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Optimal Clock Synchronization in Networks

Optimal Clock Synchronization in Networks. Christoph Lenzen Philipp Sommer Roger Wattenhofer. Time in Sensor Networks. Synchronized clocks are essential for many applications:. Localization. Sensing. Duty-Cycling. TDMA. Time Synchronization (RBS, TPSN, FTSP, ...). rate. 1+ ². 1.

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Optimal Clock Synchronization in Networks

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  1. Optimal Clock Synchronization in Networks Christoph Lenzen Philipp Sommer Roger Wattenhofer

  2. Philipp Sommer, ETH Zurich @ SenSys‘09 Time in Sensor Networks • Synchronized clocks are essential for many applications: Localization Sensing Duty-Cycling TDMA Time Synchronization(RBS, TPSN, FTSP, ...)

  3. Philipp Sommer, ETH Zurich @ SenSys‘09 rate 1+² 1 1-² t Hardware Clocks Experience Drift • Hardware clock • Counter register of the microcontroller • Sourced by an external crystal (32kHz, 7.37 MHz) • Clock drift • Random deviation from the nominal rate dependent on ambient temperature, power supply, etc. (30-100 ppm) Mica2

  4. Philipp Sommer, ETH Zurich @ SenSys‘09 Messages Experience Jitter in the Delay • Problem: Jitter in the message delay • Various sources of errors (deterministic and non-deterministic) • Solution: Timestamping packets at the MAC layer (Maróti et al.) • → Jitter in the message delay is reduced to a few clock ticks 1-10 ms 0-100 ms 0-500 ms timestamp Send Access Transmission timestamp Reception Receive 0-100 ms t frequency (%) time Expected delay T Jitter J

  5. Philipp Sommer, ETH Zurich @ SenSys‘09 Summary: Clock Synchronization • Goal: • Send time information (beacons) to synchronize clocks • Problems: • Hardware clocks exhibit drift • Jitter in the message delay Expected delay T Jitter J

  6. Philipp Sommer, ETH Zurich @ SenSys‘09 Preview: Experimental Results • Sychnronization error vs. hop distance FTSP PulseSync NEW!

  7. Philipp Sommer, ETH Zurich @ SenSys‘09 Outline • Introduction • Theory • Practice

  8. Philipp Sommer, ETH Zurich @ SenSys‘09 Synchronizing Nodes: Single-Hop • How do we synchronize the clocks of two sensor nodes? reference clock 1 0

  9. Philipp Sommer, ETH Zurich @ SenSys‘09 Synchronizing Nodes • Sending periodic beacons to synchronize nodes Beacon interval B 100 130 reference clock 0 t t=100 t=130 1 t T T J J

  10. Philipp Sommer, ETH Zurich @ SenSys‘09 How accurately can we synchronize two Nodes? • Message delay jitter affects clock synchronization quality y 0 r ^ ^ r y(x) = r·x + ∆y clock offset relative clock rate(estimated) ∆y x J J 1 Beacon interval B

  11. Philipp Sommer, ETH Zurich @ SenSys‘09 How accurately can we synchronize two Nodes? • Message delay jitter affects clock synchronization quality y 0 r ^ ^ ^ r r y(x) = r·x + ∆y relative clock rate(estimated) clock offset x ∆y J J 1 Beacon interval B

  12. Philipp Sommer, ETH Zurich @ SenSys‘09 Clock Skew between two Nodes • Lower Bound on the clock skew between two neighbors y 0 r • Error in the rate estimation: • Jitter in the message delay • Beacon interval • Number of beacons k • Synchronization error: ^ ^ r r x ∆y J J 1 (complete proof is in the paper) Beacon interval B

  13. Philipp Sommer, ETH Zurich @ SenSys‘09 Synchronizing Nodes: Multi-hop • How do we synchronize the clocks of multiple sensor nodes? reference clock 1 2 0

  14. Philipp Sommer, ETH Zurich @ SenSys‘09 Now we have a network of nodes! • How does the network diameter affect synchronization errors? • Examples for sensor networks with high diameter • Bridge, road or pipeline monitoring • Deployment at Golden Gate Bridge with 46 hops(Kim et al., IPSN’07) ... 0 1 2 3 4 d

  15. Philipp Sommer, ETH Zurich @ SenSys‘09 Multi-hop Clock Synchronization • Nodes forward their current estimate of the reference clock • Each synchronization beacon is affected by a random jitter J • Sum of the jitter grows with the square-root of the distance • stddev(J1 + J2 + J3 + J4 + J5 + ... Jd) = √d×stddev(J) ... 0 1 2 3 4 d J1 J2 J3 J4 J5 Jd Multi-hop: Single-hop: (proof is in the paper)

  16. Philipp Sommer, ETH Zurich @ SenSys‘09 Outline • Introduction • Theory • Practice

  17. Philipp Sommer, ETH Zurich @ SenSys‘09 Clock Synchronization in Practice • Flooding Time Synchronization Protocol (FTSP) • Nodes synchronize to a root (leader) node • Leader-election phase (by smallest id) • Periodic synchronization beacons (unaligned) • Linear-regression table to correct clock drift • Maroti et al. (SenSys‘04) 2 3 4 1 0 5 root node 6

  18. Philipp Sommer, ETH Zurich @ SenSys‘09 Testbed Experiments (FTSP) • Measurement results from testbed with 20 Mica2 nodes • Synchronization error grows exponentially • Nodes far away from the root failed to synchronize with their parent node ... 20 4 0 1 3 2

  19. Philipp Sommer, ETH Zurich @ SenSys‘09 Linear Regression (FTSP) • FTSP uses linear regression to compensate for clock drift • Jitter is amplified before it is sent to the next hop y 0 r Example for k=2 synchronization error ^ r y(x) = r·x + ∆y ^ clock offset relative clock rate(estimated) ∆y x J J 1 Beacon interval B

  20. Philipp Sommer, ETH Zurich @ SenSys‘09 Linear Regression (FTSP) • Simulation of FTSP with regression tables of different sizes(k = 2, 8, 32) Log Scale!

  21. Philipp Sommer, ETH Zurich @ SenSys‘09 The PulseSync Protocol • Send fast synchronization pulses through the network • Speed-up the initialization phase • Faster adaptation to changes in temperature or network topology 0 0 Beacon time B Beacon time B 1 1 2 2 FTSP 3 3 4 4 Expected time = D·B/2 t PulseSync Expected time = D·tpulse t tpulse

  22. Philipp Sommer, ETH Zurich @ SenSys‘09 The PulseSync Protocol (2) • Remove self-amplification of synchronization error • Fast flooding cannot completely eliminate amplification y 0 r Example for k=2 synchronization error ^ r y(x) = r·x + ∆y ^ clock offset ^ r relative clock rate ∆y x J J The green line is calculated using kmeasurement points that are statistically independent of the red line (see paper). 1 Beacon interval B

  23. Philipp Sommer, ETH Zurich @ SenSys‘09 Evaluation • Testbed setup • 20 Crossbow Mica2 sensor nodes • PulseSync implemented in TinyOS 2.1 • FTSP from TinyOS 2.1 • Network topology • Single-hop setup, basestation • Virtual network topology (white-list) • Acknowledgments for time sync beacons Probe beacon ... 4 0 1 3 2 20

  24. Philipp Sommer, ETH Zurich @ SenSys‘09 Experimental Results • Global Clock Skew • Maximum synchronization error between any two nodes FTSP PulseSync

  25. Philipp Sommer, ETH Zurich @ SenSys‘09 Experimental Results (2) • Sychnronization Error vs. distance from root node FTSP PulseSync

  26. Philipp Sommer, ETH Zurich @ SenSys‘09 Outlook • Extension to more general network topologies • Schedule synchronization beacons without collisions • Time information has to propagate quickly through the network • Avoid loss of synchronization pulses due to collisions This is known as wireless broadcasting, a well-studied problem (in theory)

  27. Philipp Sommer, ETH Zurich @ SenSys‘09 Conclusions • Theoretical insights into clock synchronization • Lower bound on the global clock skew • PulseSync: a novel clock synchronization algorithm • Flooding sync pulses at high speed through the network • Matches the lower bound on the global skew (shown in the paper) • Testbed experiments on a 20-node line topology • Prototype implementation of PulseSync • PulseSync outperforms FTSP for this setting

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