27,381 research outputs found
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
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
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
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
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
Comparison of SAGE and classical multi-antenna algorithms for multipath mitigation in real-world environment
The performance of the Space Alternating Generalized Expectation Maximisation (SAGE) algorithm for multipath mitigation is assessed in this paper. Numerical simulations have already proven the potential of SAGE in navigation context, but practical aspects of the implementation of such a technique in a GNSS receiver are the topic for further investigation. In this paper, we will present the first results of SAGE implementation in a real world environmen
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)
Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains
Recently, several high-resolution parameter estimation algorithms have been
developed to exploit the structure of strictly second-order (SO) non-circular
(NC) signals. They achieve a higher estimation accuracy and can resolve up to
twice as many signal sources compared to the traditional methods for arbitrary
signals. In this paper, as a benchmark for these NC methods, we derive the
closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the
multi-dimensional parameter estimation of strictly non-circular (rectilinear)
signal sources. Assuming a separable centro-symmetric R-D array, we show that
in some special cases, the deterministic R-D NC CRB reduces to the existing
deterministic R-D CRB for arbitrary signals. This suggests that no gain from
strictly non-circular sources (NC gain) can be achieved in these cases. For
more general scenarios, finding an analytical expression of the NC gain for an
arbitrary number of sources is very challenging. Thus, in this paper, we
simplify the derived NC CRB and the existing CRB for the special case of two
closely-spaced strictly non-circular sources captured by a uniform linear array
(ULA). Subsequently, we use these simplified CRB expressions to analytically
compute the maximum achievable asymptotic NC gain for the considered two source
case. The resulting expression only depends on the various physical parameters
and we find the conditions that provide the largest NC gain for two sources.
Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4
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