10 research outputs found
Semiparametric CRB and Slepian-Bangs formulas for Complex Elliptically Symmetric Distributions
The main aim of this paper is to extend the semiparametric inference
methodology, recently investigated for Real Elliptically Symmetric (RES)
distributions, to Complex Elliptically Symmetric (CES) distributions. The
generalization to the complex field is of fundamental importance in all
practical applications that exploit the complex representation of the acquired
data. Moreover, the CES distributions has been widely recognized as a valuable
and general model to statistically describe the non-Gaussian behaviour of
datasets originated from a wide variety of physical measurement processes. The
paper is divided in two parts. In the first part, a closed form expression of
the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint
estimation of complex mean vector and complex scatter matrix of a set of
CES-distributed random vectors is obtained by exploiting the so-called
\textit{Wirtinger} or -\textit{calculus}. The second part
deals with the derivation of the semiparametric version of the Slepian-Bangs
formula in the context of the CES model. Specifically, the proposed
Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and
ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM)
for the estimation of a parameter vector parametrizing the complex mean and the
complex scatter matrix of a CES-distributed vector in the presence of unknown,
nuisance, density generator. Furthermore, we show how to exploit the derived
SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for
Direction of Arrival (DOA) estimation under a random signal model assumption.
Simulation results are also provided to clarify the theoretical findings and to
demonstrate their usefulness in common array processing applications.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: substantial text overlap with arXiv:1807.08505, arXiv:1807.0893
Slepian-Bangs formula and Cramér Rao bound for circular and non-circular complex elliptical symmetric distributions
International audienceThis letter is mainly dedicated to an extension of the Slepian-Bangs formula to non-circular complex elliptical symmetric (NC-CES) distributions, which is derived from a new stochastic representation theorem. This formula includes the non-circular complex Gaussian and the circular CES (C-CES) distributions. Some general relations between the Cramér Rao bound (CRB) under CES and Gaussian distributions are deduced. It is proved in particular that the Gaussian distribution does not always lead to the largest stochastic CRB (SCRB) as many authors tend to believe it. Finally a particular attention is paid to the noisy mixture where closed-form expressions for the SCRBs of the parameters of interest are derived
Robust and Sparse M-Estimation of DOA
A robust and sparse Direction of Arrival (DOA) estimator is derived for array
data that follows a Complex Elliptically Symmetric (CES) distribution with
zero-mean and finite second-order moments. The derivation allows to choose the
loss function and four loss functions are discussed in detail: the Gauss loss
which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex
Gaussian distribution, the ML-loss for the complex multivariate
-distribution (MVT) with degrees of freedom, as well as Huber and
Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian
Learning (SBL). The root mean square DOA error of the derived estimators is
discussed for Gaussian, MVT, and -contaminated data. The robust SBL
estimators perform well for all cases and nearly identical with classical SBL
for Gaussian noise
Robust M-Estimation Based Bayesian Cluster Enumeration for Real Elliptically Symmetric Distributions
Robustly determining the optimal number of clusters in a data set is an
essential factor in a wide range of applications. Cluster enumeration becomes
challenging when the true underlying structure in the observed data is
corrupted by heavy-tailed noise and outliers. Recently, Bayesian cluster
enumeration criteria have been derived by formulating cluster enumeration as
maximization of the posterior probability of candidate models. This article
generalizes robust Bayesian cluster enumeration so that it can be used with any
arbitrary Real Elliptically Symmetric (RES) distributed mixture model. Our
framework also covers the case of M-estimators that allow for mixture models,
which are decoupled from a specific probability distribution. Examples of
Huber's and Tukey's M-estimators are discussed. We derive a robust criterion
for data sets with finite sample size, and also provide an asymptotic
approximation to reduce the computational cost at large sample sizes. The
algorithms are applied to simulated and real-world data sets, including
radar-based person identification, and show a significant robustness
improvement in comparison to existing methods
Neural Network-Based DOA Estimation in the Presence of Non-Gaussian Interference
This work addresses the problem of direction-of-arrival (DOA) estimation in
the presence of non-Gaussian, heavy-tailed, and spatially-colored interference.
Conventionally, the interference is considered to be Gaussian-distributed and
spatially white. However, in practice, this assumption is not guaranteed, which
results in degraded DOA estimation performance. Maximum likelihood DOA
estimation in the presence of non-Gaussian and spatially colored interference
is computationally complex and not practical. Therefore, this work proposes a
neural network (NN) based DOA estimation approach for spatial spectrum
estimation in multi-source scenarios with a-priori unknown number of sources in
the presence of non-Gaussian spatially-colored interference. The proposed
approach utilizes a single NN instance for simultaneous source enumeration and
DOA estimation. It is shown via simulations that the proposed approach
significantly outperforms conventional and NN-based approaches in terms of
probability of resolution, estimation accuracy, and source enumeration accuracy
in conditions of low SIR, small sample support, and when the angular separation
between the source DOAs and the spatially-colored interference is small.Comment: Submitted to IEEE Transactions on Aerospace and Electronic System
Corrections to “Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions”
Errors in [1] are corrected below. (Formula Presented)