Amanda Dinstel

M.S. FinalSep 21, 2012, 10:00am

ECE Conference Room C101B Engineering

Wideband Near-Field Array Signal Processing Using the Sparse Representation Framework

Abstract: Recently, the field of sparse representation has attracted a great deal of attention from the perspective of target bearing (angle of arrival) estimation. This strategy takes the approach that a target present in a sensor array's field of view may be treated as a sparse signal, e.g. if a discrete grid is defined over the search area, very few of the points in the grid will contain sources. Source localization reduces to identifying the sparse grid point(s) which correspond to the highest concentration of energy. Tools from the sparse representation framework may be used to provide exceptionally high resolution solutions to this localization problem.

While sparse representation offers a high-resolution detection and localization solution, the application of sparse representation-based techniques to the specific problem of sonar signal processing is challenging for several reasons. Firstly, the general sparse representation-based angle of arrival problem formulation arises from a far-field array signal model, whereas the underwater targets under consideration in this work lie in the near-field. Secondly, a majority of current studies that use sparse representation to localize targets focus on narrowband signal processing. A handful of researchers have explored the extension of sparse recovery to the wideband problem, but most of these approaches require assumptions about the structure (i.e. sparsity profile) of the data, and these assumptions are not applicable to the sonar returns studied in this work. Lastly, sparse representation-based source localization methods suffer from many of the same limitations as traditional sonar processing techniques, such as sensitivity to the effects of sonar platform motion and other sources of measurement error. Such uncertainties may present themselves as errors in the observed data, mismatch of the defined search grid, or both, and ultimately serve to degrade the performance of sparse representation-based source localization algorithms. In this work, a sparse representation-based SAS-like imaging solution is developed which attempts to address each of these sonar-specific challenges.

First, a near-field array signal processing problem is formulated which leverages tools from the sparse representation framework. Near-field source localization does not lend itself readily to the application of sparse representation algorithms because the signal energy is a function of both the source angle of arrival and source range. These two quantities are effectively coupled, which prevents the sparse recovery of a unique target localization result, i.e. many combinations of bearing and range may concurrently solve this problem. To address this issue, one must either 1) measure or estimate the unknown range and then treat this as a known, fixed quantity in the sparse representation problem to estimate the unknown angle of arrival, or 2) reformulate the near-field problem such that the dependence on target range is eliminated. In this work, it is ideal to develop a solution that does not require position measurement or inertial sensors, so the second approach is pursued and the near-field problem is reformulated into a more mathematically friendly far-field-like form. This is accomplished by exploiting a transformation that exists between signals received by corresponding sensor elements in two identical subarrays. Conveniently, this transformation can be shown to depend only on the unknown source angle of arrival and the fixed geometry of the sensor subarrays, and is independent of the unknown range. The fundamental idea here is to formulate a sparse representation problem with respect to the transformation that relates signals received by corresponding elements in symmetric subarrays.

Secondly, derivations are provided which allow for sparse representation-based detection and localization of sources in wideband signals like those typical of sonar data. From the perspective of sparse representation, two general strategies exist for handling wideband data. The first is to reformulate the localization problem to allow for sparse estimation in both the frequency and angle of arrival dimensions. This method requires making certain assumptions about the sparsity structure of the data, e.g. that each frequency band has the same sparsity profile, or that the signal is sparse in frequency as well as angle of arrival. Because such assumptions cannot readily be made about the sonar data under consideration, an alternative wideband approach is adopted in this work. Essentially, each frequency in the wideband data is treated as a separate narrowband problem which may be solved using narrowband sparse recovery methods. In order to coherently combine the results across all frequencies at each ping and generate SAS-like images, a frequency focusing operation is applied to the data at each frequency which effectively transforms all of the frequencies results to a common frequency.

Lastly, strategies are evaluated for alleviating the degrading effects of platform motion and other sources of measurement uncertainty that are inherent to sonar data acquisition. In the context of sparse representation-based localization, errors of this nature manifest themselves as a mismatch between the true and assumed overcomplete basis. In the sparse representation localization problem, the search grid is defined with respect to the orientation of the sensor array(s). Thus, if the true array position deviates from the array position which is used to construct this dictionary, an effective basis mismatch will occur. The result is essentially that true source location cannot be accurately represented using the inappropriately defined dictionary, leading to diminished detection and localization capability. In the work described by this thesis, a mismatch compensation algorithm which is an extension of the total least-squares framework for the special case of perturbed underdetermined systems is evaluated for use in sonar data processing.

While sparse representation offers a high-resolution detection and localization solution, the application of sparse representation-based techniques to the specific problem of sonar signal processing is challenging for several reasons. Firstly, the general sparse representation-based angle of arrival problem formulation arises from a far-field array signal model, whereas the underwater targets under consideration in this work lie in the near-field. Secondly, a majority of current studies that use sparse representation to localize targets focus on narrowband signal processing. A handful of researchers have explored the extension of sparse recovery to the wideband problem, but most of these approaches require assumptions about the structure (i.e. sparsity profile) of the data, and these assumptions are not applicable to the sonar returns studied in this work. Lastly, sparse representation-based source localization methods suffer from many of the same limitations as traditional sonar processing techniques, such as sensitivity to the effects of sonar platform motion and other sources of measurement error. Such uncertainties may present themselves as errors in the observed data, mismatch of the defined search grid, or both, and ultimately serve to degrade the performance of sparse representation-based source localization algorithms. In this work, a sparse representation-based SAS-like imaging solution is developed which attempts to address each of these sonar-specific challenges.

First, a near-field array signal processing problem is formulated which leverages tools from the sparse representation framework. Near-field source localization does not lend itself readily to the application of sparse representation algorithms because the signal energy is a function of both the source angle of arrival and source range. These two quantities are effectively coupled, which prevents the sparse recovery of a unique target localization result, i.e. many combinations of bearing and range may concurrently solve this problem. To address this issue, one must either 1) measure or estimate the unknown range and then treat this as a known, fixed quantity in the sparse representation problem to estimate the unknown angle of arrival, or 2) reformulate the near-field problem such that the dependence on target range is eliminated. In this work, it is ideal to develop a solution that does not require position measurement or inertial sensors, so the second approach is pursued and the near-field problem is reformulated into a more mathematically friendly far-field-like form. This is accomplished by exploiting a transformation that exists between signals received by corresponding sensor elements in two identical subarrays. Conveniently, this transformation can be shown to depend only on the unknown source angle of arrival and the fixed geometry of the sensor subarrays, and is independent of the unknown range. The fundamental idea here is to formulate a sparse representation problem with respect to the transformation that relates signals received by corresponding elements in symmetric subarrays.

Secondly, derivations are provided which allow for sparse representation-based detection and localization of sources in wideband signals like those typical of sonar data. From the perspective of sparse representation, two general strategies exist for handling wideband data. The first is to reformulate the localization problem to allow for sparse estimation in both the frequency and angle of arrival dimensions. This method requires making certain assumptions about the sparsity structure of the data, e.g. that each frequency band has the same sparsity profile, or that the signal is sparse in frequency as well as angle of arrival. Because such assumptions cannot readily be made about the sonar data under consideration, an alternative wideband approach is adopted in this work. Essentially, each frequency in the wideband data is treated as a separate narrowband problem which may be solved using narrowband sparse recovery methods. In order to coherently combine the results across all frequencies at each ping and generate SAS-like images, a frequency focusing operation is applied to the data at each frequency which effectively transforms all of the frequencies results to a common frequency.

Lastly, strategies are evaluated for alleviating the degrading effects of platform motion and other sources of measurement uncertainty that are inherent to sonar data acquisition. In the context of sparse representation-based localization, errors of this nature manifest themselves as a mismatch between the true and assumed overcomplete basis. In the sparse representation localization problem, the search grid is defined with respect to the orientation of the sensor array(s). Thus, if the true array position deviates from the array position which is used to construct this dictionary, an effective basis mismatch will occur. The result is essentially that true source location cannot be accurately represented using the inappropriately defined dictionary, leading to diminished detection and localization capability. In the work described by this thesis, a mismatch compensation algorithm which is an extension of the total least-squares framework for the special case of perturbed underdetermined systems is evaluated for use in sonar data processing.

Adviser: Mahmood Azimi-Sadjadi

Co-Adviser: N/A

Non-ECE Member: Jay Breidt, Statistics

Member 3: Edwin Chong, ECE

Addional Members: Ali Pezeshki, ECE

Co-Adviser: N/A

Non-ECE Member: Jay Breidt, Statistics

Member 3: Edwin Chong, ECE

Addional Members: Ali Pezeshki, ECE

Publications:

N/A

N/A

Program of Study:

ECE512

ECE513

ECE514

ECE651

ECE681A1

STAT525

ECE520

N/A

ECE512

ECE513

ECE514

ECE651

ECE681A1

STAT525

ECE520

N/A