### Abstract

For many applications, distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time. Most of the widely used clock synchronization algorithms in such systems employ the sender-receiver protocol based on a two-way timing message exchange paradigm. Maximum likelihood estimator (MLE) of the clock offset based on the timing message exchanges between two clocks was derived in D. R. Jeske, On maximum likelihood estimation of clock offset[IEEE Trans. Commun., vol. 53, pp. 53-54, Jan. 2005], when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean. Herein, the best linear unbiased estimate using order statistics (BLUE-OS) of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays, respectively. The Rao-Blackwell-Lehmann- Scheffé theorem is then exploited to obtain the minimum variance unbiased estimate (MVUE) for the clock offset which it is shown to coincide with the BLUE-OS. In addition, it is found that the MVUE of the clock offset in the presence of symmetric network delays also coincides with the MLE. Finally, in the presence of asymmetric network delays, although the MLE is biased, it is shown to achieve lesser mean-square error (MSE) than the MVUE in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified.

Original language | English |
---|---|

Article number | 2046233 |

Pages (from-to) | 2893-2904 |

Number of pages | 12 |

Journal | IEEE Transactions on Information Theory |

Volume | 56 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Clock
- Estimation
- Signal processing
- Synchronization
- Wireless sensor networks

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*56*(6), 2893-2904. [2046233]. https://doi.org/10.1109/TIT.2010.2046233

**On minimum variance unbiased estimation of clock offset in a two-way message exchange mechanism.** / Chaudhari, Qasim M.; Serpedin, Erchin; Qaraqe, Khalid.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 56, no. 6, 2046233, pp. 2893-2904. https://doi.org/10.1109/TIT.2010.2046233

}

TY - JOUR

T1 - On minimum variance unbiased estimation of clock offset in a two-way message exchange mechanism

AU - Chaudhari, Qasim M.

AU - Serpedin, Erchin

AU - Qaraqe, Khalid

PY - 2010/6

Y1 - 2010/6

N2 - For many applications, distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time. Most of the widely used clock synchronization algorithms in such systems employ the sender-receiver protocol based on a two-way timing message exchange paradigm. Maximum likelihood estimator (MLE) of the clock offset based on the timing message exchanges between two clocks was derived in D. R. Jeske, On maximum likelihood estimation of clock offset[IEEE Trans. Commun., vol. 53, pp. 53-54, Jan. 2005], when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean. Herein, the best linear unbiased estimate using order statistics (BLUE-OS) of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays, respectively. The Rao-Blackwell-Lehmann- Scheffé theorem is then exploited to obtain the minimum variance unbiased estimate (MVUE) for the clock offset which it is shown to coincide with the BLUE-OS. In addition, it is found that the MVUE of the clock offset in the presence of symmetric network delays also coincides with the MLE. Finally, in the presence of asymmetric network delays, although the MLE is biased, it is shown to achieve lesser mean-square error (MSE) than the MVUE in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified.

AB - For many applications, distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time. Most of the widely used clock synchronization algorithms in such systems employ the sender-receiver protocol based on a two-way timing message exchange paradigm. Maximum likelihood estimator (MLE) of the clock offset based on the timing message exchanges between two clocks was derived in D. R. Jeske, On maximum likelihood estimation of clock offset[IEEE Trans. Commun., vol. 53, pp. 53-54, Jan. 2005], when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean. Herein, the best linear unbiased estimate using order statistics (BLUE-OS) of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays, respectively. The Rao-Blackwell-Lehmann- Scheffé theorem is then exploited to obtain the minimum variance unbiased estimate (MVUE) for the clock offset which it is shown to coincide with the BLUE-OS. In addition, it is found that the MVUE of the clock offset in the presence of symmetric network delays also coincides with the MLE. Finally, in the presence of asymmetric network delays, although the MLE is biased, it is shown to achieve lesser mean-square error (MSE) than the MVUE in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified.

KW - Clock

KW - Estimation

KW - Signal processing

KW - Synchronization

KW - Wireless sensor networks

UR - http://www.scopus.com/inward/record.url?scp=77957587744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957587744&partnerID=8YFLogxK

U2 - 10.1109/TIT.2010.2046233

DO - 10.1109/TIT.2010.2046233

M3 - Article

VL - 56

SP - 2893

EP - 2904

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 6

M1 - 2046233

ER -