57 research outputs found
Gridless Two-dimensional DOA Estimation With L-shaped Array Based on the Cross-covariance Matrix
The atomic norm minimization (ANM) has been successfully incorporated into
the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for
super-resolution. However, its computational workload might be unaffordable
when the number of snapshots is large. In this paper, we propose two gridless
methods for 2-D DOA estimation with L-shaped array based on the atomic norm to
improve the computational efficiency. Firstly, by exploiting the
cross-covariance matrix an ANM-based model has been proposed. We then prove
that this model can be efficiently solved as a semi-definite programming (SDP).
Secondly, a modified model has been presented to improve the estimation
accuracy. It is shown that our proposed methods can be applied to both uniform
and sparse L-shaped arrays and do not require any knowledge of the number of
sources. Furthermore, since our methods greatly reduce the model size as
compared to the conventional ANM method, and thus are much more efficient.
Simulations results are provided to demonstrate the advantage of our methods
Localization of DOA trajectories -- Beyond the grid
The direction of arrival (DOA) estimation algorithms are crucial in
localizing acoustic sources. Traditional localization methods rely on
block-level processing to extract the directional information from multiple
measurements processed together. However, these methods assume that DOA remains
constant throughout the block, which may not be true in practical scenarios.
Also, the performance of localization methods is limited when the true
parameters do not lie on the parameter search grid. In this paper we propose
two trajectory models, namely the polynomial and bandlimited trajectory models,
to capture the DOA dynamics. To estimate trajectory parameters, we adopt two
gridless algorithms: i) Sliding Frank-Wolfe (SFW), which solves the Beurling
LASSO problem and ii) Newtonized Orthogonal Matching Pursuit (NOMP), which
improves over OMP using cyclic refinement. Furthermore, we extend our analysis
to include wideband processing. The simulation results indicate that the
proposed trajectory localization algorithms exhibit improved performance
compared to grid-based methods in terms of resolution, robustness to noise, and
computational efficiency
Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective
The signal processing community currently witnesses the emergence of sensor
array processing and Direction-of-Arrival (DoA) estimation in various modern
applications, such as automotive radar, mobile user and millimeter wave indoor
localization, drone surveillance, as well as in new paradigms, such as joint
sensing and communication in future wireless systems. This trend is further
enhanced by technology leaps and availability of powerful and affordable
multi-antenna hardware platforms. The history of advances in super resolution
DoA estimation techniques is long, starting from the early parametric
multi-source methods such as the computationally expensive maximum likelihood
(ML) techniques to the early subspace-based techniques such as Pisarenko and
MUSIC. Inspired by the seminal review paper Two Decades of Array Signal
Processing Research: The Parametric Approach by Krim and Viberg published in
the IEEE Signal Processing Magazine, we are looking back at another three
decades in Array Signal Processing Research under the classical narrowband
array processing model based on second order statistics. We revisit major
trends in the field and retell the story of array signal processing from a
modern optimization and structure exploitation perspective. In our overview,
through prominent examples, we illustrate how different DoA estimation methods
can be cast as optimization problems with side constraints originating from
prior knowledge regarding the structure of the measurement system. Due to space
limitations, our review of the DoA estimation research in the past three
decades is by no means complete. For didactic reasons, we mainly focus on
developments in the field that easily relate the traditional multi-source
estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Maximum Likelihood-based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL with Grid Refinement
We consider the parametric data model employed in applications such as line
spectral estimation and direction-of-arrival estimation. We focus on the
stochastic maximum likelihood estimation (MLE) framework and offer approaches
to estimate the parameter of interest in a gridless manner, overcoming the
model complexities of the past. This progress is enabled by the modern trend of
reparameterization of the objective and exploiting the sparse Bayesian learning
(SBL) approach. The latter is shown to be a correlation-aware method, and for
the underlying problem it is identified as a grid-based technique for
recovering a structured covariance matrix of the measurements. For the case
when the structured matrix is expressible as a sampled Toeplitz matrix, such as
when measurements are sampled in time or space at regular intervals, additional
constraints and reparameterization of the SBL objective leads to the proposed
structured matrix recovery technique based on MLE. The proposed optimization
problem is non-convex, and we propose a majorization-minimization based
iterative procedure to estimate the structured matrix; each iteration solves a
semidefinite program. We recover the parameter of interest in a gridless manner
by appealing to the Caratheodory-Fejer result on decomposition of PSD Toeplitz
matrices. For the general case of irregularly spaced time or spatial samples,
we propose an iterative SBL procedure that refines grid points to increase
resolution near potential source locations, while maintaining a low per
iteration complexity. We provide numerical results to evaluate and compare the
performance of the proposed techniques with other gridless techniques, and the
CRB. The proposed correlation-aware approach is more robust to
environmental/system effects such as low number of snapshots, correlated
sources, small separation between source locations and improves sources
identifiability.Comment: Submitted to the IEEE Transactions on Signal Processing (Previous
submission date: 29-Oct-2021
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
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