Chapter 9: Localization & Positioning

Transcription

1 hapter 9: Localization & Positioning 98/5/25

2 Goals of this chapter Means for a node to determine its physical position with respect to some coordinate system (5, 27) or symbolic location (in a living room) Using the help of nchor nodes that know their position Directly adjacent Over multiple hops Using different means to determine distances/angles locally 98/5/25 2

3 Overview Properties of localization and positioning procedures Basic approaches Trilateration Single-hop schemes Multihop schemes 98/5/25 3

4 Properties of localization and positioning procedures Physical position or logical location oordinate system: position Symbolic reference: location bsolute coordinate: anchors are required entralized or distributed computation Scale (indoors, outdoors, global, ) Limitations: GPS for example, does not work indoors 98/5/25 4

5 Metrics Properties of localization and positioning procedures ccuracy how close is an estimated position to the real position? Precision for repeated position determinations, how often is a given accuracy achieved? osts, energy consumption, 98/5/ /5/25 5

6 Overview Properties of localization and positioning procedures Basic approaches Trilateration Single-hop schemes Multihop schemes 98/5/25 6

7 Main approaches (information sources) Proximity: a node wants to determine its position or location in the proximity of an anchor (Tri-/Multi-) lateration and angulation Lateration : when distances between nodes are used ngulation: when angles between nodes are used Scene analysis: the most evident form of it is to analyze pictures taken by a camera 98/5/25 7

8 Main approaches (information sources) Proximity Using information about a node s neighborhood. Exploit finite range of wireless communication E.g.: easy to determine location in a room with infrared (room number announcements) 98/5/ /5/25 8

9 Main approaches (information sources) (Tri-/Multi-)lateration and angulation Using geometric properties Lateration: distances between entities are used ngulation: angle between nodes are used: (x = 5, y = 4) ngle φ r 2 r 3 (x = 8, y = 2) Length known r (x = 2, y = ) ngle φ 2 98/5/ /5/25 9

10 Main approaches (information sources) Scene analysis nalyze characteristic properties of the position of a nods in comparison with premeasured properties Radio environment has characteristic fingerprints 98/5/25 98/5/25

11 Estimating distances RSSI Received Signal Strength Indicator Send out signal of known strength, use received signal strength and path loss coefficient to estimate distance 98/5/25

12 Estimating distances RSSI Problem: Highly error-prone process : aused by fast fading, mobility of the environment Solution: repeated measurement and filtering out incorrect values by statistical techniques 98/5/25 2

13 Estimating distances RSSI Problem: Highly error-prone process: heap radio transceivers are often not calibrated Same signal strength result in different RSSI ctual transmission power different from the intended power combination with multipath fading Signal attenuation along an indirect path is higher than along a direct path Solution: No! 98/5/ /5/25 3

14 Estimating distances RSSI PDF PDF Distance Distance Signal strength PDF of distances in a given distance 98/5/ /5/25 4

15 Estimating distances other means Time of arrival (To) Use time of transmission, propagation speed, to compute distance Problem: Exact time synchronization Usually, sound wave is used But propagation speed of sound depends on temperature or humidity 98/5/25 5

16 Estimating distances other means Time Difference of rrival (TDo) Use two different signals with different propagation speeds ompute difference between arrival times to compute distance Example: ultrasound and radio signal (ricket System) Propagation time of radio negligible compared to ultrasound Problem: expensive/energy-intensive hardware 98/5/ /5/25 6

17 Directional antennas Determining angles Node mount a directional antennas Supporting infrastructure anchors Multiple antennas mounted on a device at known separation Measuring the time difference between a signal s arrival at the different antennas 98/5/25 7

18 Overview Properties of localization and positioning procedures Basic approaches Trilateration Single-hop schemes Multi-hop schemes 98/5/25 8

19 Trilateration ssuming distances to three points with known location are exactly given Solve system of equations (Pythagoras!) (x i, y i ) : coordinates of anchor point i, r i distance to anchor i (x u, y u ) : unknown coordinates of node 98/5/ /5/25 9

20 Trilateration =3 98/5/ /5/25 2

21 Trilateration as matrix equation We get Rewriting as a matrix equation: =3 98/5/25 2

22 Trilateration with distance errors What if only distance estimation r i = r i + ε i available? Use multiple anchors, overdetermined system of equations Use (x u, y u ) that minimize mean square error, i.e, 98/5/ /5/25 22

23 Minimize mean square error Look at square of the of Euclidean norm expression (note that for all vectors v) Look at derivative with respect to x, set it equal to : 98/5/25 23

24 Overview Properties of localization and positioning procedures Basic approaches Trilateration Single-hop schemes Multihop schemes 98/5/25 24

25 Single-hop localization ctive Badge Uses diffused infrared as transmission medium Exploits the natural limitation of infrared waves by walls as a delimiter for its location granularity badge periodically sends a globally unique identifier via infrared to receivers, at least one of which is installed in every room 98/5/25 25

26 Single-hop localization ctive office use ultrasound with receivers placed at well-known position, mounted in array at the ceiling of a room; devices for which the position is to be determined act as ultrasound senders Process: entral controller sends a radio containing the devices s address The devices upon receiving this radio message, sends out a short ultrasound pulse The receiver array compute the difference of the arrival time of the radio and ultrasound pulse 98/5/ /5/25 26

27 Single-hop localization RDR Scene analysis techniques Both the anchors and the mobile device can be used to send the signal, which is then measured by the counterpart device(s) ricket ombines radio wave and ultrasound pulses to allow measuring of the TDo 98/5/25 27

28 Single-hop localization Overlapping connectivity Without any numeric range measurement Use connectivity to a set of anchors The underlying assumption is that transmissions from an anchor can be received within a circular area of known radius 98/5/ /5/25 28

29 Single-hop localization Overlapping connectivity Process: nchor nodes periodically send out transmissions identifying themselves node has received these announcements, it can determine that it is in the intersection of the circles Suppose node knows about all the anchors nchor announcements are not received implies that the node is outside the respective circles Problem: accuracy depends on the number of anchors 98/5/ /5/25 29

30 Single-hop localization pproximate point in triangle By pure connectivity information Idea: decide whether a node is within or outside of a triangle formed by any three anchors 98/5/25 3

31 Single-hop localization pproximate point in triangle (PIT) Inside a triangle: irrespective of the direction of the movement, the node must be closed to at least one of the corners of the triangle 98/5/ /5/25 3

32 Single-hop localization pproximate point in triangle Outside a triangle: There is at least one direction for which the node s distance to all corners increases D B 98/5/ /5/25 32

33 PIT pproximation: Normal nodes test only directions towards neighbors 3 M 2 3 M B. Inside ase B. OutSide ase B 98/5/25 33

34 34 PIT (cont.) PIT (cont.) Grid-Based ggregation Narrow down the area where the normal node can potentially reside anchor node normal node 2 98/5/25

35 Single-hop localization pproximate point in triangle However, moving a sender node to determine its position is hardly practical! Solution: inquire all its neighbors about their distance to the given three corner anchors 98/5/ /5/25 35

36 Single-hop localization Using angle of arrival information 98/5/ /5/25 36

37 Overview Properties of localization and positioning procedures Basic approaches Trilateration Single-hop schemes Multihop schemes 98/5/25 37

38 Multihop range estimation How to estimate range to a node to which no direct radio communication exists? No RSSI, TDo, But: Multi-hop communication is possible B X 98/5/25 38

39 Multihop range estimation Idea : ount number of hops, assume length of one hop is known (DV-Hop) Start by counting hops between anchors, divide known distance B X 98/5/ /5/25 39

40 Multihop range estimation Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance) B X 98/5/ /5/25 4

41 DV-Based Scheme Must work in a network which is dense enough DV-hop approach used the hop of the shortest path to approximately estimate the distance between a pair of nodes Drawback: Requires lots of communications anchor 98/5/25 anchor 4

42 Discussion number of anchors Euclidean method increase accuracy as the number of anchors goes up The distance vector -link methods are better suited for a low ratio for anchors Uniformly distributed network Distance vector methods perform less well in anisotropic networks Euclidean method is not very sensitive to this effect 98/5/25 42

43 Iterative multilateration 98/5/25 43 (2,) (8,) (8,2) B (2,) (8,) (8,2) B (2,) (8,) (8,2) B (2,) (8,) (8,2) (2,4) B (2,) (8,) (8,2) (2,4) B (2,) (8,) (8,2) (2,4) B (2,) (8,) (8,2) (3,2) (2,4) B (2,) (8,) (8,2) (3,2) (2,4) B (2,) (8,) (8,2) (3,2) (2,4) B (2,) (8,) (8,2) (22,2) (3,2) (2,4) B (2,) (8,) (8,2) (22,2) (3,2) (2,4) B (2,) (8,) (8,2) (22,2) (3,2) (2,4) B I: II: III: IV:

44 Iterative multilateration ssume some nodes can hear at least three anchors (to perform triangulation), but not all Idea: let more and more nodes compute position estimates, spread position knowledge in the network Problem: Errors accumulate When not all nodes in the network will have three nodes with position estimates 98/5/25 44

45 (3,2) IV: (2,) (2,) (2,) (2,4) (8,2) B ollaborative multilateration (2,) (8,) (8,) (2,) B (8,) (2,4) (3,2) (2,) II: I: IV: (8,2) IV: (8,2) (8,2) (8,2) (8,) (8,) IV: (8,2) B (3,2) B (3,2) (22,2) (3,2) B (3,2)(8,) B (3,2) (2,4) (3,2) IV: 2,4) III: (8,2) B (2,4) (2,) (2,) (2,) (2,) (2,4) (2,) B (3,2) (2,4) (8,) (8,) (2,) (8,) (8,) (22,2) (2,) (22,2) (8,) (22,2) 98/5/25 45

46 (2,4) II: (8,2) (2,4) (8,) (2,) IV: (2,) (8,2) B (38,5 IV: (8,2) (8,2) 3,2) B (3,2) (8,) (2,) (8,) (2,) (2,4) B (3,2) B (3,2) (2,) 4) (2,4) II: I: IV: (8,2) IV: (8,2) (8,2) (8,2) (8,) (8,) (2,) B (8,) (3,2) B (3,2) (22,2) 3,2) B (3,2) B (2,4) IV: III: 2,4) (8,2) (2,4) (8,) (22,2) (2,) (2,) (2,) (2,)?,?) I: ollaborative multilateration (3,2) (38,5 (2,4) (8,) (8,) (2,) (8,) (8,) (22,2) (2,) (22,2) 98/5/25 B 46

47 Iterative multilateration Solution : Participating nodes Have at least three anchors or other participating nodes as neighbors Solution 2: Sound Have at least three independent references to anchor nodes The path to the anchors have to be edge-disjoint. Discussion: solution 2 is suited to low anchor ratios 98/5/ /5/25 47

48 Probabilistic position description Similar idea to previous one, but accept problem that position of nodes is only probabilistically known Represent this probability explicitly, use it to compute probabilities for further nodes PDF 98/5/25 Distance 48

49 Probabilistic position description 98/5/ /5/25 49

50 onclusions Determining location or position is a vitally important function in WSN, but fraught with many errors and shortcomings Range estimates often not sufficiently accurate Many anchors are needed for acceptable results nchors might need external position sources (GPS) Multilateration problematic (convergence, accuracy) 98/5/25 5

51 Impact of anchor placement preference for anchor to be placed on the perimeter of a given area Solution : Mobile entity is wandering around the given area Measuring position error Solution 2: nchors try to estimate the positioning error Decide where an additional anchor should be placed 98/5/25 5