1. Wireless Links & Localization Wireless Sensor Networks and Laboratories Link Characteristics Localization Ranging Techniques

2. Ideal Wave Propagation Simplest model: Wavefront propagation from an isotropic source in free space P r = P t A / (4∏r 2 ) –Signal intensity drops as second power of distance. r Isotropic source Dipole antenna z xy

3. Propagation Characteristics Path Loss Shadowing (due to obstructions) Multipath Fading P r /P t d=vt PrPr PtPt v

4. Hardware technology: Frequency, antenna type, TX power level, amplifier, RX sensitivity, modulation, encoding Application issues: MAC, packet size, retransmission schemes, traffic pattern Environmental conditions: Environment (e.g. forest, office), type of materials (e.g. walls, trees), deployment conditions (e.g. with or w/o line of sight), weather (e.g. temperature, humidity) Link Characteristics Depends on …

5. CC1000 Radio Propagation *Zhou et. al. 04, Polastre et al, 04 Real Wave Propagation Zigbee Radio Propagation

6. *Zhou et. al. 04 1. Direction Continuous variation –Path loss varies –Reflection, diffraction and scattering in environment –Antenna gain –Hardware issues

7. Connectivity is not a simple disk! Low transmit powerHigh transmit power

8. 2. Distance Woo et al, 2003 Many neighbors are likely to be in this wide, high- variance, transitional region. Also called “grey area”

9. Packet Loss Rate vs Distance Grey Area with high variance

10. 3. Time

11. Time  Energy Level Different nodes have different signal sending powers due to: –Different battery status –Different hardware calibration (a) One mote with different battery status (b) Different motes with the same battery status

12. 4. Asymmetric Links Kotz et al

13. Asymmetric Links no Good? A thinks B is a neighbor and sends packet to B but never gets an ACK! Existence of asymmetries requires careful identification of “good neighbors”

14. Why Asymmetric Links? Do the laws of physics allow for the existence of asymmetric links? NO – transmitted signal strength, path loss, shadow fading, and multipath fading are all symmetric effects

15. When swapping the asymmetric links node pairs, the asymmetric links were inverted (91.1% ± 8.32) Link asymmetries are often caused by differences in transmitter/receiver calibration What Causes Asymmetry?

16. Short Summary Real communication channel is not isotropic Variability over distance (50 to 80% of radio range) –Reception rate is not normally distributed around the mean and std. dev. (more later) –The region of highly variable reception rates is 50% or more of the radio range Variability over time (energy) Variability over Tx/Rx calibration (asymmetric links)

17. Localization

18. What is Localization A mechanism for discovering spatial relationships between objects

19. Why is Localization Important? Fundamental for many other services –GPS does not work everywhere –Geographic routing & coverage problems Localization gives raw sensor readings a physical context –Temperature readings  temperature map –Asset tagging  asset tracking –“ Smart spaces ”  context dependent behavior

20. Localization Problem Output: nodes ’ location. –Global location, e.g., what GPS gives. –Relative location. Input: –Connectivity, hop count –Distance measurement of an incoming link. –Angle measurement of an incoming link. –Combinations of the above.

21. Triangulation, Trilateration Anchors advertise their coordinates & transmit a reference signal Other nodes use the reference signal to estimate distances anchor nodes.

22. Optimization Problem Distance measurements are noisy! Solve an optimization problem: minimize the mean square error.

23. Problem Formulation k beacons at positions Assume node 0 has position Distance measurement between node 0 and beacon i is Error: The objective function is This is a non-linear optimization problem

24. Linearization Ideally, we would like the error to be 0 Re-arrange: Subtract the last equation from the previous ones to get rid of quadratic terms. Note that this is linear.

25. Min Mean Square Estimate (MMSE) In general, we have an over-constrained linear system A x = b

26. Solve Least Square Equation The linearized equations in matrix form become Now we can use the least squares equation to compute an estimation.

27. Recursive Least Squares Linearize the measurement equations using Taylor expansion where Neglecting higher-order terms, and choosing an initial “ guess ” X u, solve linear equations for “” that minimizes error

28. The linearized equations in matrix form become Now we can use the least squares equation to compute a correction to our initial estimate Update the current position estimate Repeat the same process until δ comes very close to 0

29. Ranging Techniques

30. Distance Measurements Hop Count 1. Received Signal Strength Indicator (RSSI) 2. Phase Difference 3. Time of Arrival (ToA) 4. Time Difference of Arrival (TDoA) 5. Angle-of-Arrival (AOA)

31. 1. RSSI: Radio-based Localization using Triangulation Signal decays linearly with log distance in laboratory setting –S j = b 0j + b 1j log D j –D j = sqrt((x-x j ) 2 + (y-y j ) 2 ) –Use triangulation to compute (x,y) » Problem solved [-80,-67,-50] Fingerprint or RSS (x?,y?)

32. 1a. RSSI: Radio-based Localization using Triangulation Signal decays linearly with log distance in laboratory setting –S j = b 0j + b 1j log D j –D j = sqrt((x-x j ) 2 + (y-y j ) 2 ) –Use triangulation to compute (x,y) » Problem solved Not in real life!! –noise, multi-path, reflections, systematic errors, etc. Distance RSSI Path loss Shadowing Fading

33. 1b. RSSI: Radio-Based Localization using Supervised Learning fs [-80,-67,-50] RSS (x j,y j ) (x?,y?) [(x,y),s1,s2,s3] Offline Training phase –Collect “ labeled ” training data [(x,y), S1,S2,S3,..] Online phase –Match “ unlabeled ” RSS –[(?,?), S1,S2,S3,..] to existing “ labeled ” training fingerprints

34. 2. Radio Interferometric Ranging Interference: superposition of two or more waves resulting in a new wave pattern Interferometry: cross-correlates a signal from a single source recorded by 2 observers, used in geodesy, astronomy, … 1.Signal strength is not crucial: no dependence on orientation, power level, hardware deviations 2.Low freq envelope (of composite signal): inexpensive HW 3.High carrier freq: high accuracy

35. Geometry φ CD = ( d AD -d BD +d BC -d AC ) mod λ Senders (A, B) transmit simultaneously pure sinusoid waves high carrier freq (400 MHz) small freq difference (500 Hz) Receivers (C, D) measure radio interference sample RSSI (9 KHz) find beat frequency (500 Hz) measure phase offset of RSSI use 1 μs timesync to correlate phase offsets result: (d AD -d BD +d BC -d AC ) mod λ d XY : distance of X and Y λ: wave length of carrier freq AB CD

36. 3. Time of Arrival (ToA) Gather four satellite signals and solve the non-linear system of equations. Satellite have atomic clocks (four on each), kept within 250 ns of each other. Figure source: http://www.dependability.org/wg10.4/timedepend/03-Schmi.pdf Can we use radio-based ToA for short-range localization?

37. Using Acoustics for Ranging Pros: –Sound travels slowly, so easy to measure ToF –Tight synchronization easily achieved using RF signaling Cons: –Acoustic/Ultrasound emitters are power-hungry (must move air) –Solid obstructions block sound completely  detector picks up reflections –Audible sound has good channel properties but isn ’ t always appropriate. Ultrasound is better.

38. Acoustic/Ultrasound Ranging Acoustic Mote UCB/UCLA UCLA NESL MK-II Ultrasound Localization MIT Cricket Project Ultrasound Localization

39. Typical Time-of-Flight AR System Radio channel is used to synchronize the sender and receiver (or use a timesync service) Coded acoustic signal is emitted at the sender and detected at the emitter. TOF determined by comparing arrival of RF and acoustic signals CPU Speaker Radio CPU Microphone Radio

40. 4. Time Difference of Arrival (TDoA) Anchor B1 and B2 send signal to A simultaneously. The time difference of arrival is recorded. A stays on the hyperbola: Do this for B2 and B3. A stays at the intersection of the two hyperbolas. If the two hyperbolas have 2 intersections, one more measurement is needed.

41. Beacons on ceiling Mobile device Cricket listener with RF and ultrasonic sensors The Cricket Compass Architecture Z X Y RF + Ultrasonic Pulse (x1,y1,z1) (x0,y0,z0) (x2,y2,z2) ( x, y, z) (x3,y3,z3) vt 3 vt 0 vt 1 vt 2 

42. Use Differential Distance d1 d2 z  Beacon S2 S1 d L

43. Estimating Differential Distance using Time Difference of Arrival Error in estimating  d is high when using time difference of arrival (TDoA) For angle error 52 cm (too large) Expt: Fix beacon location, rotate the rotary table to change orientation

44. Solution: Differential Distance (d2- d1) from Phase Difference (  ) Observation: The differential distance (d2-d1) is reflected as a phase difference between the signals received at two sensors d2d1 t  = 2  (d2 – d1)/ Beacon Estimate phase difference between ultrasonic waveforms to find (d2-d1)! S1S2 tt

45. Problem: Two Sensors Are Inadequate Phase difference is periodic  ambiguous solutions We don ’ t know the sign of the phase difference to differentiate between positive and negative angles Cannot place two sensors less than 0.5 apart –Sensors are not tiny enough!!! –Placing sensors close together produces inaccurate measurements

46. Solution: Use Three Sensors d1 t L 12 = 3  d2 d3 L 23 = 4  Estimate 2 phase differences to find unique solution for (d2-d1) Can do this when L 12 and L 23 are relatively-prime multiples of  Accuracy increases! Beacon S1 S2 S3

47. RF module (xmit) Cricket Compass RF antenna Ultrasonic transmitter BeaconSensor Module Ultrasound Sensor Bank 1.25 cm x 4.5 cm

48. 5. Angle Measurements Angle of Arrival (AoA) –Determining the direction of propagation of a radio-frequency wave incident on an antenna array. Directional Antenna Special hardware, e.g., laser transmitter and receivers.

49. Angle of Arrival (AoA) A measures the direction of an incoming link by radio array. By using 2 anchors, A can determine its position.

50. Acoustic Angle-of-Arrival System TOF AR system with multiple receiver channels Time difference of arrivals at receiver used to estimate angle of arrival CPU Speaker Radio CPU Radio Microphone Array

51. Localization for Multihop Network

52. Multihop Node Localization Problem Beacon nodes Localize nodes in an ad-hoc multihop network Based on a set of inter-node distance measurements

53. Iterative multilateration –a node with at least 3 neighboring beacons estimates its position and becomes a beacon. –Iterate until all nodes with 3 beacons are localized. Beacon node (known position) Unknown node (unknown position) Error Accumulates over multiple hops!

54. Minimizing Error: Mass-Spring System Nodes are “ masses ”, edges are “ springs ”. Length of the spring equals the distance measurement. Springs put forces to the nodes. Nodes move. Until the system stabilizes.

55. Mass-Spring System Node n i ’ s current estimate of its position: p i. The estimated distance d ij between n i and n j. The measured distance r ij between n i and n j. Force: F ij =d ij - r ij, along the direction p i p j. j pipi pjpj d ij F ij i

56. Mass-Spring System (cont.) Total force on n i : F i =Σ F ij. Move the node n i by a small distance (proportional to F i ). Recurse. pipi pjpj d ij F ij FiFi

57. Mass-Spring System (cont.) Total energy n i : E i =Σ E ij = Σ (d ij - r ij ) 2. Make sure that the total energy E=Σ E i goes down. Stop when the force (or total energy) is small enough. pipi pjpj d ij F ij FiFi

58. Mass-Spring System (cont.) Advantage: Naturally a distributed algorithm. Problem 1: may stuck in local minima. –Need to start from a reasonably good initial estimation, e.g., the iterative multi-lateration. –Typically not used alone. Problem 2: not robust to outliers. –If one measurement is off too much, the error gets distributed everywhere in the system.