Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

Corr, Jamie; Thompson, Keith; Weiss, Stephan; Proudler, Ian K.; McWhirter, J.G.

doi:10.1109/eusipco.2015.7362503

Cited by 39 publications

(65 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…I. Two roots at z = −2 and z = − 1 2 match closely, but do not entirely coincide due to estimation errors by the SMD algorithm as well as due to trimming of the polynomial matrix factors [14]. As a results, root finding algorithms such the one in [25] cannot determine the GCD exactly, and roots here have been matched by inspection.…”

Section: Numerical Examplementioning

confidence: 92%

See 1 more Smart Citation

Identification of Broadband Source-Array Responses from Sensor Second Order Statistics

Weiss

Goddard²,

Somasundaram

et al. 2017

2017 Sensor Signal Processing for Defence Conference (SSPD)

View full text Add to dashboard Cite

Abstract-This paper addresses the identification of sourcesensor impulse responses from the measured space-time covariance matrix in the absence of any further side information about the source or the propagation environment. Using polynomial matrix decomposition techniques, the responses can be narrowed down to an indeterminacy of a common polynomial factor. If at least two different measurements for a source with constant power spectral density are available, this indeterminacy can be reduced to an ambiguity in the phase response of the sourcesensor paths.

show abstract

Section: Numerical Examplementioning

confidence: 92%

“…(M − 1) will still form valid eigenvectors satisfying (8). This allpass filter must be common to all elements of q m (z), and can in the simplest case form a delay [14]. Note that therefore q m (z) and q ′ m (z) will have an identical magnitude but different phase responses.…”

Section: A Existencementioning

confidence: 99%

Identification of Broadband Source-Array Responses from Sensor Second Order Statistics

Weiss

Goddard²,

Somasundaram

et al. 2017

2017 Sensor Signal Processing for Defence Conference (SSPD)

View full text Add to dashboard Cite

show abstract

“…Since current PEVD algorithms can be shown to either favour or can even be proven to yield spectral majorisation (McWhirter and Wang, 2016), they result in matrix factors with high polynomial order to approximate the factors in (5). Therefore, some mechanisms to curb the order of these polynomial (Foster et al, 2006) and specifically the paraunitary factors (Ta and Weiss, 2007b;McWhirter et al, 2007;Corr et al, 2015c;Corr et al, 2015d) have been suggested, which are generally based on a truncation with limited error impact, and in some cases judiciously exploit the arbitrary phase response of the eigenvectors.…”

Section: Algorithms For Polynomial Matrix Evdmentioning

confidence: 99%

Extending Narrowband Descriptions and Optimal Solutions to Broadband Sensor Arrays

Weiss¹

2018

Proceedings of the 8th International Joint Conference on Pervasive and Embedded Computing and Communication Systems

Self Cite

View full text Add to dashboard Cite

Abstract:This overview paper motivates the description of broadband sensor array problems by polynomial matrices, directly extending notation that is familiar from the characterisation of narrowband problems. To admit optimal solutions, the approach relies on extending the utility of the eigen-and singular value decompositions, by finding decompositions of such polynomial matrices. Particularly the factorisation of parahermitian polynomial matrices -including space-time covariance matrices that model the second order statistics of broadband sensor array data -is important. The paper summarises recent findings on the existence and uniqueness of the eigenvalue decomposition of such parahermitian polynomial matrices, demonstrates some algorithms that implement such factorisations, and highlights key applications where such techniques can provide advantages over state-of-the-art solutions.

show abstract

“…In this paper we use the recently developed row-shift corrected truncation method [11], this approach takes advantage of an ambiguity in the paraunitary matrix to further reduce its polynomial order.…”

Section: General Anatomymentioning

confidence: 99%

Impact of source model matrix conditioning on PEVD algorithms

Corr¹,

Thompson²,

Weiss³

et al. 2015

2nd IET International Conference on Intelligent Signal Processing 2015 (ISP)

View full text Add to dashboard Cite

Polynomial parahermitian matrices can accurately and elegantly capture the space-time covariance in broadband array problems. To factorise such matrices, a number of polynomial EVD (PEVD) algorithms have been suggested. At every step, these algorithms move various amounts of off-diagonal energy onto the diagonal, to eventually reach an approximate diagonalisation. In practical experiments, we have found that the relative performance of these algorithms depends quite significantly on the type of parahermitian matrix that is to be factorised. This paper aims to explore this performance space, and to provide some insight into the characteristics of PEVD algorithms.

show abstract

Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

Cited by 39 publications

References 9 publications

Identification of Broadband Source-Array Responses from Sensor Second Order Statistics

Identification of Broadband Source-Array Responses from Sensor Second Order Statistics

Extending Narrowband Descriptions and Optimal Solutions to Broadband Sensor Arrays

Impact of source model matrix conditioning on PEVD algorithms

Contact Info

Product

Resources

About