Time-Synchronization in Mobile Sensor Networks from Difference - - PowerPoint PPT Presentation

Chenda Liao and Prabir Barooh

Time-Synchronization in Mobile Sensor Networks from Difference Measurements

Distributed Control System Lab

• Dept. of Mechanical and Aerospace Eng.

University of Florida, Gainesville, FL

49th IEEE Conference on Decision and Control Dec, 15th, 2010 Atlanta, Georgia, USA

Sensor Networks

• Environment/Structure

Monitoring

• Event/Fault Detection
• Home/office Automation
• Healthcare
• Industrial Automation
• Military Application

Limited power

=global/reference time =local time =skew =offset

Time Synchronization in Sensor Network

Time synchronization problem is equivalent to determining and ,

Motivation: Meaning of Sync. : Global time u ref v Local time:

Literature review

 Static sensor network

• Elson et al., Fine-grained network time synchronization using reference broadcasts

(RBS), 2002

• Ganeriwal et al., Timing-Sync Protocol for Sensor Network (TPSN), 2003
• Barooah et al., Distributed optimal estimation from relative measurements for

localization and time synchronization, 2006

• Suyong Yoon et al., Tiny-Sync: Tight Time Synchronization for Wireless Sensor

Networks, 2007

 Mobile sensor network

• Miklós et al., Flooding Time Synchronization Protocol (FTSP), 2004
• Su et.al., Time-Diffusion Synchronization Protocol for Wireless Sensor Networks

(TDP), 2005

Noisy measurement of the relative skews and offsets for pairs of nodes

Time Sync on Mobile Sensor Network

Goal:

To estimate the skews and offsets of clocks of all the nodes with respect to an reference clock in mobile sensor network.

Algorithm: 

• Model the time variation of the network (graph) as a Markov chain.
• Prove the mean square convergence of the estimation error (Markov jump linear

system).

• Corroborate the predictions using Monte Carlo simulations.

Pair-wise synchronization: Network-wise synchronization: Each node estimates its offset/skew from noisy measurements by communicating

• nly with its neighbors iteratively.

Measurement Algorithm

• Directly measure and ? No!
• But node u can measure and .
• Method: pairs of nodes exchange time-stamped packet with two rounds communication.

u v

Measurement Algorithm Noisy measurement Time-stamp Gaussian zero mean

Details in [Technical Report] Liao et al. Time Synchronization in Mobile Sensor Networks from Relative Measurements

Relative Measurement

Errors Node variables Noisy measurements Same formulation for relative skew and offset measurement Where Relative measurement Reference variable =0 Task: Estimate all of the unknown nodes variables from the measurements and the reference variables.

Distributed Algorithm for Estimation

 Algorithm:  Remark:

Where is the estimate of node variable at time k is the neighbor set of node u at time k is the number of neighbors in

• , if for all u by using flagged initialization.
• If node u has no neighbor, then .

 Example:

4 3 6 Similar to an algorithm in time sync of static sensor network. (e.g., Barooah et.al., 06)

• If evolution of satisfies Markovian property
• can be modeled as the realization of a Markov chain.
• Example

Performance Analysis

• Consider the graphs with 25 nodes, the number of different graphs is

State space and An edge exists if Euclidean distance between pair of nodes is less than certain value.

Position Projection function Random vector

• and are governed by Markov chain,
• is W.S.S, and
• and

Convergence Analysis

Theorem: mean square convergent

• is entry-wise positive
• At least one element of is a

connected graph Conjecture:

• Markov chain is ergodic
• The union of all the graphs

in is a connected graph Discrete-time Markov Jump Linear system modeling calculable mean square convergent

Proof in [Technical Report] Liao et al. Time Synchronization in Mobile Sensor Networks from Relative Measurements

Simulation (4 nodes)

4 snapshots Mean of estimates of variables of node 3 Variance of estimates of variables of node 3 Number of edges of node 3 along time Sample trajectory of estimates of node 3

Simulation (25 nodes)

4 snapshots Mean of estimates of variables of node 25 Variance of estimates of variables of node 25 Number of edges of node 25 along time Sample trajectory of estimates of node 25

Simulation for Conjecture

All three possible graphs Mean of estimates of variables of node 3 Variance of estimates of variables of node 3 Number of edges of node 3 along time Sample trajectory of estimates of node 3

Summary and Future Work

• A distributed time-synchronization protocol for mobile sensor networks.
• Mean square convergent under certain conditions.

 Summary:

• Weaker sufficient conditions for mean square convergence
• Convergence rate in terms of the Markov chain's properties.

 Future work:

Thank you!

This work has been supported by the National Science Foundation by Grants CNS-0931885 and ECCS-0955023.

Back up

Start from here

Algorithm for Measuring Offset

• Suppose , then
• Goal: Measure relative clock offset
• Method: Exchange time-stamped packet with a round trip.
• Let denote the measurement node u can obtain and

denote measurement error with mean 0 and variance Where and are Gaussian i.i.d. random delay with mean and variance

• Finally, we obtain noisy measurement of relative clock offset (4)

Algorithm for Measuring Skew and Offset

• Now, consider
• Goal: Estimate both relative clock offset and skew
• Method: Exchange time-stamped packet with two round trips.

Estimating Relative Skew

• From (6), (7), (8) and (9), we obtain

(10) Finally, after taking log on both side, (10) can be simplified as (11) Here, and where We make reasonably large by extending and shortening . Then, implement Taylor series, we get . Therefore, it is not hard to

• btain and .

Estimating Relative Offset

• Reusing first four time stamp equations, we obtain

(12) Again, let and . Express (12) as Distributed Algorithm ① ②

Sphere Graph

Position evolution: The projection function:

Formula of Steady State Value

Let be the state space of real matrices. Let be the set of all N-sequences of real matrices The operator and is defined as follows: Let then , where and For , then and Then, let Define and