DOA estimation for conformal vector-sensor array using geometric algebra

Tao, Meng; Wu, Meiping; Yuan, Naichang

doi:10.1186/s13634-017-0503-y

Cited by 6 publications

(9 citation statements)

References 21 publications

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“…Referring to ( 2 ) and ( 3 ), a

matrix with m -row and n -column, noted

, is constructed as follows [ 20 ]

where

for

are all

real number matrices. The transpose with reversion of

is denoted by

where

for

denotes the transpose.…”

Section: Preliminariesmentioning

confidence: 99%

“…In view of the paucity of research on calculations with multi-vector, the Complex Representation Matrix (CRM) [ 20 ] is introduced because of the mature matrix theories. Consider a matrix

, the CRM is defined by

…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Since

and

commutes with all elements in

, one can identify it with the complex imaginary unit j [ 20 ], and so we can view

given in ( 8 ) as a complex matrix.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…In other words, there are two possible eigenvalues, namely the left and the right eigenvalue for

matrix. In the proposed algorithm, the right eigenvalue is selected because the right ED of

matrix can be converted to the right ED of its CRM [ 20 ].…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…The traditional model for EMVS is just a linear combination of each component, which somehow locally destroy the orthogonality of the signal components [ 20 ]. Meanwhile, the heavy computational efforts and memory requirements during data processing for the DOA estimation cannot be ignored [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Geometric Algebra-Based ESPRIT Algorithm for DOA Estimation

Wang

et al. 2021

Sensors

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Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array; however, existing ESPRIT algorithms treat the output of the EMVS array either as a “long vector”, which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.

show abstract

“…Referring to ( 2 ) and ( 3 ), a

matrix with m -row and n -column, noted

, is constructed as follows [ 20 ]

where

for

are all

real number matrices. The transpose with reversion of

is denoted by

where

for

denotes the transpose.…”

Section: Preliminariesmentioning

confidence: 99%

“…In view of the paucity of research on calculations with multi-vector, the Complex Representation Matrix (CRM) [ 20 ] is introduced because of the mature matrix theories. Consider a matrix

, the CRM is defined by

…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Since

and

commutes with all elements in

, one can identify it with the complex imaginary unit j [ 20 ], and so we can view

given in ( 8 ) as a complex matrix.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…In other words, there are two possible eigenvalues, namely the left and the right eigenvalue for