Approximate Unconditional Maximum Likelihood Direction of Arrival Estimation for Two Closely Spaced Targets

We consider Direction of Arrival (DoA) estimation in the case of two closely spaced sources. In this case, most high resolution techniques fail to estimate the two DoAs if the waveforms are highly correlated. Maximum Likelihood Estimators (MLE) are known to be more robust, but their excessive computational load limits their use in practice. In this paper, we propose an asymptotic approximation of the Unconditional Maximum Likelihood (UML) procedure in the case of a Uniform Linear Array (ULA) and two closely spaced targets. This approximation is based on an asymptotically (in the number of observations) equivalent formulation of the UML criterion, and on its Taylor series approximation for small DoA separation. This simplified procedure, which requires solving a 1D-optimization problem only, is shown to be accurate for source separation lower than half the mainlobe. Furthermore, it outperforms conventional high resolution algorithms in the case of two correlated sources

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrade when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1-D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

Robust DoA estimation in case of multipath environment for a sense and avoid airborne radar

This paper deals with the sense and avoid problem for an helicopter. The objective of such a system is to early detect collision targets (typically high voltage wires). The Direction of Arrival (DoA) of the target is then a crucial information. In severe multipath environments (flight over a river, for instance) classical DoA estimation schemes dramatically degrade. In this paper, we make use of a method based on the Maximum Likelihood (ML) principle that can resolve two highly correlated and close targets. The major drawback of ML algorithms, namely the computational burden, is removed using an approximation for closely space targets. The contribution of this paper is twofold. We first extend the approximated ML DoA estimation to the case of Non Uniform Linear Antennas (NULA) and we complete the procedure by a detection scheme. Second, we attest the validity of this new processing on real radar data. Hence, we show that the proposed procedure is able to detect a high voltage wire, over a river, at ranges up to 1 km, where a capon beamformer cannot

Topics in the accuracy and resolution of superresolution systems

Since their introduction in the 1970s and 1980s superresolution systems for point source parameter estimation have received theoretical attention regarding their potential performance. Two aspects of performance in particular are of interest, the accuracy of the parameter estimation and the resolution achievable. Limitations on performance may be considered to be due to noise affecting the data, or to errors in the system. Superresolution methods divide roughly into two groups – ‘spectral’ methods and maximum likelihood (ML) methods. MUSIC is perhaps the most effective example of a spectral method and has been studied in considerable detail, in both performance measures, but mainly only for the case of a single parameter. In this study the accuracy of MUSIC in the application of two-dimensional direction finding (DF) has been analysed, with and without system errors, using a general array. Theoretical results are confirmed by simulations. An aim has been to produce simpler results for use in estimating the potential performance of practical systems. Little work has been reported on the resolution of ML methods and this is the second main topic of this work, particularly for the two-dimensional DF case using a general array, with a ML method (IMP) similar to the better known Alternating Projection. Some results are obtained for resolution with and without errors for the case of noncoherent signals. For coherent signals (including the standard radar case) the performance is found to depend on the relative phase of the signals, varying from the quadrature case, where the performance is as for the non-coherent case, to the in-phase (or antiphase) case where only one signal peak is seen

High resolution source localization in near field sensor arrays by MVDR technique

Research over the last decade has led to technological advances in high frequency active and passive detection technology and signal processing. An emerging application area is the standoff detection of concealed objects such as weapons and explosives using penetrating electromagnetic radiation such as terahertz waves (THz). Here sensor arrays are employed in the near field to image the concealed objects. A new approach is investigated to improve upon methods such as Fourier inversion and sum and delay beamforming. A method based on the Minimum Variance Distortionless Response (MVDR) filter technique is developed to localize source points in the electric field coming from a subject. To pinpoint near field sources with precision, this MVDR routine calculates filter responses along a plane that has direction of arrival angle and range axes. To understand its limitations, this new method is tested for angular resolution in various directions of arrival, ranges, and SNR levels. The results show that this technique has potential to accurately detect closely spaced point sources when only a few sensors are used to collect measurements