On the influence of detection tests on deterministic parameters estimation

In non-linear estimation problems three distinct regions of operation can be observed. In the asymptotic region, the Mean Square Error (MSE) of Maximum Likelihood Estimators (MLE) is small and, in many cases,close to the Cramer-Rao bound (CRB). In the a priory performance region where the number of independent snapshots and/or the SNR are very low, the MSE is close to that obtained from the prior knowledge about the problem. Between these two extremes, there is an additional transition region where MSE of estimators deteriorates with respect to CRB. The present paper provides exemples of improvement of MSE prediction by CRB, not only in the transition region but also in the a priori region, resulting from introduction of a detection step, which proves that this renement in MSE lower bounds derivation is worth investigating

Statistics of the MLE and Approximate Upper and Lower Bounds - Part 1: Application to TOA Estimation

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accurateness of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation

Performance analysis of symbol timing estimators for time-varying MIMO channels

The purpose of this thesis is to derive and analyze the theoretical limits for estimatingthe symboltiming delayof Multiple-Input Multiple-Output (MIMO)systems. Two main N X M system models are considered, where N represents the number of transmit antennas and M denotes the number of receive antennas, the 2 X 2 system used by S.-A. Yangand J. Wu and the 4 X 4system used by Y.-C. Wu and E. Serpedin. The second model has been extended to take into account the symbol time-varying fading. The theoretical estimation limits are shown by several bounds: modified Cramer-Rao bound (MCRB), Cramer-Rao bound (CRB) and Barankin bound (BB). BB will be exploited to obtain accurate information regarding the necessary length of data to obtain good estimation. Two scenarios for synchronization are presented: data-aided (DA) and non-data-aided (NDA). Two models for the fading process are considered: block fading and symbol time-varying fading, respectively, the second case being assumed to be Rayleigh distributed. The asymptotic Cramer-Rao bounds for low signal-to-noise ratio (low-SNR) and for high-SNR are derived and the performance of several estimators is presented. The performance variation of bounds and estimators is studied byvarying different parameters, such as the number of antennas, the length of data taken into consideration during the estimation process, the SNR, the oversampling factor, the power and the Doppler frequency shift of the fading

Statistical Methods for Image Registration and Denoising

This dissertation describes research into image processing techniques that enhance military operational and support activities. The research extends existing work on image registration by introducing a novel method that exploits local correlations to improve the performance of projection-based image registration algorithms. The dissertation also extends the bounds on image registration performance for both projection-based and full-frame image registration algorithms and extends the Barankin bound from the one-dimensional case to the problem of two-dimensional image registration. It is demonstrated that in some instances, the Cramer-Rao lower bound is an overly-optimistic predictor of image registration performance and that under some conditions, the Barankin bound is a better predictor of shift estimator performance. The research also looks at the related problem of single-frame image denoising using block-based methods. The research introduces three algorithms that operate by identifying regions of interest within a noise-corrupted image and then generating noise free estimates of the regions as averages of similar regions in the image

Underwater Direction-of-Arrival Finding: Maximum Likelihood Estimation and Performance Analysis

In this dissertation, we consider the problems of direction-of-arrival: DOA) finding using acoustic sensor arrays in underwater scenarios, and develop novel signal models, maximum likelihood: ML) estimation methods, and performance analysis results. We first examine the underwater scenarios where the noise on sensor arrays are spatially correlated, for which we consider using sparse sensor arrays consisting of widely separated sub-arrays and develop ML DOA estimators based on the Expectation-Maximization scheme. We examine both zero-mean and non-zero-mean Gaussian incident signals and provide detailed estimation performance analysis. Our results show that non-zero means in signals improve the accuracy of DOA estimation. Then we consider the problem of DOA estimation of marine vessel sources such as ships, submarines, or torpedoes, which emit acoustic signals containing both sinusoidal and random components. We propose a mixed signal model and develop an ML estimator for narrow-band DOA finding of such signals and then generalize the results to the wide-band case. We provide thorough performance analysis for the proposed signal model and estimators. We show that our mixed signal model and ML estimators improve the DOA estimation performance in comparison with the typical stochastic ones assuming zero-mean Gaussian signals. At last, we derive a Barankin-type bound: BTB) on the mean-square error of DOA estimation using acoustic sensor arrays. The typical DOA estimation performance evaluation are usually based on the Cram\u27{e}r-Rao Bound: CRB), which cannot predict the threshold region of signal-to-noise ratio: SNR), below which the accuracy of the ML estimation degrades rapidly. Identification of the threshold region has important applications for DOA estimation in practice. Our derived BTB provides an approximation to the SNR threshold region

Modeling And Detection Of Uterine Contractions Using Magnetomyography

In this dissertation, we develop a novel mathematical framework for modeling and analyzing uterine contractions using biomagnetic measurements. The study of myometrium contractility during pregnancy is relevant to the field of reproductive assessment. Its clinical importance is grounded in the need for a better understanding of the bioreproduction mechanisms. For example, in the last decade the number of preterm labors has increased significantly. Preterm birth can cause health problems or even be fatal for the fetus if it happens too early, and, at the same time, it imposes significant financial burdens on health care systems. Therefore, it is critical to develop models and statistical tools that help to monitor non-invasively the uterine activities during pregnancy. We derive a forward electromagnetic model of uterine contractions during pregnancy. Existing models of myometrial contractions approach the problem either at an organ level or lately at a cellular level. At the organ level, the models focus on generating contractile forces that closely resemble clinical measurements of normal intrauterine pressure during contractions in labor. At the cellular level, the models focus on predicting the changes of ionic concentrations in a uterine myocyte during a contraction, and, as a consequence, on modeling the transmembrane potential evolution as a function of time. In this work, we propose an electromagnetic modeling approach taking into account electrophysiological and anatomical knowledge jointly at the cellular, tissue, and organ levels. Our model aims to characterize myometrial contractions using magnetomyography: MMG) and electromyography: EMG) at different stages of pregnancy. In particular, we introduce a four-compartment volume conductor geometry, and we use a bidomain approach to model the propagation of the myometrium transmembrane potential on the human uterus. The bidomain approach is given by a set of reaction-diffusion equations. The diffusion part of the equations governs the spatial evolution of the transmembrane potential, and the reaction part is given by the local ionic current cell dynamics. Here we introduce a modified version of the Fitzhugh-Nagumo: FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential. We incorporate the anisotropic nature of the uterus by considering conductivity tensors in our model. In particular, we propose a general approach to design the conductivity-tensor orientation and to estimate the conductivity-tensor values in the extracellular and intracellular domains for any uterine shape. We use finite element methods: FEM) to solve our model, and we illustrate our approach by presenting a numerical example to model a uterine contraction at term. Our results are in good agreement with the values reported in the experimental technical literature, and these are potentially important as a tool for helping in the characterization of contractions and for predicting labor. We propose an automatic, robust, single-channel statistical detector of uterine MMG contractions. One common restriction of previous techniques is that algorithm parameters, such as the detection threshold and the window length of analysis need to be calibrated experimentally, based on a particular data set. Therefore, the detection performance might change from patient to patient, for example, because of differences in the pregnancy stage and tissue conductivities. In contrast, the proposed algorithm does not require the use of a sliding window of analysis, and the detection threshold is determined analytically; thus, it does not need to be calibrated. Our detection algorithm consists of two stages: In the first stage, we segment the measurements using a multiple change-point estimation algorithm and assuming a piecewise constant time-varying autoregressive model of the measurements; In the second stage, we apply the non-supervised K-means cluster algorithm to classify each time segment, using the RMS and FOZC as candidate features. As a result a discrete-time binary decision signal is generated indicating the presence of a contraction. Moreover, since each single channel detector provides local information regarding the presence of a contraction, we propose a spatio-temporal estimator of the magnetic activity generated by uterine contractions. The algorithm, when evaluated with real MMG measurements, detects uterine activity much earlier than the patient begins to sense it. It also enables visualizing the relative location of the origin of uterine contraction and quantifying the amount of energy delivered during a contraction. These results are important in obstetrics, e.g., as a tool for helping to characterize contractions and to predict labor. For the aforementioned problem of multiple change-point estimation, a class of one-dimensional segmentation, we also compute fundamental mathematical results for minimal bounds on mean-square error estimation. Indeed, if an estimator is available, the evaluation of its performance depends on knowing whether it is optimal or if further improvement is still possible. In our segmentation problem the parameters are discrete therefore the conventional Cramer-Rao bound does not apply. Hence, we derive Barankin-type lower bounds, the greatest lower bound on the covariance of any unbiased estimator, which are applicable to discrete parameters. The computation of the bound is challenging, as it requires finding the supremum on a finite set of symmetric matrices with respect to the Loewner ordering, which is not a lattice order. Therefore, we discuss the existence of the supremum, propose a minimal upper-bound by using tools from convex geometry, and compute closed-form solutions for the Barankin information matrix for several distributions. The results have broad biomedical applications, such as DNA sequence segmentation, MEG and EEG segmentation, and uterine contraction MMG detection, and they also have applications for signal segmentation in general, such as speech segmentation and astronomical data analysis

A Nonparametric Approach to Segmentation of Ladar Images

The advent of advanced laser radar (ladar) systems that record full-waveform signal data has inspired numerous inquisitions which aspire to extract additional, previously unavailable, information about the illuminated scene from the collected data. The quality of the information, however, is often related to the limitations of the ladar camera used to collect the data. This research project uses full-waveform analysis of ladar signals, and basic principles of optics, to propose a new formulation for an accepted signal model. A new waveform model taking into account backscatter reflectance is the key to overcoming specific deficiencies of the ladar camera at hand, namely the ability to discern pulse-spreading effects of elongated targets. A concert of non-parametric statistics and familiar image processing methods are used to calculate the orientation angle of the illuminated objects, and the deficiency of the hardware is circumvented. Segmentation of the various ladar images performed as part of the angle estimation, and this is shown to be a new and effective strategy for analyzing the output of the AFIT ladar camera

The deep space network

Deep space network progress in flight support tracking and data acquisition research and technology is reported