### Abstract

A fully distributed algorithm for estimating the center and the radius of the smallest sphere that contains a wireless sensor network is proposed. The center finding problem is formulated as a convex optimization problem in summation form by using a soft-max approximation to the maximum function. Diffusion adaptation method is used where states of nodes converge to the estimated center distributively. Then, distributed max consensus is used to compute the radius. The proposed algorithm is fully distributed in the sense that each node in the network only needs to know its own location, and nodes do not need to be pre-labeled. The algorithm works for any connected graph structure. The performance of the proposed algorithm is analyzed and it is shown that there is a trade-off: a larger design parameter results in a more accurate center estimation but also makes the convergence speed of the distributed algorithm slower. It is also shown that the proposed algorithm can also be used to estimate the center and radius of the (not necessarily location-based) data at sensor nodes in a distributed way, thereby providing information and insights about the global data at each sensor. Simulation results corroborating the theory are also provided.

Original language | English (US) |
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Journal | IEEE Sensors Journal |

DOIs | |

State | Accepted/In press - May 22 2018 |

### Fingerprint

### Keywords

- Convex functions
- Distributed
- Estimation
- Linear programming
- Mathematical model
- Max Consensus
- Network Center
- Network Radius
- Optimization
- Sensors
- Soft-max
- Wireless sensor networks
- Wireless Sensor Networks

### ASJC Scopus subject areas

- Instrumentation
- Electrical and Electronic Engineering

### Cite this

**Distributed Network Center and Size Estimation.** / Zhang, Sai; Tepedelenlioglu, Cihan; Spanias, Andreas.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Distributed Network Center and Size Estimation

AU - Zhang, Sai

AU - Tepedelenlioglu, Cihan

AU - Spanias, Andreas

PY - 2018/5/22

Y1 - 2018/5/22

N2 - A fully distributed algorithm for estimating the center and the radius of the smallest sphere that contains a wireless sensor network is proposed. The center finding problem is formulated as a convex optimization problem in summation form by using a soft-max approximation to the maximum function. Diffusion adaptation method is used where states of nodes converge to the estimated center distributively. Then, distributed max consensus is used to compute the radius. The proposed algorithm is fully distributed in the sense that each node in the network only needs to know its own location, and nodes do not need to be pre-labeled. The algorithm works for any connected graph structure. The performance of the proposed algorithm is analyzed and it is shown that there is a trade-off: a larger design parameter results in a more accurate center estimation but also makes the convergence speed of the distributed algorithm slower. It is also shown that the proposed algorithm can also be used to estimate the center and radius of the (not necessarily location-based) data at sensor nodes in a distributed way, thereby providing information and insights about the global data at each sensor. Simulation results corroborating the theory are also provided.

AB - A fully distributed algorithm for estimating the center and the radius of the smallest sphere that contains a wireless sensor network is proposed. The center finding problem is formulated as a convex optimization problem in summation form by using a soft-max approximation to the maximum function. Diffusion adaptation method is used where states of nodes converge to the estimated center distributively. Then, distributed max consensus is used to compute the radius. The proposed algorithm is fully distributed in the sense that each node in the network only needs to know its own location, and nodes do not need to be pre-labeled. The algorithm works for any connected graph structure. The performance of the proposed algorithm is analyzed and it is shown that there is a trade-off: a larger design parameter results in a more accurate center estimation but also makes the convergence speed of the distributed algorithm slower. It is also shown that the proposed algorithm can also be used to estimate the center and radius of the (not necessarily location-based) data at sensor nodes in a distributed way, thereby providing information and insights about the global data at each sensor. Simulation results corroborating the theory are also provided.

KW - Convex functions

KW - Distributed

KW - Estimation

KW - Linear programming

KW - Mathematical model

KW - Max Consensus

KW - Network Center

KW - Network Radius

KW - Optimization

KW - Sensors

KW - Soft-max

KW - Wireless sensor networks

KW - Wireless Sensor Networks

UR - http://www.scopus.com/inward/record.url?scp=85047611110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047611110&partnerID=8YFLogxK

U2 - 10.1109/JSEN.2018.2840048

DO - 10.1109/JSEN.2018.2840048

M3 - Article

JO - IEEE Sensors Journal

JF - IEEE Sensors Journal

SN - 1530-437X

ER -