Part III: Time & Space Problems in Sensor Networks Mani Srivastava

1. Part III: Time & Space Problems in Sensor NetworksMani Srivastava

2. Time and Space Problems • Timing synchronization • Node Localization • Sensor Coverage

3. Time Synchronization • Time sync is critical at many layers in sensor nets • Beam-forming, localization, tracking, distributed DSP Ref: based on slides by J. Elson

4. Time Synchronization • Time sync is critical at many layers in sensor nets • Beam-forming, localization, tracking, distributed DSP • Data aggregation & caching t=1 t=0 t=2 t=3 Ref: based on slides by J. Elson

5. Conventional Approaches • GPS at every node • E.g. some GPSs provide 1 pps @ O(10ns) accuracy • But • doesn’t work everywhere • cost, size, and energy issues • NTP • some well known “primary time servers” are synchronized via GPS, atomic clock etc. • pre-defined server hierarchy (stratums) • nodes synchronize with one of a pre-specified list of time servers • Problems: • potentially long and varying paths to time-servers due to multi-hopping and short-lived links • delay and jitter due to MAC and store-and-forward relaying • discovery of time servers • Perfectly acceptable for most cases • E.g. Internet (coarse grain synchronization) • Inefficient when fine-grain sync is required • e.g. sensor net applications: localization, beamforming, TDMA etc

6. Limitations of What Exists • Existing work is a critical building block BUT… • Energy • e.g., we can’t always be listening or using CPU! • Wide range of requirements within a single app; no method optimal on all axes • Cost and form factor: can disposable motes have GPS receivers, expensive oscillators? Completely changes the economics… • Needs to be fully decentralized, infrastructure-free Ref: based on slides by J. Elson

7. Sources of time synchronization error • Send time • Kernel processing • Context switches • Transfer from host to NIC • Access time • Specific to MAC protocol • E.g. in Ethernet, sender must wait for clear channel • Propagation time • Dominant factor in WANs • Router-induced delays • Very small in LANs • Receive time • Common denominator: non-determinism

8. About Computer Clocks • Clocks in computers • Clock Skew  • Due to the clock drift, the local clock need to be periodically synchronized to maintain an accurate global time

9. [Romer2000] Scheme for Ad Hoc Networks • Don’t try to synchronize local clocks all the time • Generate time stamps to record the events’ occurring time • The time stamps are updated along its way by each node using its own local clock • As the result of clock shift and message propagation delay, the final time stamp is expressed as a lower and upper bound

10. Example 1 2 3 N • When 1 senses an event, it starts counting time with its clock. • 1 sends 2 a message regarding the event, and a time stamp including how long the time has elapsed since the event • 2 estimates the transmission delay to the time stamp and continues counting the time • Messages are forwarded the same fashion as 12 to node N • N is able to recover the time by looking at the time stamp 1 2 3 N

11. Analysis • Assumptions • Maximum clock skew is known • The link can survive long enough so that a synchronization message can be sent after the application message • Time transformation • Recall • Real time estimation based on clock 1 • Time difference in local clock 2

12. Message Delay t4 t5 t6 M1 ACK1 M2 ACK2 t3 t1 t2 • Estimate delay for M2 • Sender: • Receiver: • A transmission of M2 is necessary for receiver to obtain an estimation of delay! Dummy message might need to be sent • It is desirable to make the interval between M1 and M2 short Receiver Sender

13. Add Them Together ! 1 2 3 N idle1 idle2 • Node N puts together the time counted by all the nodes and message delays • Notation • idle=t2-t1 • rtt=t3-t2 rtt1 rtt2 r1 r2 r3 rN s1 sN s2 s3 3 N 1 2

14. This Leads To … • Inaccuracy is proportional to time stamp length • Time stamp length increases linearly with • the age of time stamp • the number of hops S1 S2

15. Results • Simulation • Number of hops <= 5 • Age of time stamp <= 500 s • Length of time stamp <= 3 ms • Able to distinguish two events with time separation >= 6 ms • Improvements • Store and forward the history of time stamp. • Look for common node in history when two time stamps overlap • When events have overlapping time stamps • Use statistical tools to analyze the probability that one event happens before another

16. New Sync Method: Reference Broadcast [Elson2001] • Reference-broadcast synchronization: Very high precision sync with slow radios • Beacons are transmitted, using physical-layer broadcast, to a set of receivers • Time sync is based on the difference between reception times; don’t sync sender w/ receiver! • Post-facto synchronization: Don’t waste energy on sync when it is not needed • Timestamp events using free-running clocks • After the fact, reconcile clocks • Peer-to-peer sync: no master clock • Tiered Architectures: Range of node capabilities Ref: based on slides by J. Elson

17. Traditional Sync Problem: Many sources of unknown, nondeterministic latency between timestamp and its reception Sender Receiver Send time Receive Time At the tone: t=1 NIC NIC Access Time Propagation Time Physical Media Ref: based on slides by J. Elson

18. Reference Broadcast Sync Sync 2 receivers with each other, NOT sender with receiver Sender Receiver Receiver Receive Time NIC NIC NIC I saw it at t=4 I saw it at t=5 Propagation Time Physical Media Ref: based on slides by J. Elson

19. RBS reduces error by removing much of it from the critical path NIC NIC Sender Sender Receiver Receiver 1 Critical Path Receiver 2 Time Critical Path Traditional critical path: From the time the sender reads its clock, to when the receiver reads its clock RBS: Only sensitive to the differences in receive time and propagation delay Ref: based on slides by J. Elson

20. Observations about RBS • RBS removes send and accesstime errors • Broadcast is used as a relative time reference • Each receiver synchronizing to a reference packet • Ref. packet was injected into the channel at the same instant for all receivers • Message doesn’t contain timestamp • Almost any broadcast packet can be used, e.g ARP, RTS/CTS, route discovery packets, etc Ref: based on slides by J. Elson

21. Phase Offset Estimation • Simplest case: single pulse, two receivers • Xmitter broadcasts reference packet • Each receiver records the time that beacon was received according to its local clock • Receivers exchange observations • Sufficient information to form a local (relative) timescale • However, global timescales are also important • Extending simple case to many receivers • Assumptions • Propagation delay is zero • No clock skew • Receiver non-determinism (error) is Gaussian • Sending more messages increases precision • Transmitter broadcasts m packets • Each receiver records time the beacon was observed • Receivers exchange observations • Receiver i computes phase offset to receiver j as the average of the offsets implied by each pulse received by both nodes • Result:

22. Receiver Determinism Testbed: Berkeley motes with narrowband (19.2K) radios Ref: based on slides by J. Elson

23. Gaussian = Good! • Well behaved distributions are useful • Error can be reduced statistically, by sending multiple pulses over time and averaging • Also, easier to model/simulate • Problem: Clock skew • It takes time to send multiple pulses • By the time we do, clocks will have drifted • Oscillator characteristics • Accuracy: difference between expected and actual frequency • Difference: Frequency error (usually 10-4 – 10-6) • Stability: tendency to stay at same frequency over time • Phase difference between two nodes’ clocks will change due to frequency differences • Solution: don’t average; fit a line instead! • Frequency and phase of local node’s clock recovered from slope and intercept of the line • Fitting a line assumes that frequency is stable • Assume high short-term frequency stability • Ignore data more than a few minutes old Ref: based on slides by J. Elson

24. Clock Skew Estimation Results • 2 receivers (motes): r1, r2 • Point (0,0) marks the first pulse • Receivers synchronized, no clock skew • Clock skew increases as time increases • Linear fit gives good results • With clock skew estimation, sufficient information exists to convert any time value generated by r1’s clock to a time value that would have been generated by r2’s clock Time Ref: based on slides by J. Elson

25. RBS: Phase offset estimation Numerical analysis results • Numerical analysis for m=1..50, n=2..20 • 1000 trials for each m, n • Results: mean dispersion, std.dev • 2-receiver case • 30 broadcasts improve precision from 11 usec to 1.6 usec • 20-receiver case • Dispersion reduced down to 5.6 usec

26. RBS Sync Advantages • 11usec precision over 19.2K radios: wow! • local or relative time: “peer to peer sync” • allows seamless exchange of messages about the local area; no error due to the master sync server being far away • (NTP allows sync without an external ref., but some node still needs to be defined as “time”) • Graceful handling of lost packets, outliers Ref: based on slides by J. Elson

27. Comparison to NTP • Second implementation: • Compaq IPAQs (small Linux machines) • 11mbit 802.11 PCMCIA cards • Ran NTP, RBS-Userspace, RBS-Kernel • NTP synced to GPS clock every 16 secs • NTP with phase correction, too; it did worse (!) • In each case, asked 2 IPAQs to raise a GPIO line high at the same time; differences measured with logic analyzer Ref: based on slides by J. Elson

28. Clock Resolution Ref: based on slides by J. Elson

29. Clock Resolution RBS degraded slightly (6us to 8us); NTP degraded severely (51us to 1542us) Ref: based on slides by J. Elson

30. Multihop RBS • Some nodes broadcast RF synchronization pulses • Receivers in a neighborhood are synced by using the pulse as a time reference. (The pulse senders are not synced.) • Nodes that hear both can relate the time bases to each other “Blue pulse 2 secafter red pulse!” “Here 3 sec after blue pulse!” “Here 1 sec after red pulse!” “Here 1 sec afterblue pulse!” “Here 0 sec after red pulse!” Ref: based on slides by J. Elson

31. Time Routing 1 2 5 6 3 4 7 8 9 10 11 The physical topology can be easily converted to a logical topology; links represent possible clock conversions 1 2 5 A B 6 3 4 7 C 8 9 D 10 11 Use shortest path search to find a “time route”; Edges can be weighted by error estimates Ref: based on slides by J. Elson

32. External Standards (UTC) 1 2 5 6 3 4 7 8 9 10 11 The multihop algorithm can also be easily used to sync an RBS domain to an external standard such as UTC 1 2 5 A B 6 3 4 7 C 8 9 GPS D GPS 10 11 GPS’s PPS generates a series of “fake broadcasts”: “received” by node 11’s local clock and UTC Ref: based on slides by J. Elson

33. Post-facto Sync (well, pre) Sync pulses Drift Estimate Test pulses 7usec error after 60 seconds of silence Ref: based on slides by J. Elson

34. RBS Summary • RBS can improve accuracy by removing sender from the critical path • RBS outperforms NTP • 8 times better for light load • Remarkable performance on heavy load • Multi-hop algorithm can extend RBS property across broadcast domains, and to external standards such as UTC • Facilitates tiered architectures (some nodes have GPS, some don’t) • Facilitates post-facto sync (save energy by only syncing after an event of interest) • Cannot be applied to the Internet at large • Only works with broadcast medium, not point-to-point links Ref: based on slides by J. Elson

35. References on Timing Synchronization • Kay Romer Time Synchronization in Ad Hoc Networks • Jeremy Elson et al. Fine-Grained Network Time Synchronization Using Reference Broadcasts • http://www.gpsclock.com/gps.html

36. Localization • Localization of sensor nodes has many uses • Beamforming for localization of targets and events • Geographical forwarding • Geographical addressing • Why not just GPS at every node? • Large size • High power consumption • Works only when LOS to satellites • Over kill – often only relative position is needed • Works only on earth (e.g. sensor nets on other planets)

37. What is Location? • Absolute position on geoid • e.g. GPS • Location relative to fixed beacons • e.g. LORAN • Location relative to a starting point • e.g. inertial platforms • Most applications: • location relative to other people or objects, whether moving or stationary, or the location within a building or an area • Range and resolution of the position location needs to be proportionate to the scale of the objects being located

38. Self-positioning vs. Remote-Positioning • Self-positioning • Mobile node formulates its own position • e.g. by sensing signals received at the mobile from the transmitters in the infrastructure • Remote-positioning • Position of mobile node calculated at a remote location • e.g. by using signals received from the mobile by sensors in the infrastructure • Indirect positioning • Using a data link it is possible to send position measurements from a self-positioning receiver to a remote site, or vice versa • A self-positioning system that sends data to a remote location is called indirect remote-positioning • A remote-positioning system transmitting an object’s position to the object is called indirect self-positioning

39. Techniques for Location Sensing • Measure proximity to “landmarks” • e.g. near a basestation in a room • example systems: • Olivetti’s Active Badge for indoor localization • infrared basestations in every room • localizes to a room as room walls act as barriers • Most commercial RF ID Tag systems • strategically located tag readers • improved localization if near more than one landmark • Estrin’s system for outdoor sensor networks • grid of outdoor beaconing nodes with know position • position = centroid of nodes that can be heard • # of periodic beacon packets received in a time interval exceeds a theshold • a problem: not really location sensing • it really is proximity sensing • accuracy of location is a function of the density of landmarks • Location accuracy = O(distance between landmarks)

40. Techniques for Location Sensing (contd.) • Dead reckoning: position relative to an initialization point • work as supplement to a primary location sensing techniques • resynchronize when the primary location sensing technique works, and takes over if the primary fails • e.g. supplement GPS during signal outages • Use wheel and steering information in vehicles • Integrating accelerometers mounted on gyroscopically stabilized platforms • Point Research’s Pointman Dead Reckoning Module • inertial measurement unit for personnel on foot • Latitude and longitude relative to the start point • magnetic compass + MEMS-based electronic pedometer + barometric altimeter + DSP • position error of 2-5% of total distance traveled since last resynchronization • no drift with time • U. S. Patent No. 5,583,776. • www.pointresearch.com

41. Pointman Dead Reckoning Module Size: 1.9" x 2.9" x 0.6“ Weight: 1.5 oz. Power: 0.5 Watts @ 3.3 V (250 mW in new low-power DRM)

42. Trackman Personnel Locator • Combines a DRM with a GPS and a radio transmitter to provide continuous location tracking • Kalman filter is used to combine the dead reckoning data with GPS data when it is available • Specifications: • Size: 3.2" x 7.5" x 2.3" • Weight: 12 oz. • Range: 0.25 miles

43. Techniques for Location Sensing (contd.) BS 2 BS 1 MS 3 BS • Measure direction of landmarks • Simple geometric relationships can be used to determine the location by finding the intersections of the lines-of-position • e.g. Radiolocation based on angle of arrival (AoA) measurements of beacon nodes (e.g. basestations) • can be done using directive antennas or antenna arrays • need at least two measurements

44. Techniques for Location Sensing (contd.) • Measure distance to landmarks, or Ranging • e.g. Radiolocation using signal-strength or time-of-flight • also done with optical and acoustic signals • Distance via received signal strength • use a mathematical model that describes the path loss attenuation with distance • each measurement gives a circle on which the MS must lie • use pre-measured signal strength contours around fixed basestation (beacon) nodes • can combat shadowing • location obtained by overlaying contours for each BS • Distance via Time-of-arrival (ToA) • distance measured by the propagation time • distance = time * c • each measurement gives a circle on which the MS must lie • active vs. passive • active: receiver sends a signal that is bounced back so that the receiver know the round-trip time • passive: receiver and transmitter are separate • time of signal transmission needs to be known • N+1 BSs give N+1 distance measurements to locate in N dimensions

45. Radiolocation via ToA and RSSI x2 d2 BS BS x1 MS d1 d3 BS x3

46. Location in 3D

47. Location in 3D

48. Location in 3D

49. Techniques for Location Sensing (contd.) • Measure difference in distances to two landmarks • Time-difference-of-arrival (TDoA) • Time of signal transmission need not be known • Each TDoA measurement defines line-of-position as a hyperbola • hyperbola is a curve of constant difference in distance from two fixed points (foci) • Location of MS is at the intersection of the hyperbolas • N+1 BSs give N TDoA measurements to locate in N dimensions

50. Algorithms for Location • Depends on whether ToA (RSSI is similar) or TDoA is used • Straightforward approach: geometric interpretation • Intersection of circles for ToA • Intersection of hyperbolas for TDoA • But what if the circles or hyperbolas do not intersect at a point due to measurement errors?