Arye Nehorai

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

Performance study of conditional and unconditional direction-of-arrival estimation

A numerical and analytical study of conditional and unconditional direction-of-arrival (DOA) estimation is presented. Explicit expressions for the unconditional Cramer-Rao bounds on the DOA estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given. It is shown that many DOA estimation methods have the same asymptotic statistical properties under conditional and unconditional models. The situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed. >

Vector-sensor array processing for electromagnetic source localization

The authors present a new approach for localizing electromagnetic sources using sensors where the output of each is a vector consisting of the complete six electric and magnetic field components. Two types of source transmissions are considered: (1) single signal transmission (SST), and (2) dual signal transmission (DST). The model is given in terms of several parameters, including the wave direction of arrival (DOA) and state of polarization. A compact expression is derived for the Cramer-Rao bound (CRB) on the estimation errors of these parameters for the multi-source multi-vector-sensor model. Quality measures including mean-square angular error (MSAE) and covariance of vector angular error (CVAE) are introduced, and their lower bounds are derived. The advantage of using vector sensors is highlighted by explicit evaluation of the MSAE and CVAE bounds for source localization with a single vector sensor. A simple algorithm for estimating the source DOA with this sensor is presented along with its statistical performance analysis. >

MUSIC, maximum likelihood, and Cramer-Rao bound: further results and comparisons

The problem of determining the direction-of-arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied. A number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization (MUSIC) and the maximum likelihood (ML) estimators for the above problems. This work extends those results in several directions. First, it establishes that in the class of weighted MUSIC estimators, the unweighted MUSIC achieves the best performance (i.e. the minimum variance of estimation errors), in large samples. Next, it derives the covariance matrix of the ML estimator and presents detailed analytic studies of the statistical efficiency of MUSIC and ML estimators. These studies include performance comparisons of MUSIC and MLE with each other, as well as with the ultimate performance corresponding to the Cramer-Rao bound. Finally, some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays. >

Acoustic vector-sensor array processing

A method is presented for localizing acoustic sources using an array of sensors, the output of each being a vector consisting of the acoustic pressure and acoustic particle velocity. The authors derive a compact expression for the Cramer-Rao bound (CRB) on the estimation errors of the source direction-of-arrival (DOA) parameters in the multi-source multi-vector-sensor model. An explicit expression is found for the mean-square angular error (MSAE) bound for source localization with a single vector sensor. The authors present two simple algorithms for estimating the source DOA with this sensor, along with their statistical performance analyses. >

Exact and Large Sample ML Techniques for Parameter Estimation and Detection in Array Processing

Sensor array signal processing deals with the problem of extracting information from a collection of measurements obtained from sensors distributed in space. The number of signals present is assumed to be finite, and each signal is parameterized by a finite number of parameters. Based on measurements of the array output, the objective is to estimate the signals and their parameters. This research area has attracted considerable interest for several years. A vast number of algorithms has appeared in the literature for estimating unknown signal parameters from the measured output of a sensor array.

Deconvolution methods for 3-D fluorescence microscopy images

This paper presents an overview of various deconvolution techniques of 3D fluorescence microscopy images. It describes the subject of image deconvolution for 3D fluorescence microscopy images and provides an overview of the distortion issues in different areas. The paper presents a brief schematic description of fluorescence microscope systems and provides a summary of the microscope point-spread function (PSF), which often creates the most severe distortion in the acquired 3D image. Finally, it discusses the ongoing research work in the area and provides a brief review of performance measures of 3D deconvolution microscopy techniques. It also provides a summary of the numerical results using simulated data and presents the results obtained from the real data.

Adaptive comb filtering for harmonic signal enhancement

A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input. The second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise.

MUSIC, maximum likelihood and Cramer-Rao bound: further results and comparisons

A number of results have been presented recently on the statistical performance of the multiple signal characterization (MUSIC) and the maximum-likelihood (ML) estimators for determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements. It is shown that in the class of weighted MUSIC estimators, the unweighted MUSIC achieves the best performance (i.e. the minimum variance of estimation errors) in large samples. The covariance matrix of the ML estimator is derived, and detailed analytic studies of the statistical efficiency of MUSIC and ML estimators are presented. These studies include performance comparisons of MUSIC and MLE with each other as well as with the ultimate performance corresponding to the Cramer-Rao bound (CRB).<<ETX>>

A game-theoretic approach for optimal time-of-use electricity pricing

Demand for electricity varies throughout the day, increasing the average cost of power supply. Time-of-use (TOU) pricing has been proposed as a demand-side management (DSM) method to influence user demands. In this paper, we describe a game-theoretic approach to optimize TOU pricing strategies (GT-TOU). We propose models of costs to utility companies arising from user demand fluctuations, and models of user satisfaction with the difference between the nominal demand and the actual consumption. We design utility functions for the company and the users, and obtain a Nash equilibrium using backward induction. In addition to a single-user-type scenario, we also consider a scenario with multiple types of users, each of whom responds differently to time-dependent prices. Numerical examples show that our method is effective in leveling the user demand by setting optimal TOU prices, potentially decreasing costs for the utility companies, and increasing user benefits. An increase in social welfare measure indicates improved market efficiency through TOU pricing.