability (HRV), which are combined using different algorithms. Nevertheless, the algorithms are not standardized, making it difficult to draw solid conclusions from these studies. Therefore, the first aim of this thesis was to develop a framework to evaluate algorithms for RSA estimation. To ...

Assertive diagnosis of cancer, Alzheimer’s disease, epilepsy and other metabolic diseases is essential to provide patients with the adequate treatment. Recently, different invasive and non-invasive techniques have been developed for this purpose, nevertheless, due to their harmless properties the non-invasive techniques have gained more value. Magnetic Resonance is a well-known non-invasive technique that provides spectra (metabolite peaks) and images (anatomical structures) of the examined tissue. In Magnetic Resonance Spectroscopy (MRS), molecules containing certain excitable nuclei, such as 1H, provide the metabolite information. As a consequence, the peaks in the MR spectra correspond to observable metabolites which are the biomarkers of diseases. Finally, metabolite concentrations are computed and compared against normal values in order to establish the diagnosis. The method to obtain such amplitudes is also called quantification and its accuracy is essential for diagnosis assessment. Quantification of MRS signals is ...

Over the past years magnetic resonance spectroscopy (MRS) has been of significant importance both as a fundamental research technique in different fields, as well as a diagnostic tool in medical environments. With MRS, for example, spectroscopic information, such as the concentrations of chemical substances, can be determined non-invasively. To that end, the signals are first modeled by an appropriate model function and mathematical techniques are subsequently applied to determine the model parameters. In this thesis, signal processing algorithms are developed to quantify in-vivo and ex-vivo MRS signals. These are usually characterized by a poor signal-to-noise ratio, overlapping peaks, deviations from the model function and in some cases the presence of disturbing components (e.g. the residual water in proton spectra). The work presented in this thesis addresses a part of the total effort to provide accurate, efficient and automatic data analysis ...

This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is ...