174 research outputs found
Joint ML calibration and DOA estimation with separated arrays
This paper investigates parametric direction-of-arrival (DOA) estimation in a
particular context: i) each sensor is characterized by an unknown complex gain
and ii) the array consists of a collection of subarrays which are substantially
separated from each other leading to a structured noise covariance matrix. We
propose two iterative algorithms based on the maximum likelihood (ML)
estimation method adapted to the context of joint array calibration and DOA
estimation. Numerical simulations reveal that the two proposed schemes, the
iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint
array calibration and DOA estimation, outperform the state of the art methods
and the MIML algorithm reaches the Cram\'er-Rao bound for a low number of
iterations
DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition
We consider the problem of direction-of-arrival (DOA) estimation in unknown
partially correlated noise environments where the noise covariance matrix is
sparse. A sparse noise covariance matrix is a common model for a sparse array
of sensors consisted of several widely separated subarrays. Since interelement
spacing among sensors in a subarray is small, the noise in the subarray is in
general spatially correlated, while, due to large distances between subarrays,
the noise between them is uncorrelated. Consequently, the noise covariance
matrix of such an array has a block diagonal structure which is indeed sparse.
Moreover, in an ordinary nonsparse array, because of small distance between
adjacent sensors, there is noise coupling between neighboring sensors, whereas
one can assume that nonadjacent sensors have spatially uncorrelated noise which
makes again the array noise covariance matrix sparse. Utilizing some recently
available tools in low-rank/sparse matrix decomposition, matrix completion, and
sparse representation, we propose a novel method which can resolve possibly
correlated or even coherent sources in the aforementioned partly correlated
noise. In particular, when the sources are uncorrelated, our approach involves
solving a second-order cone programming (SOCP), and if they are correlated or
coherent, one needs to solve a computationally harder convex program. We
demonstrate the effectiveness of the proposed algorithm by numerical
simulations and comparison to the Cramer-Rao bound (CRB).Comment: in IEEE Sensor Array and Multichannel signal processing workshop
(SAM), 201
EM-Type Algorithms for DOA Estimation in Unknown Nonuniform Noise
The expectation--maximization (EM) algorithm updates all of the parameter
estimates simultaneously, which is not applicable to direction of arrival (DOA)
estimation in unknown nonuniform noise. In this work, we present several
efficient EM-type algorithms, which update the parameter estimates
sequentially, for solving both the deterministic and stochastic
maximum--likelihood (ML) direction finding problems in unknown nonuniform
noise. Specifically, we design a generalized EM (GEM) algorithm and a
space-alternating generalized EM (SAGE) algorithm for computing the
deterministic ML estimator. Simulation results show that the SAGE algorithm
outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for
computing the stochastic ML estimator, in which the first updates the DOA
estimates simultaneously while the second updates the DOA estimates
sequentially. Simulation results show that the second SAGE algorithm
outperforms the first one.Comment: arXiv admin note: text overlap with arXiv:2208.0751
Efficient Computation of ML DOA Estimates Under Unknown Nonuniform Sensor Noise Powers
This paper presents an efficient method for computing Maximum Likelihood (ML) direction-of-arrival (DOA) estimates in scenarios in which the sensor noise powers are nonuniform and unknown. The method combines the Alternating Projection (AP) algorithm for coarsely locating additional DOAs and Newton iterations for finally obtaining the ML estimates. Compared with the existing approaches, the method reduces the computational burden significantly due to the small number of Newton iterations required and to the efficient computation of each iteration. Specifically, the iterations are computed in a small number of arithmetic operations thanks to the closed-form formulas for the gradient and Hessian of the ML cost functions presented in this paper. The method’s total computational burden is of just a few mega-flops (mega floating-point operations) in typical cases. We present the method for the deterministic and stochastic ML estimators. Then, an analysis of the deterministic ML cost function’s gradient reveals an unexpected drawback: its associated estimator is either degenerate or inconsistent. Finally, we assess the method’s root-mean-square (RMS) error and computational burden numerically and compare it with other relevant estimators in the literature.This work was supported by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Project PID2020-117303GB-C22
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
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