Localization in Wireless Sensor Networks

Transcription

1 Localization in Wireless Sensor Networks Part 2: Localization techniques Department of Informatics University of Oslo Cyber Physical Systems,

2 Localization problem in WSN In a localization problem in WSN we have two groups of sensors: Anchors nodes of the network with known positions. Non-anchors nodes of the network to be localized. There are many algotihms leading to localize the non-anchors. These algorithms use different physical measurements to investigate the position of a non-anchor.

3 Table of Contents 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

4 Table of Contents AOA measurements Distance-related measurements RSS profiling measurements 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

5 Angle-of-arrival measurement AOA measurements Distance-related measurements RSS profiling measurements In this method we measure the angle between the transmitter receiver line and the reference direction. In order to do this we must use an anisotropic antenna. Actually AOA measurements use either amplitude or phase response of the antenna.

6 AOA measurements Distance-related measurements RSS profiling measurements AOA measurement using antenna s amplitude response The rotated beam of the receiver anisotropic antenna The direction corresponding to the maximum signal strength is taken as the direction of the transmitter Problem: varying signal strength Second non-rotating isotropic antenna to normalize the signal strength. Use a minimum of two (typically at least four) stationary antennas with known, anisotropic antenna patterns.

7 AOA measurements Distance-related measurements RSS profiling measurements AOA measurement using antenna s phase response Large receiver antenna (relative to λ) or antenna array. Phase difference between adjacent antenna elements: 2π d cos θ λ Problems in case of: Weak (relative to noise) signals Strong co-channel interference Multipath signals

8 Limitations of AOA measurements AOA measurements Distance-related measurements RSS profiling measurements Directivity of the antenna measurement strongly depends of antenna angular resolution. Shadowing transmitters and receivers must lie in line-of-sight. Multipath reflections

9 Table of Contents AOA measurements Distance-related measurements RSS profiling measurements 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

10 AOA measurements Distance-related measurements RSS profiling measurements Distance-related measurement techniques Propagation time measurement techniques Time-difference-of-arrival (TDOA) measurement techniques Lighthouse approach to distance measurement Distance estimation using received signal strength (RSS) measurement

11 Propagation time measurements AOA measurements Distance-related measurements RSS profiling measurements One-way propagation time measurements Measure the difference between the sending time of a signal at the transmitter and the receiving time of the signal at the receiver. Requires synchronized local times at the transmitter and receiver. Interesting approach: two signals (RF and ultrasonic) sent simultaneously. Since v sound c, the time difference between the receipt of signals can be used to calculate the distance.

12 Propagation time measurements AOA measurements Distance-related measurements RSS profiling measurements Roundtrip propagation time measurements Measure the difference between the time when a signal is sent by a sensor and the time when the returned signal is received. No synchronization problem. The major error source: the dalay required for handling the signal in the second sensor. A priori known internal delay. Delay measured by the second sensor and sent to the first sensor to be substracted.

13 AOA measurements Distance-related measurements RSS profiling measurements Time-difference-of-arrival measurements In this method we measure the time-difference-of-arrival for each pair of receivers. TDOA between receiver i and receiver j is given by: t i,j = t i t j, where t i, t j the time when a signal is received at receivers i and j respectively

14 AOA measurements Distance-related measurements RSS profiling measurements Time-difference-of-arrival measurements The accuracy of TDOA measurements will improve when the separation between receivers increases. Closely spaced multiple receivers may give rise to multiple received signals that cannot be separated. Overlapping signals due to multipath often cannot be resolved.

15 AOA measurements Distance-related measurements RSS profiling measurements Lighthouse approach to distance measurements Parallel rotating optical beam By measuring the time duration t that the receiver dwells in the beam we can calculate the distance from the rotational axis of the optical beam. d b 2 sin(ωt/2).

16 AOA measurements Distance-related measurements RSS profiling measurements Lighthouse approach to distance measurements The unknown angular velocity ω can be derived from the time interval between the two consecutive detections of the beam. Adventage: The optical receiver can be of a very small size. However the transmitter may be large. This approach requires a direct line-of-sight between the optical receiver and the transmitter.

17 AOA measurements Distance-related measurements RSS profiling measurements Distance estimation using RSS measurements These techniques are based on a received signal strength indicator (RSSI). Advantage: They require no additional hardware. They are unlikely to significantly impact local power consumption, sensor size and cost. In free space the received power of signal varies as the inverse square of the distance d between the transmitter and the receiver P(d) 1 d 2 In fact the propagation of a signal is affected by reflection, diffraction and scattering.

18 Table of Contents AOA measurements Distance-related measurements RSS profiling measurements 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

19 RSS profiling measurements AOA measurements Distance-related measurements RSS profiling measurements In addition to anchor nodes, a large number of sample points are distributed throughout the coverage area of the sensor network. At each sample point, a vector of RSS from all the anchors is obtained. The collection of all these vectors provides (by extrapolation) a map of the whole region, stored in a central location. By referring to this map, a non-anchor node can estimate its location.

20 Table of Contents 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

21 One-hop and multi-hop localization techniques One-hop localization technique The non-anchor node to be localized is the one-hop neighbor of a sufficient number of anchors with known positions.

22 Measured angles β i Known functions θ i (x) Maximum likelihood estimator method to find x t. In the simpliest case it s equivalent to least squares method: x t = arg min = arg min n i=1 ε 2 i n (θ i (x) β i ) 2 i=1

23 AOA maximum likelihood estimator (MLE) x t minimizes the following sum: x t = arg min n (θ i (x) β i ) 2 In general, ε i = (θ i (x) β i ) are assumed to be zero-mean Gaussian noises with variance σi 2. Therefore in matrix notation: i=1 x t = arg min(θ(x) β) T S 1 (θ(x) β), where: θ(x) = (θ 1 (x),..., θ n (x)), β = (β 1,..., β n ), and a covariance matrix of ε i, S = diag{σ 2 1,..., σ2 n}.

24 AOA maximum likelihood estimator (MLE) Minimization problem: x t = arg min(θ(x) β) T S 1 (θ(x) β), First solution: Newton-Gauss iteration method. x t,k+1 = x t,k + ( θ x (x t,k ) T S 1 θ x (x t,k )) 1 θx (x t,k ) T S 1 (β θ(x t,k )), where θ x (x t,k ) denotes the partial derterivative of θ with respect to x evaluated at point x t,k. This method requires an initial estimate close enough to the true minimum of the cost function.

25 AOA Stansfield approach x t = arg min(θ(x) β) T S 1 (θ(x) β), Second solution: Stansfield approach. Assumption: measurement error is small enough such that ε i sin ε i. The cost function to minimize becomes: n sin 2 (θ i (x) β i ) σi 2 i=1 We can use the relation sin(θ i (x) β i ) = sin θ i (x) cos β i cos θ i (x) sin β i where r i = (x x i ) 2 + (y y i ) 2. = (y y i) cos β i (x x i ) sin β i r i,

26 AOA Stansfield approach Cost function to minimize: n sin 2 (θ i (x) β i ) n [(y y i ) cos β i (x x i ) sin β i ] 2 σi 2 = σi 2r i 2 i=1 i=1 where = (Ax b) T R 1 S 1 (Ax b), sin β 1 cos β 1 A =.. sin β n cos β n x 1 sin β 1 y 1 cos β 1 b =. x n sin β n y n cos β n R = diag{r 2 1,..., r 2 n }

27 AOA Stansfield approach Cost function to minimize: x t = arg min(ax b) T R 1 S 1 (Ax b), Stansfield assumes that the cost function weakly depends on R. Under these assumptions, the minimization of cost function with respect to x t is a well known problem and the solution is given by: x t = ( A T R 1 S 1 A) 1 A T R 1 S 1 b

28 Table of Contents 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

29 Global Positioning System (GPS) 31 GPS satellites sending the information about satellites positions and precise time the message was transmitted. One-way propagation time measurement. Theoretically, measure of distance from 3 satellites is sufficient to calculate the position of the receiver. Practically, the distance from fourth satellite is necessary for clock synchronization.

30 Generally in a WSN, we measure vector of distances d = ( d 1,..., d n ) to n anchors. Let d(x) = (d 1 (x),..., d n (x)) be the vector of real distances from point x to anchors. Then the location estimation problem can be formulated using a maximum likelihood approach as: [ T x t = arg min d(x) d] [ ] S 1 d(x) d, where S is the covariance matrix of the distance measurement errors. This equation can be solved in similar way to AOA-based technique.

31 TDOA-based localization techniques Given the TDOA measurement t i,j we get a hyperbola equation t i,j = t i t j = 1 c ( r i r t r j r t ), for r t. In fact we must consider the difference between the measured value t i,j and the real value t i,j. t i,j = t i,j + ε i,j

32 TDOA-based localization techniques For n receivers we get a system of n 1 linearly independent equations: t 1,n. t n 1,n = r 1 r t r n r t c. r n 1 r t r n r t c + ε 1,n. ε n 1,n Let t = ( t 1,n,..., t n 1,n ), f(r) denotes the vector ( 1 c ( r 1 r r n r ),..., 1 ) c ( r n 1 r r n r ) and ε = (ε 1,n,..., ε n 1,n )

33 TDOA-based localization techniques We can write our system of equations in the following way: t f(r t ) = ε We want to minimize the sum n i=1 ε2 i. We can again assume that ε i is a zero-mean Gaussian noise with variance σ 2 i. Denote the covariance matrix diag{σ2 1,..., σ2 n} by S. We get the same equation as in AOA case: r t = arg min [ t f(r) ] T S 1 [ t f(r) ] T. Therefore the recursive solution is ( ) 1 r t,k+1 = r t,k + f r (r t,k ) T S 1 f r (r t,k ) fr (r t,k ) T S 1 [ t f(r t,k ) ]

34 Lighthouse approach to one-hop localization Using lighthouse approach we measure the distances d X, d Y, d Z from 3 perpendicular axes X, Y, Z. Equations for receiver coordinates: d 2 X = y 2 + z 2 d 2 Y = z2 + x 2 d 2 Z = x 2 + y 2 8 solutions corresponding 8 quadrants in the coordinate system. We know a priori in which quadrant the receiver is located.

35 Table of Contents 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

36 This technique consists of two phases: Building the RSS map of the entire area, Fitting the measured RSS vector from a non-anchor node into the appropriate part of the map. The accuracy of this techique depends on both phases accuracy. The major practical obstacle: changes in the environment require (possibly costly) recalculation of the model.

37 LANDMARC Indoor Location Sensing Using Active RFID LANDMARC An experiment presenting the application of RSS-based localization technique with use of the RFID system. Radio-frequency identification (RFID) RFID system consists of RFID readers and RFID tags. RFID reader can read data emitted from RFID tags. RFID readers and tags use a defined radio frequency and protocol to transmit and receive data. RFID reader used in this experiment has 8 different power levels, therefore it can estimate the distance to the RFID tag using RSS technique.

38 LANDMARC Measurement techniques used in localization 16 reference RFID tags with known positions, 8 tracking RFID tags to localize, 4 RFID readers estimating the distance to tags due to measurements on power levels 1 8.

39 LANDMARC Measurement techniques used in localization RSS varies due to both static obstructions and dynamic human movement. Therefore, direct estimation of the distance to a tracking tag from RSS leads to big errors. Instead we can compare RSS from a tracking tag to RSS from a reference tag with a known position. Let P i (t) denotes a RSS from tag t (either tracking or referenced) measured by reader i (i {1,..., n}). The distance between tags a and b can be defined as follows: E a,b = n (P i (a) P i (b)) 2 i=1

40 LANDMARC Measurement techniques used in localization Coordinates of the tracking tag can be estimated as a weighted mean of coordinates of the k closest (due to E a,b ) reference tags: k r t = w i r i. i=1 Empirically, in LANDMARC, weights w i are given by: w i = 1/Et,i 2 k j=1 1/E. t,j 2 Experiments for different values of k {1, 2, 3, 4, 5} showed that the best accuracy of this estimation we get for k = 4. This result was easy to predict, because all the reference tags were placed in a grid array.

41 Summary of LANDMARC experiment We can implement relatively cheap indoor localization system with accuracy under 2 m using RFID. Unfortunately, RFID products do not provide RSS measurement, only report detectable or not detectable in each of 8 power levels. Moreover, it takes about 1 minute to scan in all 8 power levels. Another problem: the power levels detected from two tags may be different due to the variation of the chips and circuits, as well as batteries. Dynamic environment is one of the main reasons for increasing measurement errors. (A person standing in front of a tag may greatly increase the error).

42 Table of Contents Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

43 Multi-hop localization techniques Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Multi-hop localization technique The non-anchor nodes are not necessarily the one-hop neighbors of the anchors.

44 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Connectivity-based multi-hop localization algorithms Connectivity-based algorithms They do not rely on any of the described measurement techniques. Instead they use the connectivity information who is within the communications range of whom. Connectivity metric The ratio of the number of transmitter signals succesfully received to the total number of signals from that transmitter. Transmitters whose connectivity metric exceeds a certain threshold (e.g. 90%) are called reference points. A receiver at an unknown location uses the centroid of its reference points as its location estimate.

45 Distance vector (DV-hop) approach Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms All anchors flood their locations to other nodes in the network. The messages are propagated hop-by-hop and there is a hop-count in the message. Each node maintains the least number of hops that is away from an anchor. When an anchor receives a message from another anchor, it estimates the average distance of one hop to this anchor and sends it back to the network as a correction factor. When receiving the correction factor, a non-anchor node is able to estimate its distance to anchors and performs estimate its location.

46 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Connectivity-based multi-hop localization algorithms The most attractive feature Simplicity of algorithms Limitations They can only provide a coarse grained estimate of location. The localization error is highly dependent on the node density, the number of anchors and the network topology (i.e. requires a high node density, a lot of anchors and a regular network).

47 Table of Contents Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

48 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Distance-based multi-hop localization algorithms The core of distance-based localization algorithms Use of inter-sensor distance measurements in a sensor network to locate the entire network. Centralized algorithms use a single central processor to collect all the individual inter-sensor distance data and produce a map of the entire sensor network. Distributed algorithms rely on self-localization of each node in the sensor network using the distances the node measures and the local information it collects from its neighbors.

49 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Centralized distance-based localization algorithms Centralized distance-based multi-hop localization algorithms Technique widely used in road traffic monitoring and control, environmental monitoring, health monitoring and precision agriculture monitoring networks. Feasible to implement. High likelihood of providing more accurate location estimates than those provided by distributed algorithms.

50 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Centralized distance-based localization algorithms Multidimensional scaling (MDS) approach The whole sensor network is divided into smaller groups where adjacent groups may share common sensors. Each group contains at least three anchors or sensors whose locations have already been estimated. MDS is used to estimate the relative locations of sensors in each group and build local maps. Local maps are then stitched together to form an estimated global map by utilizing common sensors between adjacent local maps.

51 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Distributed distance-based localization algorithms Distributed distance-based multi-hop localization algorithms Extension of the distributed connectivity-based localization algorithms. DV-distance algorithm Obtained from DV-hop connectivity-based algorithm Propagates measured distance among neighboring nodes instead of hop count.

52 Table of Contents Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms 1 Measurement techniques used in localization Angle-of-arrival (AOA) measurements Distance-related measurements Received signal strength (RSS) profiling measurements 2 3 Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms

53 Centralized vs distributed algorithms Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Pro centralized algorithms Centralized algorithms are likely to provide more accurate location estimates than distributed algorithms. In distributed algorithms error propagation may cause bigger inaccuracies of the final results. Distributed algorithms are more difficult to design (locally optimal algorithms may not perform well in a global sense). Distributed algorithms generally require multiple iterations to arrive a stable solution and therefore may be slower than centralized.

54 Centralized vs distributed algorithms Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Pro distributed algorithms Decentralized localization is harder than centralized any algorithm for decentralized localization can be applied to centralized problems, but not the reverse. Centralized algorithms are not feasible to be implemented for large scale sensor networks. Centralized algorithms require higher computational complexity than distributed algoritms. In large networks distributed algorithms are more energy-efficient than centralized algorithms.

55 Summary Measurement techniques used in localization Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms There are many different techniques available for WSN localization. Typically, localization algorithms based on AOA and propagation time measurements are able to achieve better accuracy than RSS techniques. However, that accuracy is achieved at the expense of higher equipment cost. It is possible to establish relatively cheap indoor localization system in WSN using RFID equipment.

56 Bibliography I Connectivity-based multi-hop localization algorithms Distance-based multi-hop localization algorithms Centralized vs distributed algorithms Guoqiang Mao, Barıs Fidan and Brian D.O. Anderson Wirless Sensor Network Localization Techniques. Computer Networks, , Lionel M. Ni and Yunhao Liu. LANDMARC: Indoor Location Sensing using active RFID Wireless Networks 10, , 2004.