## 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.

Original 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 |