Application of the Matrix Pencil Approach to Direction Finding

1991 ◽  
Author(s):  
Braham Himed ◽  
Donald D. Weiner
Keyword(s):  
Matrix Pencil ◽  
Direction Finding ◽  
The Matrix

scholarly journals Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5065
Author(s):  
Daniel Chaparro-Arce ◽  
Sergio Gutierrez ◽  
Andres Gallego ◽  
Cesar Pedraza ◽  
Felix Vega ◽  
...  
Keyword(s):  
Time Reversal ◽  
Communication Channel ◽  
Matrix Pencil ◽  
Acoustic Signals ◽  
Underwater Acoustic ◽  
Low Bit Rate ◽  
Matrix Pencil Method ◽  
The Matrix ◽  
Resonance Expansion ◽  
Passive Sensors

This paper presents a technique, based on the matrix pencil method (MPM), for the compression of underwater acoustic signals produced by boat engines. The compressed signal, represented by its complex resonance expansion, is intended to be sent over a low-bit-rate wireless communication channel. We demonstrate that the method can provide data compression greater than 60%, ensuring a correlation greater than 93% between the reconstructed and the original signal, at a sampling frequency of 2.2 kHz. Once the signal was reconstituted, a localization process was carried out with the time reversal method (TR) using information from four different sensors in a simulation environment. This process sought to achieve the identification of the position of the ship using only passive sensors, considering two different sensor arrangements.

scholarly journals Linearization schemes for Hermite matrix polynomials

2015 ◽  
Author(s):  
Nikta Shayanfar ◽  
Heike Fassbender
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Matrix Polynomial ◽  
Multiple Input Multiple Output ◽  
Matrix Pencil ◽  
Least Square ◽  
Coupled Systems ◽  
Matrix Polynomials ◽  
Polynomial Eigenvalue Problem ◽  
The Matrix

The polynomial eigenvalue problem is to find the eigenpair of $(\lambda,x) \in \mathbb{C}\bigcup \{\infty\} \times \mathbb{C}^n \backslash \{0\}$ that satisfies $P(\lambda)x=0$, where $P(\lambda)=\sum_{i=0}^s P_i \lambda ^i$ is an $n\times n$ so-called matrix polynomial of degree $s$, where the coefficients $P_i, i=0,\cdots,s$, are $n\times n$ constant matrices, and $P_s$ is supposed to be nonzero. These eigenvalue problems arise from a variety of physical applications including acoustic structural coupled systems, fluid mechanics, multiple input multiple output systems in control theory, signal processing, and constrained least square problems. Most numerical approaches to solving such eigenvalue problems proceed by linearizing the matrix polynomial into a matrix pencil of larger size. Such methods convert the eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploit and preserve the structure and properties of the original eigenvalue problem. The linearizations have been extensively studied with respect to the basis that the matrix polynomial is expressed in. If the matrix polynomial is expressed in a special basis, then it is desirable that its linearization be also expressed in the same basis. The reason is due to the fact that changing the given basis ought to be avoided \cite{H1}. The authors in \cite{ACL} have constructed linearization for different bases such as degree-graded ones (including monomial, Newton and Pochhammer basis), Bernstein and Lagrange basis. This contribution is concerned with polynomial eigenvalue problems in which the matrix polynomial is expressed in Hermite basis. In fact, Hermite basis is used for presenting matrix polynomials designed for matching a series of points and function derivatives at the prescribed nodes. In the literature, the linearizations of matrix polynomials of degree $s$, expressed in Hermite basis, consist of matrix pencils with $s+2$ blocks of size $n \times n$. In other words, additional eigenvalues at infinity had to be introduced, see e.g. \cite{CSAG}. In this research, we try to overcome this difficulty by reducing the size of linearization. The reduction scheme presented will gradually reduce the linearization to its minimal size making use of ideas from \cite{VMM1}. More precisely, for $n \times n$ matrix polynomials of degree $s$, we present linearizations of smaller size, consisting of $s+1$ and $s$ blocks of $n \times n$ matrices. The structure of the eigenvectors is also discussed.

scholarly journals Utilization of Bandpass Filtering for the Matrix Pencil Method

1993 ◽  
Vol 41 (1) ◽  
pp. 442 ◽  
Author(s):  
Fengduo Hu ◽  
T.K. Sarkar ◽  
Yingbo Hua
Keyword(s):  
Matrix Pencil ◽  
Matrix Pencil Method ◽  
The Matrix
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