110 research outputs found
Direction of Arrival Estimation and Tracking with Sparse Arrays
Direction of Arrival (DOA) estimation and tracking of a plane wave or multiple plane waves impinging on an array of sensors from noisy data are two of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. It is well-known that the estimation accuracy, angular resolution, tracking capacity, computational complexity, and hardware implementation cost of a DOA estimation and/or tracking technique depend largely on the array geometry. Large arrays with many sensors provide accurate DOA estimation and perfect target tracking, but they usually suffer from a high cost for hardware implementation. Sparse arrays can yield similar DOA estimates and tracking performance with fewer elements for the same-size array aperture as compared to the traditional uniform arrays. In addition, the signals of interest may have rich temporal information that can be exploited to effectively eliminate background noise and significantly improve the performance and capacity of DOA estimation and tracking, and/or even dramatically reduce the computational burden of estimation and tracking algorithms. Therefore, this thesis aims to provide some solutions to improving the DOA estimation and tracking performance by designing sparse arrays and exploiting prior knowledge of the incident signals such as AR modeled sources and known waveforms.
First, we design two sparse linear arrays to efficiently extend the array aperture and improve the DOA estimation performance. One scheme is called minimum redundancy sparse subarrays (MRSSA), where the subarrays are used to obtain an extended correlation matrix according to the principle of minimum redundancy linear array (MRLA). The other linear array is constructed using two sparse ULAs, where the inter-sensor spacing within the same ULA is much larger than half wavelength. Moreover, we propose a 2-D DOA estimation method based on sparse L-shaped arrays, where the signal subspace is selected from the noise-free correlation matrix without requiring the eigen-decomposition to estimate the elevation angle, while the azimuth angles are estimated based on the modified total least squares (TLS) technique.
Second, we develop two DOA estimation and tracking methods for autoregressive (AR) modeled signal source using sparse linear arrays together with Kalman filter and LS-based techniques. The proposed methods consist of two common stages: in the first stage, the sources modeled by AR processes are estimated by the celebrated Kalman filter and in the second stage, the efficient LS or TLS techniques are employed to estimate the DOAs and AR coefficients simultaneously. The AR-modeled sources can provide useful temporal information to handle cases such as the ones, where the number of sources is larger than the number of antennas. In the first method, we exploit the symmetric array to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity, while in the second method, we use the ordinary sparse arrays to provide a more accurate DOA estimation.
Finally, we study the problem of estimating and tracking the direction of arrivals (DOAs) of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a sparse sensor array. The core idea is to consider the output of each sensor as a linear regression model, each of whose coefficients contains a pair of DOAs and gain information corresponding to one target. These coefficients are determined by solving a linear least squares problem and then updating recursively, based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. It is shown that the coefficients from different sensors have the same amplitude, but variable phase information for the same signal. Then, simple algebraic manipulations and the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space
Localization and tracking of electronic devices with their unintended emissions
The precise localization and tracking of electronic devices via their unintended emissions has a broad range of commercial and security applications. Active stimulation of the receivers of such devices with a known signal generates very low power unintended emissions. This dissertation presents localization and tracking of multiple devices using both simulation and experimental data in the form of five papers.
First the localization of multiple emitting devices through active stimulation under multipath fading with a Smooth MUSIC based scheme in the near field region is presented. Spatial smoothing helps to separate the correlated sources and the multipath fading and results confirm improved accuracy. A cost effective near-field localization method is proposed next to locate multiple correlated unintended emitting devices under colored noise conditions using two well separated antenna arrays since colored noise in the environment degrades the subspace-based localization techniques.
Subsequently, in order to track moving sources, a near-field scheme by using array output is introduced to monitor direction of arrival (DOA) and the distance between the antenna array and the moving source. The array output, which is a nonlinear function of DOA and distance information, is employed in the Extended Kalman Filter (EKF). In order to show the near- and far-field effect on estimation accuracy, computer simulation results are included for localization and tracking techniques.
Finally, an L-shaped array is constructed and a suite of schemes are introduced for localization and tracking of such devices in the three-dimensional environment. Experimental results for localization and tracking of unintended emissions from single and multiple devices in the near-field environment of an antenna array are demonstrated --Abstract, page iv
Optimal Mixed-ADC arrangement for DOA Estimation via CRB using ULA
We consider a mixed analog-to-digital converter (ADC) based architecture for
direction of arrival (DOA) estimation using a uniform linear array (ULA). We
derive the Cram{\'e}r-Rao bound (CRB) of the DOA under the optimal time-varying
threshold, and find that the asymptotic CRB is related to the arrangement of
high-precision and one-bit ADCs for a fixed number of ADCs. Then, a new concept
called ``mixed-precision arrangement" is proposed. It is proven that better
performance for DOA estimation is achieved when high-precision ADCs are
distributed evenly around the edges of the ULA. This result can be extended to
a more general case where the ULA is equipped with various precision ADCs.
Simulation results show the validity of the asymptotic CRB and better
performance under the optimal mixed-precision arrangement.Comment: 5 pages, 3 figures, accepted by ICASSP202
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
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
Computationally Efficient DOA Tracking Algorithm in Monostatic MIMO Radar with Automatic Association
We consider the problem of tracking the direction of arrivals (DOA) of multiple moving targets in monostatic multiple-input multiple-output (MIMO) radar. A low-complexity DOA tracking algorithm in monostatic MIMO radar is proposed. The proposed algorithm obtains DOA estimation via the difference between previous and current covariance matrix of the reduced-dimension transformation signal, and it reduces the computational complexity and realizes automatic association in DOA tracking. Error analysis and Cramér-Rao lower bound (CRLB) of DOA tracking are derived in the paper. The proposed algorithm not only can be regarded as an extension of array-signal-processing DOA tracking algorithm in (Zhang et al. (2008)), but also is an improved version of the DOA tracking algorithm in (Zhang et al. (2008)). Furthermore, the proposed algorithm has better DOA tracking performance than the DOA tracking algorithm in (Zhang et al. (2008)). The simulation results demonstrate effectiveness of the proposed algorithm. Our work provides the technical support for the practical application of MIMO radar
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