### Abstract

The paper considers one of the modern parametric methods of signal processing - the matrix pencil method (MPM). The method makes it possible to effectively estimate signal parameters from its samples which is the sum of complex exponentials. The number of exponentials is not assumed to be known in advance and can also be estimated using a singular value decomposition of a matrix constructed from the signal samples. The object of this work is a vector process - a set of signals having the same frequencies and damping factors (i.e., the same poles of the signal), but different complex amplitudes. Such signals occur, for example, when considering a phased array antenna, when it is necessary to evaluate the parameters of a signal generated by the same sources but coming from many antenna elements with their amplitudes and phases. A similar problem arises in the evaluation of signals parameters from two spatially-distributed motion sensors of a Coriolis flowmeter. When processing several signals with classical MPM, we obtain several different sets of poles of these signals, which then, for example, need to be averaged to obtain the desired values of the poles assumed to be the same for all signals. The proposed modification of the MPM works with the entire set of signals at once, giving one set of signal poles, and at the same time it proves to be more effective both in terms of speed and in the accuracy of determining the signal parameters. The algorithms of the classical MPM and its modifications for the vector process are presented, as well as numerical experiments with model and real signals taken from one of the commercially available Coriolis flowmeters Dul5. Experiments show that the proposed algorithm yields more accurate results in a shorter (approximately 1,5 times) time than the classical MPM.

Original language | English |
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Pages (from-to) | 92-104 |

Number of pages | 13 |

Journal | Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software |

Volume | 10 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Nov 2017 |

Externally published | Yes |

### Keywords

- Matrix pencil method
- Parametric methods of signal processing
- Singular value decomposition
- Sum of complex exponentials
- Vector processes

### ASJC Scopus subject areas

- Software
- Modelling and Simulation
- Computational Mathematics
- Computational Theory and Mathematics

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## Cite this

*Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software*,

*10*(4), 92-104. https://doi.org/10.14529/mmp170409