Approximate maximum likelihood direction of arrival estimation for two closely spaced sources

Abstract—Most high resolution direction of arrival (DoA) estimation algorithms exploit an eigen decomposition of the sample covariance matrix (SCM). However, their performance dramatically degrade in case of correlated sources or low number of snapshots. In contrast, the maximum likelihood (ML) DoA estimator is more robust to these drawbacks but suffers from a too expensive computational cost which can prevent its use in practice. In this paper, we propose an asymptotic simplification of the ML criterion in the case of two closely spaced sources. This approximated ML estimator can be implemented using only 1-D Fourier transforms. We show that this solution is as accurate as the exact ML one and outperforms all high-resolution techniques in case of correlated sources. This solution can also be used in the single snapshot case where very few algorithms are known to be effective

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

Angular resolution limit for deterministic correlated sources

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cram\'er-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation

Array signal processing for maximum likelihood direction-of-arrival estimation

Emitter Direction-of-Arrival (DOA) estimation is a fundamental problem in a variety of applications including radar, sonar, and wireless communications. The research has received considerable attention in literature and numerous methods have been proposed. Maximum Likelihood (ML) is a nearly optimal technique producing superior estimates compared to other methods especially in unfavourable conditions, and thus is of significant practical interest. This paper discusses in details the techniques for ML DOA estimation in either white Gaussian noise or unknown noise environment. Their performances are analysed and compared, and evaluated against the theoretical lower bounds

A robust sequential hypothesis testing method for brake squeal localisation

This contribution deals with the in situ detection and localisation of brake squeal in an automobile. As brake squeal is emitted from regions known a priori, i.e., near the wheels, the localisation is treated as a hypothesis testing problem. Distributed microphone arrays, situated under the automobile, are used to capture the directional properties of the sound field generated by a squealing brake. The spatial characteristics of the sampled sound field is then used to formulate the hypothesis tests. However, in contrast to standard hypothesis testing approaches of this kind, the propagation environment is complex and time-varying. Coupled with inaccuracies in the knowledge of the sensor and source positions as well as sensor gain mismatches, modelling the sound field is difficult and standard approaches fail in this case. A previously proposed approach implicitly tried to account for such incomplete system knowledge and was based on ad hoc likelihood formulations. The current paper builds upon this approach and proposes a second approach, based on more solid theoretical foundations, that can systematically account for the model uncertainties. Results from tests in a real setting show that the proposed approach is more consistent than the prior state-of-the-art. In both approaches, the tasks of detection and localisation are decoupled for complexity reasons. The localisation (hypothesis testing) is subject to a prior detection of brake squeal and identification of the squeal frequencies. The approaches used for the detection and identification of squeal frequencies are also presented. The paper, further, briefly addresses some practical issues related to array design and placement. (C) 2019 Author(s)

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