### Abstract

We examine the problem of estimating the periods of interleaved periodic point processes. We are particularly interested in the case where times of arrival (TOAs) are either measured with noise or not measured at all. This can arise in communications surveillance, where communications signals of different bauds may lie within the same surveillance bandwidth, and likewise in Electronic Surveillance (ES), where pulses or scans from different radars are observed together. In [1], the authors developed a general asymptotic theory for the Bartlett point-process periodogram estimator of the period of a single periodic process. In this paper, we extend the model to multiple periodic processes, each with a distinct period. The TOAs are observed unlabelled and in time order, i.e., they are interleaved. The largest local maximizers of the periodogram are shown to be good estimators of the unknown periods, asymptotically, and central limit theorems are proved. Simulations highlight a number of practical problems, and some problems with outstanding solutions are suggested.

Language | English |
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Title of host publication | 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 |

Place of Publication | Piscataway, NJ |

Publisher | Institute of Electrical and Electronics Engineers (IEEE) |

Pages | 232-235 |

Number of pages | 4 |

ISBN (Print) | 9781479949755 |

DOIs | |

Publication status | Published - 2014 |

Event | 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 - Gold Coast, QLD, Australia Duration: 29 Jun 2014 → 2 Jul 2014 |

### Other

Other | 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 |
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Country | Australia |

City | Gold Coast, QLD |

Period | 29/06/14 → 2/07/14 |

### Fingerprint

### Cite this

*2014 IEEE Workshop on Statistical Signal Processing, SSP 2014*(pp. 232-235). [6884618] Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/SSP.2014.6884618

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*2014 IEEE Workshop on Statistical Signal Processing, SSP 2014.*, 6884618, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 232-235, 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014, Gold Coast, QLD, Australia, 29/06/14. https://doi.org/10.1109/SSP.2014.6884618

**On the periodogram estimators of periods from interleaved sparse, noisy timing data.** / Quinn, Barry G.; Clarkson, I. Vaughan L; McKilliam, Robby.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › Research › peer-review

TY - GEN

T1 - On the periodogram estimators of periods from interleaved sparse, noisy timing data

AU - Quinn, Barry G.

AU - Clarkson, I. Vaughan L

AU - McKilliam, Robby

PY - 2014

Y1 - 2014

N2 - We examine the problem of estimating the periods of interleaved periodic point processes. We are particularly interested in the case where times of arrival (TOAs) are either measured with noise or not measured at all. This can arise in communications surveillance, where communications signals of different bauds may lie within the same surveillance bandwidth, and likewise in Electronic Surveillance (ES), where pulses or scans from different radars are observed together. In [1], the authors developed a general asymptotic theory for the Bartlett point-process periodogram estimator of the period of a single periodic process. In this paper, we extend the model to multiple periodic processes, each with a distinct period. The TOAs are observed unlabelled and in time order, i.e., they are interleaved. The largest local maximizers of the periodogram are shown to be good estimators of the unknown periods, asymptotically, and central limit theorems are proved. Simulations highlight a number of practical problems, and some problems with outstanding solutions are suggested.

AB - We examine the problem of estimating the periods of interleaved periodic point processes. We are particularly interested in the case where times of arrival (TOAs) are either measured with noise or not measured at all. This can arise in communications surveillance, where communications signals of different bauds may lie within the same surveillance bandwidth, and likewise in Electronic Surveillance (ES), where pulses or scans from different radars are observed together. In [1], the authors developed a general asymptotic theory for the Bartlett point-process periodogram estimator of the period of a single periodic process. In this paper, we extend the model to multiple periodic processes, each with a distinct period. The TOAs are observed unlabelled and in time order, i.e., they are interleaved. The largest local maximizers of the periodogram are shown to be good estimators of the unknown periods, asymptotically, and central limit theorems are proved. Simulations highlight a number of practical problems, and some problems with outstanding solutions are suggested.

UR - http://www.scopus.com/inward/record.url?scp=84907392833&partnerID=8YFLogxK

U2 - 10.1109/SSP.2014.6884618

DO - 10.1109/SSP.2014.6884618

M3 - Conference proceeding contribution

SN - 9781479949755

SP - 232

EP - 235

BT - 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

ER -