An asymptotically efficient ARMA estimator based on sample covariances

An asymptotically efficient autoregressive moving-average (ARMA) spectral estimator is presented, based on the sample covariances of observed time series. The estimate of the autoregressive (AR) part is shown to be identical to the optimal instrumental variable (IV) estimator in [7] although derived here using a different approach. The moving-average (MA) spectral parameter estimate is new.     

Mutual coupling of two collocated orthogonally oriented circular thin-wire loops

Coupling between two collocated orthogonal circular thin-wire loops is analyzed in this paper. Two coupled integral equations for the loop currents are derived and their solution in general form is found in terms of Fourier series. An analytical expression for currents induced through the mutual coupling is obtained for the case when all loop current harmonics higher than first can be ignored. It is found that strong coupling can exist for all loop current harmonics, except for the fundamental. It is also found that coupling for orthogonal collocated loop antennas depends on the relative locations of the loop terminals.     

Direction-of-arrival estimation in applications with multipath and few snapshots

This paper analyzes two direction-of-arrival (DOA) estimation algorithms used in the presence of multipath propagation and with very few snapshots. The conditional maximum likelihood (CML) algorithm and the method of direction estimation (MODE) are discussed. The estimates provided by these algorithms are shown to coincide for large number of snapshots or large signal-to-noise ratio. Necessary and sufficient conditions are derived for the algorithms to yield unique estimates. It is shown that their uniqueness conditions coincide with the minimal uniqueness condition on the array, that is independent of the algorithm used (if the array does not satisfy this minimal condition, no DOA estimation method can give unique estimates). Numerical examples are presented to demonstrate the theoretical results.The work of A. Nehorai and D. Starer was supported by the Air Force Office of Scientific Research under Grant No. AFOSR-90-0164 and by the Office of Naval Research under Grant No. N00014-91-J-1298.     

Adaptive parameter estimation for a constrained low-pass system

A novel algorithm is presented for adaptive parameter estimation for a constrained low-pass Butterworth system model. The algorithm will estimate the system cutoff frequency and gain online. When it is known that the true system has a low-pass Butterworth structure or some transfer function similar to it and its true order is used, the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms. Potential applications include filter design and adaptive decision on Nyquist rate for systems     

Cross-product algorithms for source tracking using an EM vectorsensor

We present an adaptive cross-product algorithm for tracking the direction to a moving source using an electromagnetic vector sensor and analyze its performance. We then propose a multiple forgetting factor variant of the same algorithm, which has self-tuning capability, numerical examples are included     

Adaptive Polarized Waveform Design for Target Tracking Based on Sequential Bayesian Inference

In this paper, we develop an adaptive waveform design method for target tracking under a framework of sequential Bayesian inference. We employ polarization diversity to improve the tracking accuracy of a target in the presence of clutter. We use an array of electromagnetic (EM) vector sensors to fully exploit the polarization information of the reflected signal. We apply a sequential Monte Carlo method to track the target parameters, including target position, velocity, and scattering coefficients. This method has the advantage of being able to handle nonlinear and non-Gaussian state and measurement models. The measurements are the output of the sensor array; hence, the information about both the target and its environment is incorporated in the tracking process. We design a new criterion for selecting the optimal waveform one-step ahead based on a recursion of the posterior Cramer-Rao bound. We also derive an algorithm using Monte Carlo integration to compute this criterion and a suboptimal method that reduces the computation cost. Numerical examples demonstrate both the performance of the proposed tracking method and the advantage of the adaptive waveform design scheme.     

Landmine detection and localization using chemical sensor arrayprocessing

We develop methods for automatic detection and localization of landmines using chemical sensor arrays and statistical signal processing techniques. The transport of explosive vapors emanating from buried landmines is modeled as a diffusion process in a two-layered system consisting of ground and air. Measurement and statistical models are then obtained from the associated concentration distribution. We derive two detectors (the generalized likelihood ratio (GLR) test and the mean detector) and determine their performance in terms of the probabilities of false alarm and detection. To determine the unknown location of a landmine, we derive a maximum likelihood (ML) estimation algorithm and evaluate its performance by computing the Cramer-Rao bound (CRB). The results are applied to the design of chemical sensor arrays, satisfying criteria specified in terms of detection and estimation performance measures and for optimally selecting the number and positions of sensors and the number of time samples. To illustrate the potential of the proposed techniques in a realistic demining scenario, we derive a moving-sensor algorithm in which the stationary sensor array is replaced by a single moving sensor. Numerical examples are given to demonstrate the applicability of our results     

A Biologically Inspired Compound-Eye Detector Array—Part II: Statistical Performance Analysis

This is the second part of our paper. In this paper, we propose, model, and analyze the performance of a detector array for localizing far-field particle-emitting sources, which is inspired by but generalizes the compound eye of insects. The array consists of multiple eyelets, each having a conical module with a lens on its top and an inner subarray containing multiple particle detectors. Using a parametric measurement model introduced for the array in Part I, in this part we analytically and numerically analyze the statistical performance of the array. First, we compute the statistical Cramer-Rao bounds (CRBs) on the errors in estimating the direction of arrival of the incident particles; then we derive a lower bound on the mean-square angular error (MSAE) of source localization for any specific array configuration; thirdly, we consider two source-direction estimators, the maximum likelihood estimator (MLE) and the weighted direction estimator (WDE), and analyze their MSAE performance. In the numerical examples, we quantitatively compare the performance of the proposed array with the biological compound eye; show the array performance as a function of the array configuration variables; optimally design the array configuration; illustrate that the MLE asymptotically attains the performance bound, whereas the WDE is nearly optimal for sufficiently large SNR; and analyze the hardware efficiency by comparing the two MSAE bounds. Potential applications of this work include artificial vision in medicine or robotics, astronomy assisted, security, and particle communications.     

A Competitive Mean-Squared Error Approach to Beamforming

We treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). However, this does not guarantee a small mean-squared error (MSE), so that on average the resulting signal estimate can be far from the true signal. Here, we consider strategies that attempt to minimize the MSE between the estimated and unknown signal waveforms. The methods we suggest all maximize the SINR but at the same time are designed to have good MSE performance. Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio (SNR) values. Finally, we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal.     

Decentralized array processing using the MODE algorithm

Centralized methods for source location using sensor arrays have computational and communication burdens that increase significantly with the number of sensors in the array. Therefore, these methods may not be usable in the applications involving very large arrays. In such applications, the data processing may need to be decentralized. This paper introduces two methods for decentralized array processing, based on the recently proposed MODE algorithm. For prescribed nonoverlapping subarrays, both methods are shown to be statistically optimal in the sense that asymptotically they provide the most accurate decentralized estimates of source location parameters. The problem of subarray selection to further optimize the estimation accuracy is only briefly addressed. The two methods are intended for different types of applications: the first should be preferred when there exist significant possibilities for local processing or for parallel computation in the central processor; otherwise the second method should be preferred. The accuracy of the two decentralized methods is compared to the centralized Cramér-Rao bound, both analytically and numerically, in order to provide indications about the loss of accuracy associated with decentralized processing.The work of P. Stoica was supported by a grant from the Royal Swedish Academy of Engineering Sciences and by the Swedish Research Council for Engineering Sciences under contract 91-676. The work of A. Nehorai was supported by the Air Force Office of Scientific Research under grant no. AFOSR-90-0164, and by the Office of Naval Research under grant no. N00014-91-J-1298.on leave at the Department of Applied Electronics, Chalmens University of Technology, 2-41296 Göthensberg, Sweeden.