GLRT-Based Direction Detectors in Homogeneous Noise and Subspace Interference

In this paper, we derive and assess decision schemes to discriminate, resorting to an array of sensors, between the H0 hypothesis that data under test contain disturbance only (i.e., noise plus interference) and the H1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables. The disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace. We assume that a set of noise-only (secondary) data is available, which possess the same statistical characterization of noise in the cells under test. At the design stage, we resort to either the plain generalized-likelihood ratio test (GLRT) or the two-step GLRT-based design procedure. The performance analysis, conducted resorting to simulated data, shows that the one-step GLRT performs better than the detector relying on the two-step design procedure when the number of secondary data is comparable to the number of sensors; moreover, it outperforms a one-step GLRT-based subspace detector when the dimension of the signal subspace is sufficiently high

A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family

International audienceMinimal bounds on the mean square error (MSE) are generally used in order to predict the best achievable performance of an estimator for a given observation model. In this paper, we are interested in the Bayesian bound of the Weiss–Weinstein family. Among this family, we have Bayesian Cramér-Rao bound, the Bobrovsky–MayerWolf–Zakaï bound, the Bayesian Bhattacharyya bound, the Bobrovsky–Zakaï bound, the Reuven–Messer bound, and the Weiss–Weinstein bound. We present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator (MMSEE) and on a constrained optimization problem. With this approach, we obtain a useful theoretical framework to derive new Bayesian bounds. For that purpose, we propose two bounds. First, we propose a generalization of the Bayesian Bhattacharyya bound extending the works of Bobrovsky, Mayer–Wolf, and Zakaï. Second, we propose a bound based on the Bayesian Bhattacharyya bound and on the Reuven–Messer bound, representing a generalization of these bounds. The proposed bound is the Bayesian extension of the deterministic Abel bound and is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven–Messer bound, the Bobrovsky–Zakaï bound, and the Bayesian Cramér–Rao bound. We propose some closed-form expressions of these bounds for a general Gaussian observation model with parameterized mean. In order to illustrate our results, we present simulation results in the context of a spectral analysis problem

Moving Target Detection in Foliage Using Along Track Monopulse Synthetic Aperture Radar Imaging

Abstract-This paper presents a method for detecting moving targets embedded in foliage from the monostatic and bistatic Synthetic Aperture Radar (SAR) data obtained via two airborne radars. The two radars, which are mounted on the same aircraft, have different coordinates in the along track (cross-range) domain. However, unlike the interferometric SAR systems used for topographic mapping, the two radars possess a common range and altitude (i.e., slant range). The resultant monopulse SAR images are used to construct difference and interferometric images for moving target detection. It is shown that the signatures of the stationary targets are weakened in these images. Methods for estimating a moving target's motion parameters are discussed. Results for an ultrawideband UHF SAR system are presented

On Lower Bounds for Non Standard Deterministic Estimation

We consider deterministic parameter estimation and the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters. Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models

Application of pulse compression techniques to broadband acoustic scattering by live individual zooplankton

Author Posting. © Acoustical Society of America, 1998. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 104 (1998): 39-55, doi:10.1121/1.424056.Distinct frequency dependencies of the acoustic backscattering by zooplankton of different anatomical groups have been observed in our previous studies [Chu et al., ICES J. Mar. Sci. 49, 97–106 (1992); Stanton et al., ICES J. Mar. Sci. 51, 505–512 (1994)]. Based mainly on the spectral information, scattering models have been proposed to describe the backscattering mechanisms of different zooplankton groups [Stanton et al., J. Acoust. Soc. Am. 103, 236–253 (1998b)]. In this paper, an in-depth study of pulse compression (PC) techniques is presented to characterize the temporal, spectral, and statistical signatures of the acoustic backscattering by zooplankton of different gross anatomical classes. Data collected from various sources are analyzed and the results are consistent with our acoustic models. From compressed pulse (CP) outputs for all three different zooplankton groups, two major arrivals from different parts of the animal body can be identified: a primary and a secondary arrival. (1) Shrimplike animals (Euphausiids and decapod shrimp; near broadside incidence only): the primary one is from the front interface (interface closest to the transducer) of the animal and the secondary arrival is from the back interface; (2) gas-bearing animals (Siphonophores): the primary arrival is from the gas inclusion and the secondary arrival is from the body tissue ("local acoustic center of mass"); and (3) elastic shelled animals (Gastropods): the primary one is from the front interface and the secondary arrival corresponds to the subsonic Lamb wave that circumnavigates the surface of the shell. Statistical analysis of these arrivals is used to successfully infer the size of the individual animals. In conjunction with different aspects of PC techniques explored in this paper, a concept of partial wave target strength (PWTS) is introduced to describe scattering by the different CP highlights. Furthermore, temporal gating of the CP output allows rejection of unwanted signals, improves the output signal-to-noise ratio (SNR) of the spectra of selected partial waves of interest, and provides a better understanding of the scattering mechanism of the animals. In addition, it is found that the averaged PWTS can be used to obtain a more quantitative scattering characterization for certain animals such as siphonophores.This work was supported by the National Science Foundation under Grant No. OCE-9201264 and the U.S. Office of Naval Research under Grant Nos. N00014-89-J-1729, N00014-94-1-0452, and N00014-95-1-0287

Multi-Step Knowledge-Aided Iterative ESPRIT for Direction Finding

In this work, we propose a subspace-based algorithm for DOA estimation which iteratively reduces the disturbance factors of the estimated data covariance matrix and incorporates prior knowledge which is gradually obtained on line. An analysis of the MSE of the reshaped data covariance matrix is carried out along with comparisons between computational complexities of the proposed and existing algorithms. Simulations focusing on closely-spaced sources, where they are uncorrelated and correlated, illustrate the improvements achieved.Comment: 7 figures. arXiv admin note: text overlap with arXiv:1703.1052

A code-division, multiple beam sonar imaging system

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1989In this thesis, a new active sonar imaging concept is explored using the principle of code-division and the simultaneous transmission of multiple coded signals. The signals are sixteen symbol, four-bit, non-linear, block Frequency-Shift Keyed (FSK) codes, each of which is projected into a different direction. Upon reception of the reflected waveform, each signal is separately detected and the results are inverted to yield an estimation of the spatial location of an object in three dimensions. The code-division sonar is particularly effective operating in situations where the phase of the transmitted signal is perturbed by the propagation media and the target Most imaging techniques presently used rely on preservation of the phase of the received signal over the dimension of the receiving array. In the code-division sonar, spatial resolution is obtained by using the combined effects of code-to-code rejection and the a-priori knowledge of which direction each code was transmitted. The coded signals are shown to be highly tolerable of phase distortion over the duration of the transmission. The result is a high-resolution, three-dimensional image, obtainable in a highly perturbative environment Additionally, the code-division sonar is capable of a high frame rate due to the simplicity of the processing required. Two algorithms are presented which estimate the spatial coordinates of an object in the ensonified aperture of the system, and the performance of the two is compared for different signal to noise levels. Finally, the concept of code-division imaging is employed in a series of experiments in which a code-division sonar was used to image objects under a variety of conditions. The results of the experiments are presented, showing the resolution capabilities of the system

A review of closed-form Cramér-Rao Bounds for DOA estimation in the presence of Gaussian noise under a unified framework

The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case

Novel implementation technique for a wavelet-based broadband signal detection system

This thesis reports on the design, simulation and implementation of a novel Implementation for a Wavelet-based Broadband Signal Detection System. There is a strong interest in methods of increasing the resolution of sonar systems for the detection of targets at sea. A novel implementation of a wideband active sonar signal detection system is proposed in this project. In the system the Continuous Wavelet Transform is used for target motion estimation and an Adaptive-Network-based Fuzzy inference System (ANFIS) is adopted to minimize the noise effect on target detection. A local optimum search algorithm is introduced in this project to reduce the computation load of the Continuous Wavelet Transform and make it suitable for practical applications. The proposed system is realized on a Xilinx University Program Virtex-II Pro Development System which contains a Virtex II pro XC2VP30 FPGA chip with 2 powerPC 405 cores. Testing for single target detection and multiple target detection shows the proposed system is able to accurately locate targets under reverberation-limited underwater environment with a Signal-Noise-Ratio of up to -30db, with location error less than 10 meters and velocity estimation error less than 1 knot. In the proposed system the combination of CWT and local optimum search algorithm significantly saves the computation time for CWT and make it more practical to real applications. Also the implementation of ANFIS on the FPGA board indicates in the future a real-time ANFIS operation with VLSI implementation would be possible