1,721,067 research outputs found
Optimal strategies and tradeoffs for joint detection and estimation.
No full textThis thesis treats the problem of joint (simultaneous) detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. There is therefore a need to have a methodology for quantifying the performance tradeoffs between detection and estimation. This thesis provides such a methodology. We develop a theory for optimal simultaneous decisions for a finite set of intermediate and terminal decision states. This theory specifies simultaneous decision rules which minimize the worst case decision error probability under an inequality constraint on the probability of a false decision for one of the intermediate or terminal decision states. The theory also specifies achievable lower bounds on the worst case performance of identically constrained decision rules. These bounds can be used to assess the tradeoffs between optimally performing intermediate decisions and optimally performing terminal decisions. Since the analytical evaluation of these lower bounds may be intractable for large dimensional decision spaces, we also provide methods for deriving weaker but more tractable bounds based on the Fano inequality of information theory. We apply our theory to a multi-component signal in noise problem arising in spectrum estimation, multiple target tracking, and multiple access communication. We identify three decision problems: signal detection, signal power estimation (order selection), and signal component estimation (classification). We show that the optimum constrained classifier is equivalent to a maximum likelihood classifier with a built-in Akaike-type order selection penalty which is optimum in terms of minimizing the worst case probability of classification error. By implementing the optimum constrained decision rule for each one of the three decision problems, we evaluate the corresponding lower bound. Using these bounds we perform a numerical study of the tradeoffs between detection, order selection, and classification at high error levels.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103182/1/9308272.pdfDescription of 9308272.pdf : Restricted to UM users only
Error bounds in constrained estimation.
No full textParameter constraints are employed in a variety of situations in multidimensional estimation problems to incorporate prior information, design constraints, or to perform model reduction or approximation. When parameter constraints are introduced, the fundamental structure of the estimation problem is changed, and as a consequence, commonly used lower bounds on estimator error need to be modified to account for the constraints. In this dissertation, we derive general finite-sample Cramer-Rao (CR) and Bhattacharyya-type lower bounds that incorporate smooth parameter constraints. We refer to these bounds as the constrained CR and constrained Bhattacharyya bounds. In contrast to other problem-specific approaches to deriving performance bounds for constrained estimation problems, our approach does not require a global reparameterization of the parameter space. The constrained CR and Bhattacharyya bounds are derived as the local limit of a more general multivariate Chapman-Robbins-type covariance bound and are shown to depend only on local geometric properties of the likelihood function and the parameter constraints. These geometric properties reveal a simple mechanism by which parameter constraints reduce achievable estimator error covariance. In particular, constraints are incorporated into the constrained CR and constrained Bhattacharyya bounds through oblique projections of the associated Fisher information matrices onto local Taylor polynomial approximations to the constraint space. The necessary and sufficient conditions under which the constrained bounds are achievable are shown to be similar to those required for the standard CR and Bhattacharyya bounds. We use the constrained bounds to study the impact of parameter constraints on achievable estimator error covariance in a number of representative multidimensional constrained-parameter estimation problems occurring signal processing. Specific examples considered include: linear constraints for Gaussian linear models, object support constraints in image reconstruction, signal subspace constraints in sensor array processing, and average power constraints in spectral estimation and signal extraction.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105536/1/9135603.pdfDescription of 9135603.pdf : Restricted to UM users only
Time delay estimation for inhomogeneous Poisson processes in the presence of Gaussian noise.
No full textThis thesis develops Maximum Likelihood based approaches to the estimation of Poisson intensity parameters for filtered Poisson processes observed in additive Gaussian measurement noise. While the methods developed are generally applicable to arbitrary intensity parameterizations, the thesis focuses on the case of time shift parameters. The general estimation problem arises in applications where one is interested in the intensity of a sequence of partially observed discrete events occurring at random points in time or space. Examples include: photon detection for optical communications, positron emission tomography and high energy physics; processing of seismic reflections for geological remote sensing and oil exploration; and neurological activity evaluation based on evoked compound action potentials. For the observation model considered here, the exact likelihood function is analytically intractable due to imperfect observation of the Poisson point process. This intractability is attributable to the presence of additive noise and to the distortion due to filtering the points of the process. Two classes of approximations to the Maximum Likelihood estimator are developed. The first class consists of asymptotic forms of the exact likelihood function under various limiting regimes such as: low measurement noise power, high filter bandwidth, high and low average intensity levels. These asymptotic expressions are of closed form and can be maximized directly to find the maximum likelihood estimate under the respective limiting regimes. The second class of approximations is based on an iterative method founded on the Expectation-Maximization algorithm. This iterative Maximum Likelihood method alternates between two successive operations: approximation of the log-likelihood function for the perfectly observed Poisson process; and maximization of this approximate log-likelihood over unknown parameter values. A linearization of the EM algorithm is developed for the filtered Poisson process model and its convergence properties are analyzed. Results of simulations are given which indicate that significant improvements in estimator performance can be obtained in only a few iterations for time delay estimation. In particular, after less than five iterations, the algorithm yields estimates which are unbiased and come very close to achieving a theoretical lower bound on mean-square estimation error of any unbiased estimator.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103178/1/9308265.pdfDescription of 9308265.pdf : Restricted to UM users only
Recursive algorithms for digital communications using the discrete wavelet transform.
No full textThe goal in digital communications is to efficiently and reliably transmit digital information through a channel. In order to optimally decode the transmitted symbols, it is often necessary to have good estimates of the channel parameters. In this thesis a class of recursive algorithms which perform joint Maximum Likelihood (ML) estimation of the channel parameters and the symbol sequence is developed. The channel parameters are assumed to consist of an unknown fixed complex gain (amplitude and phase), and time delay. The digital information is transmitted using binary or M-ary phase modulation and received in the presence of an additive white Gaussian noise. The algorithms presented in this work are based on a decomposition with respect to an orthonormal wavelet basis. This is motivated by the fact that the wavelet decomposition retains all the information in the observation, while facilitating processing by a recursive algorithm. In addition, the localization properties of the wavelet basis enable local updates of the symbol parameters. This results in an efficient digital algorithm with low complexity and small delay. In particular, the algorithm has a complexity per iteration that is quadratic in the number of users when applied in a multiuser system, while the optimal receiver which uses the matched filter outputs as a sufficient statistic has an exponential complexity in the number of users. The class of algorithms studied in this thesis applies to both single user and multiuser systems. First, a coordinate ascent algorithm for a single user system is developed. While the direct maximization of the likelihood function is analytically intractable, the recursive algorithm has simple updates which involve polynomial rooting for time delay estimation, discrete search for symbol estimation, and an analytical solution for gain estimation. The algorithm uses a look-up table for retrieving Fourier series coefficients of the transmitted pulse shape decomposition with respect to the wavelet basis. Simulations show fast convergence and attainment of estimation bounds. Next, the algorithm is extended to the multiuser case. Two versions have been developed: one using grouped coordinate ascent, and the other using the EM algorithm. Simulation results for a two-user system are shown. In addition, the problem of initializing the algorithm is addressed. Finally, an analysis of the single user algorithm is performed under some reasonable assumptions. It is shown that the algorithm has a fixed point at the true gain and time delay parameters in the limit of a large observation time.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130118/2/9712083.pd
Optimal arrival time estimators for electromagnetic radiation detectors.
No full textIn this thesis, the problem of statistical estimation of arrival time of a quantum signal is studied based on the output waveform of an electromagnetic radiation detector. Inaccurate arrival time estimates can severely impact the performance of optical communication systems such as pulse position modulation, e.g. by limiting the data rate, and of nuclear imaging systems such as Positron Emission Tomography (PET), e.g. by limiting system sensitivity and spatial resolution. Previous studies of this problem assumed the availability of ideal direct photon counting measurements, whereas this thesis recognizes that practical radiation detector measurements are limited by measurement noise. Based on the physics of the photo-detection process, a statistical model is proposed for the measurements which consists of a filtered inhomogeneous Poisson (shot noise) process and additive Gaussian noise. The model is then experimentally validated on the basis of comparisons between simulated and experimentally determined timing errors for a scintillation counter commonly used in PET. A weighted least-squares arrival time estimator which accounts for the first and second order statistics of the radiation detector output waveform is then investigated. This optimal least-squares estimator is equivalent to the maximum likelihood arrival time estimator under a high intensity Gaussian approximation to the shot noise measurement model. The RMS estimation error of the optimal estimator is compared to the RMS error of ad hoc estimators such as the leading edge and constant fraction estimators for a Burle 8850 photomultiplier tube detector. Using simulations and experiments, it is shown that for isolated photon packets the optimal estimator can reduce timing errors by at least a factor of 3 and by as much as a factor of 8. For multiple overlapped photon pulses, the optimal estimator is capable of accurate pulse separation for a 50% overlap factor. The Cramer-Rao lower bound on achievable estimator mean-squared error is then derived for the high intensity regime. It is demonstrated that the optimal estimator can come within 40% of the lower bound for isolated pulses.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103292/1/9308421.pdfDescription of 9308421.pdf : Restricted to UM users only
Mutual information optimization and evaluation of single photon emission computed tomography.
No full textIn this thesis we study the performance of Single Photon Emission Computed Tomography using concepts and techniques of information theory. Two specific tomographic tasks are considered: image reconstruction and image feature classification. For the image reconstruction problem we derive a necessary and sufficient condition for an aperture to be information optimal. The aperture is nearly a collimator over aperture regions of high fluence, hence sacrificing fluence for better resolution, while it is nearly transparent over regions of low fluence, hence sacrificing resolution for better fluence. Simulations are presented which show that the mutual information of conventional uniform parallel hole apertures can be significantly lower than the maximum achievable information using an optimal aperture. We then study the effect of count loss side information on the mutual information for the reconstruction problem. We derive a lower bound on the information gain achievable from using count corrections. This bound increases with a quantity, the information divergence, measuring spatial dependence of the probability of losing a count from a particular emitter location. It is established that if this spatial dependence is significant high gains can be achieved when the mean number of detected gamma-rays is low. In particular, this implies that count corrections side information can greatly improve performance in dynamic studies where the reconstruction of a time varying mean source distribution mandates multi-stage data acquisition over short time intervals. For the feature classification problem we study the channel cut-off rate which is related to the information transfer from the image features to the projections data. On the basis of the cut-off rate and the information theoretic Fano bound we propose a very simple approximation to the probability of classification error of the optimal Bayes classifier. For the special case of two features, i.e. detection, we determine by simulation that the approximation is quite close to the actual Bayes minimum probability of error. We then study apertures which minimize the minimum probability of error approximation by maximizing the cut-off rate. It is determined that the optimal detection aperture can be simply approximated by an aperture which is reconstruction optimal for the Bayes averaged source distribution.PhDApplied SciencesBiological SciencesBiomedical engineeringBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128450/2/9014013.pd
ADEPT: Task-specific adaptive beamforming.
No full textIn this dissertation we develop an approach to adaptive beamforming which we call Adaptive Detection/Estimation for Particular Tasks (ADEPT). The ADEPT approach seeks to optimize the best achievable signal detection or parameter estimation performance at the output of a beamsummer array. The philosophy behind our approach is that the adaptation criterion for adaptive beamforming weights should be designed to optimize achievable performance for the primary task of interest. The methodology behind our approach is the use of weight-dependent detection criteria and estimation theoretic lower bounds to specify adaptation criteria appropriate to the specific task of interest. We focus on designing unconstrained adaptive beamsummers for signal detection, estimation of parameters of a spatially-invariant constant-modulus signal amplitude, and for signal direction-of-arrival (DOA) estimation. The adaptive beamsummer is formulated for sensor arrays operating in a broadband environment which is characteristic of slow Rayleigh fading signals. In this environment signal components in successive snapshots are uncorrelated but signal amplitudes remain coherent over the array. For the task of signal detection, we introduce a beamsummer weight adaptation rule which asymptotically maximizes a beamsummer "deflection index" in the limit of a large number of snapshots. The deflection index is closely related to the maximum detection probability achievable at the beamsummer output. We establish that the weight adaptation rule reduces to the Applebaum and Frost beamsummers in the limits of narrowband and broadband array operation, respectively. For the tasks of constant modulus parameter estimation, and DOA estimation, we introduce beamsummer weight adaptation rules which asymptotically minimize the Cramer-Rao lower bound on estimator variance at the beamsummer output. We present simulations comparing simple beampattern-based detection and estimation algorithms for our optimal beamsummer weights and the Applebaum and Frost weights. We also compare our performance to an ideal generalized likelihood ratio signal detector implemented with Akaike's signal selection criterion, and an ideal maximum-likelihood signal DOA estimator, both of which assume that raw multiple-sensor data is available, and the signal and noise powers are known. Even with such unfair disadvantages, our beamsummer-based adaptive algorithms perform remarkably well in comparison.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104103/1/9500914.pdfDescription of 9500914.pdf : Restricted to UM users only
Time delay estimation with nuisance parameters: Performance approximation and coarse acquisition.
No full textThis thesis concentrates on two topics which are related to time delay estimation. The first is a model useful for approximating the error performance of maximum likelihood type estimators of multiple unknown parameters; this is the error intensity model. The second is a methodology for joint detection and coarse estimation of signal parameters; this is the coarse acquisition method. These are important in both single parameter and multiple parameter estimation in the presence of unknown "nuisance" parameters. Three specific examples are considered. We consider the effect of coherent interference on an estimate of the time delay of a coherent signal when the receiver uses a directional array. The cases where the time delay of the interference is known or unknown are compared using both error probability and mean squared error approximation. The second example considers the effect of a known or an unknown doppler component on an estimate of time delay of a deterministic signal. This models the moving-target target tracking problem; error probability and mean squared error approximations of the time delay estimate are the basis for comparing the performances. The third major example is coarse acquisition of time delay; this is relevant to radar and sonar target range and bearing estimation. Coarse acquisition is the first stage in a two step algorithm signal detection and rough classification followed by fine acquisition of the coarsely acquired signal. This problem was attacked with the following simple objective: based on a correlator statistic, classify the time delay into one of M intervals subject to an upper bound on the probability of falsely deciding signal presence. Methods of decision theory and invariance applied to this problem took the form of a constrained min-max invariant multiple hypotheses test. The principal significance of this work is: (1) it can yield insight into poorly understood empirical behavior of delay estimators in the presence of unknown coherent interferers or doppler; and (2) it establishes an optimality property of the correlator peak comparison scheme for coarse acquisition of delayed signals.PhDElectrical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162475/1/9013940.pd
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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