Скачать презентацию Chapter 7 Localization Positioning 1 2018 3 18 Скачать презентацию Chapter 7 Localization Positioning 1 2018 3 18

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Chapter 7 Localization & Positioning 1 2018/3/18 Chapter 7 Localization & Positioning 1 2018/3/18

Goals of this chapter Means for a node to determine its physical position with Goals of this chapter Means for a node to determine its physical position with respect to some coordinate system (50, 27) or symbolic location (in a living room) Using the help of 2 Anchor nodes that know their position Directly adjacent nodes Over multiple hops 2018/3/18

Outline 3 7. 1 Properties of localization and positioning procedures 7. 2 Possible approaches Outline 3 7. 1 Properties of localization and positioning procedures 7. 2 Possible approaches 7. 3 Mathematical basics for the lateration problem 7. 4 Positioning in multi-hop environments 7. 5 Positioning assisted by anchors 2018/3/18

7. 1 Properties of localization and positioning procedures Physical position versus logical location 4 7. 1 Properties of localization and positioning procedures Physical position versus logical location 4 Coordinate system: position Symbolic reference: location Absolute versus relative coordinate Centralized or distributed computation Localized versus centralized computation Limitations: GPS for example, does not work indoors Scale (indoors, outdoors, global, …) 2018/3/18

Properties of localization and positioning procedures (cont. ) Accuracy how close is an estimated Properties of localization and positioning procedures (cont. ) Accuracy how close is an estimated position to the real position? Precision the ratio with which a given accuracy is reached 5 Costs, energy consumption, … 2018/3/18

7. 2 Possible approaches Proximity (Tri-/Multi-) lateration and angulation The most evident form of 7. 2 Possible approaches Proximity (Tri-/Multi-) lateration and angulation The most evident form of it is to analyze pictures taken by a camera Other measurable characteristic ‘fingerprints’ of a given location can be used for scene analysis e. g. , RADAR Bounding box 6 Lateration : when distances between nodes are used Angulation: when angles between nodes are used Scene analysis A node wants to determine its position or location in the proximity of an anchor to bound the possible positions of a node 2018/3/18

Proximity (range-free approach) Using information of a node’s neighborhood Exploit finite range of wireless Proximity (range-free approach) Using information of a node’s neighborhood Exploit finite range of wireless communication e. g. , easy to determine location in a room with infrared (room number announcements) 7 2018/3/18

Trilateration and triangulation (range-based approach) (Tri-/Multi-)lateration and angulation 8 Using geometric properties Lateration: distances Trilateration and triangulation (range-based approach) (Tri-/Multi-)lateration and angulation 8 Using geometric properties Lateration: distances between entities are used Angulation: angle between nodes are used 2018/3/18

Trilateration and triangulation (cont. ) Determining distances 9 To use (multi-)lateration, estimates of distances Trilateration and triangulation (cont. ) Determining distances 9 To use (multi-)lateration, estimates of distances to anchor nodes are required. This ranging process ideally leverages the facilities already present on a wireless node, in particular, the radio communication device. The most important characteristics are Received Signal Strength Indicator (RSSI), Time of Arrival (To. A), and Time Difference of Arrival (TDo. A). 2018/3/18

Distance estimation RSSI (Received Signal Strength Indicator) 10 Send out signal of known strength, Distance estimation RSSI (Received Signal Strength Indicator) 10 Send out signal of known strength, use received signal strength and path loss coefficient to estimate distance 2018/3/18

Distance estimation RSSI (cont. ) Problem: Highly error-prone process : 11 Caused by fast Distance estimation RSSI (cont. ) Problem: Highly error-prone process : 11 Caused by fast fading, mobility of the environment Solution: repeated measurement and filtering out incorrect values by statistical techniques Cheap radio transceivers are often not calibrated Same signal strength result in different RSSI Actual 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! 2018/3/18

Distance estimation PDF RSSI (cont. ) Distance PDF of distances in a given RSSI Distance estimation PDF RSSI (cont. ) Distance PDF of distances in a given RSSI value 12 Signal strength 2018/3/18

Distance estimation To. A (Time of arrival ) Use 13 time of transmission, propagation Distance estimation To. A (Time of arrival ) Use 13 time of transmission, propagation speed Problem: Exact time synchronization Usually, sound wave is used But propagation speed of sound depends on temperature or humidity 2018/3/18

Distance estimation TDo. A (Time Difference of Arrival ) Use two different signals with Distance estimation TDo. A (Time Difference of Arrival ) Use two different signals with different propagation speeds 14 Compute difference between arrival times to compute distance Example: ultrasound and radio signal (Cricket System) Propagation time of radio negligible compared to ultrasound Problem: expensive/energy-intensive hardware 2018/3/18

Scene analysis RADAR system: Comparing the received signal characteristics from multiple anchors with premeasured Scene analysis RADAR system: Comparing the received signal characteristics from multiple anchors with premeasured and stored characteristics values. 15 Radio environment has characteristic “fingerprints” The necessary off-line deployment for measuring the signal landscape cannot always be accommodated in practical systems. 2018/3/18

Bounding Box 16 The bounding box method proposed in uses squares instead of circles Bounding Box 16 The bounding box method proposed in uses squares instead of circles as in tri-lateration to bound the possible positions of a node. For each reference node i, a bounding box is defined as a square with its center at the position of this node (xi, yi), with sides of size 2 di (where d is the estimated distance) and with coordinates (xi –di, yi–di) and (xi+di, yi+di). 2018/3/18

Bounding Box (cont. ) Using range to anchors to determine a bounding box Use Bounding Box (cont. ) Using range to anchors to determine a bounding box Use center of box as position estimate B C d A 17 2018/3/18

References C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning Algorithms for Distributed Ad-Hoc References C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks, ” In Proceedings of the Annual USENIX Technical Conference, Monterey, CA, 2002. A. Savvides, C. -C. Han, and M. Srivastava. “Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors, ” Proceedings of the 7 th Annual International Conference on Mobile Computing and Networking, pages 166– 179. ACM press, Rome, Italy, July 2001. 18 N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost Outdoor Localization For Very Small Devices, ” IEEE Personal Communications Magazine, 7(5): 28– 34, 2000. S. Simic and S. Sastry, “Distributed localization in wireless ad hoc networks, ” UC Berkeley, Tech. rep. UCB/ERL M 02/26, 2002. 2018/3/18

7. 3 Mathematical basics for the lateration problem 19 2018/3/18 7. 3 Mathematical basics for the lateration problem 19 2018/3/18

Solution with three anchors and correct distance values Assuming distances to three points with Solution with three anchors and correct distance values Assuming distances to three points with known location are exactly given Solve system of equations (Pythagoras!) 20 (xi , yi) : coordinates of anchor point i, ri : distance to anchor i (xu, yu) : unknown coordinates of node 2018/3/18

Solution with three anchors and correct distance values (cont. ) 21 2018/3/18 Solution with three anchors and correct distance values (cont. ) 21 2018/3/18

Trilateration as matrix equation 22 Rewriting as a matrix equation: 2018/3/18 Trilateration as matrix equation 22 Rewriting as a matrix equation: 2018/3/18

Solving with distance errors What if only distance estimation available? Use multiple anchors, overdetermined Solving with distance errors What if only distance estimation available? Use multiple anchors, overdetermined system of equations Use (xu, yu) that minimize mean square error, 23 i. e, 2018/3/18

Minimize mean square error Look at square of the of Euclidean norm expression 24 Minimize mean square error Look at square of the of Euclidean norm expression 24 (note that for all vectors v) Look at derivative with respect to x, set it equal to 0 2018/3/18

7. 4 Positioning in multi-hop environments 25 2018/3/18 7. 4 Positioning in multi-hop environments 25 2018/3/18

Connectivity in a multi-hop network 26 Assume that the positions of n anchors are Connectivity in a multi-hop network 26 Assume that the positions of n anchors are known and the positions of m nodes is to be determined, that connectivity between any two nodes is only possible if nodes are at most R distance units apart, and that the connectivity between any two nodes is also known The fact that two nodes are connected introduces a constraint to the feasibility problem – for two connected nodes, it is impossible to choose positions that would place them further than R away 2018/3/18

Multi-hop range estimation How to estimate range to a node to which no direct Multi-hop range estimation How to estimate range to a node to which no direct radio communication exists? 27 No RSSI, TDo. A, … But: Multi-hop communication is possible 2018/3/18

Multi-hop range estimation (cont. ) Idea 1: (DV-Hop) Start by counting hops between anchors Multi-hop range estimation (cont. ) Idea 1: (DV-Hop) Start by counting hops between anchors then divide known distance 28 Count Shortest hop numbers between all two nodes. Each anchors estimate hop length and propagates to the network. Node calculates its position based on average hop length and shortest path to each anchor. 2018/3/18

DV Hop L 1 calculates average hope length : So do L 2 and DV Hop L 1 calculates average hope length : So do L 2 and L 3 : Node A uses trilateration to estimate it’s position by multiplying the average hope length of every received anchor to shortest path length it assumed. 29 2018/3/18

DV-Distance 30 Idea 2: If range estimates between neighbors exist, use them to improve DV-Distance 30 Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance) Distance between neighboring nodes is measured using radio signal strength and is propagated in meters rather than in hops. The algorithm uses the same method to estimate but shortest distance length are assumed. 2018/3/18

Multi-hop range estimation (cont. ) DV-Based Scheme • • Must work in a network Multi-hop range estimation (cont. ) DV-Based Scheme • • Must work in a network which is dense enough DVhop approach used the hop of the shortest path to approximately estimate the distance between a pair of nodes Drawback: Requires lots of communications anchor 31 anchor 2018/3/18

Discussion Number of anchors Uniformly distributed network 32 Euclidean method increase accuracy as the Discussion Number of anchors Uniformly distributed network 32 Euclidean method increase accuracy as the number of anchors goes up The “distance vector”-like methods are better suited for a low -ratio of anchors Distance vector methods perform less well in non-uniformly networks Euclidean method is not very sensitive to this effect 2018/3/18

7. 5 Positioning assisted by anchors 33 2018/3/18 7. 5 Positioning assisted by anchors 33 2018/3/18

APIT (Approximate Point in Triangle) By pure connectivity information Idea: decide whether a node APIT (Approximate Point in Triangle) By pure connectivity information Idea: decide whether a node is within or outside of a triangle formed by any three anchors However, moving a sender node to determine its position is hardly practical ! Solution: 34 inquire all its neighbors about their distance to the given three corner anchors 2018/3/18

APIT (cont. ) Inside a triangle Irrespective of the direction of the movement, the APIT (cont. ) 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 A M B 35 C 2018/3/18

APIT (cont. ) Outside a triangle: There is at least one direction for which APIT (cont. ) Outside a triangle: There is at least one direction for which the node’s distance to all corners increases M B 36 A C 2018/3/18

APIT (cont. ) 37 Approximation: Normal nodes test only directions towards neighbors 2018/3/18 APIT (cont. ) 37 Approximation: Normal nodes test only directions towards neighbors 2018/3/18

APIT (cont. ) Grid-Based Aggregation Narrow down the area where the normal node can APIT (cont. ) Grid-Based Aggregation Narrow down the area where the normal node can potentially reside 2 1 anchor node normal node 38 2018/3/18

MCL (Monte-Carlo Localization) Assumptions Time is divided into several time slots Moving distance in MCL (Monte-Carlo Localization) Assumptions Time is divided into several time slots Moving distance in each time slot is randomly chosen from [0 , Vmax ] Each anchor node periodically forwards its location to twohop neighbors Notation 39 2018/3/18 R - communication range 2018/3/18 39

MCL (cont. ) Each normal node maintains 50 samples in each time slot 40 MCL (cont. ) Each normal node maintains 50 samples in each time slot 40 2018/3/18 Samples represent the possible locations The sample selection is based on previous samples Sample (x , y) must satisfy some constraints Located in the anchor constraints 2018/3/18 40

MCL (cont. ) Anchor constraints Near anchor constraint The communication region of one-hop anchor MCL (cont. ) Anchor constraints Near anchor constraint The communication region of one-hop anchor node ( near anchor ) Farther anchor constraint The region within ( R , 2 R ] centered on two-hop anchor ( farther anchor ) Near anchor constraint R A 1 N 1 Farther anchor constraint R R A 1 N 2 41 2018/3/18 41

MCL (cont. ) Environment Anchor node Normal node A 4 A 1 N 1 MCL (cont. ) Environment Anchor node Normal node A 4 A 1 N 1 A 2 A 3 42 2018/3/18 42

MCL (cont. ) Initial Phase Sample in the last time slot Anchor node Normal MCL (cont. ) Initial Phase Sample in the last time slot Anchor node Normal node A 4 N 1 A 2 A 3 43 2018/3/18 43

MCL (cont. ) Sample in this time slot Sample in the last time slot MCL (cont. ) Sample in this time slot Sample in the last time slot Anchor node Normal node Prediction Phase & Filtering Phase Vmax A 4 R RA N 1 1 A 2 R A 3 44 2018/3/18 44

MCL (cont. ) Sample in this time slot Sample in the last time slot MCL (cont. ) Sample in this time slot Sample in the last time slot Anchor node Prediction Phase & Filtering Phase Normal node Vmax R RA Vmax 1 N 1 A 2 Vmax 45 2018/3/18 A 4 R A 3 2018/3/18 45

MCL (cont. ) Sample in this time slot Estimative position Anchor node Estimative Location MCL (cont. ) Sample in this time slot Estimative position Anchor node Estimative Location n the average of samples Normal node A 4 A 1 EN 1 A 2 A 3 46 2018/3/18 46

MCL (cont. ) Sample in this time slot Sample in the last time slot MCL (cont. ) Sample in this time slot Sample in the last time slot Anchor node Normal node Repeated Prediction Phase & Filter Phase In the next time slot Vmax A 1 A 4 N 1 A 2 R A 3 47 2018/3/18 47

DRLS Distributed Range-Free Localization Scheme There are three phases in the DRLS algorithm. Phase DRLS Distributed Range-Free Localization Scheme There are three phases in the DRLS algorithm. Phase 2 – Using improved grid-scan algorithm to get initial estimative location 48 Phase 1 – Beacon exchange Phase 3 – Refinement 2018/3/18

DRLS (cont. ) Beacon Exchange Beacon exchange via two-hop flooding A 4 Normal node DRLS (cont. ) Beacon Exchange Beacon exchange via two-hop flooding A 4 Normal node Near anchor A 3 A 1 N 3 Farther anchor N 2 A 2 N 1 49 2018/3/18

DRLS (cont. ) Improved Grid-Scan Algorithm n Calculate the overlapping rectangle up side N DRLS (cont. ) Improved Grid-Scan Algorithm n Calculate the overlapping rectangle up side N A 1 50 A 3 A 2 left side down side right side Anchor node Normal node 2018/3/18

DRLS (cont. ) Improved Grid-Scan Algorithm Divide the ER into small grids The initial DRLS (cont. ) Improved Grid-Scan Algorithm Divide the ER into small grids The initial value of the grid is 0 A 1 51 0 0 N 0 0 0 0 A 3 A 2 Anchor node Normal node Estimative location 2018/3/18

DRLS (cont. ) Improved Grid-Scan Algorithm n Initial estimative location n Apply centroid formula DRLS (cont. ) Improved Grid-Scan Algorithm n Initial estimative location n Apply centroid formula to grids with the maximum grid value A 1 52 1 2 N 3 3 N’ 3 2 2 2 1 2 2 3 3 3 2 2 A 3 A 2 Anchor node Normal node Estimative location 2018/3/18

DRLS (cont. ) Refinement Repulsive virtual force (VF) 53 Induced by farther anchor nodes DRLS (cont. ) Refinement Repulsive virtual force (VF) 53 Induced by farther anchor nodes Dinvasion : the maximum distance that the farther anchor invades the estimative region along the direction from the farther anchor towards the initial estimative location 2018/3/18

DRLS (cont. ) Refinement VFi : virtual force induced by farther anchor i Dinvasioni DRLS (cont. ) Refinement VFi : virtual force induced by farther anchor i Dinvasioni : the maximum distance that the farther anchor i invades the estimative region along the direction from i towards A 4 the initial estimative location Vi, j : the unit vector in the Dinvasion. A 4 direction from the farther anchor VFA 5 A 2 VFA 3 i towards the initial estimative n A 3 asio N’ Dinv location j A 1 NDinvasion. A 5 A 3 VFA 4 VFi = Vi, j˙Dinvasioni A 5 54 2018/3/18

DRLS (cont. ) Refinement Resultant Virtual Force (RVF) RVF = ΣVFi A 4 A DRLS (cont. ) Refinement Resultant Virtual Force (RVF) RVF = ΣVFi A 4 A 2 A 3 A 1 RVF N’ N’N A 5 55 2018/3/18

DRLS (cont. ) Refinement n Di : the moving distance caused by the farther DRLS (cont. ) Refinement n Di : the moving distance caused by the farther anchor i Dimax : the maximum moving distance caused by the farther anchor i Di Dimax = Dinvasioni a A 4 Dinvasion. A 3 max A 2 b c A 3 Dinvasionimax e d N’ A 1 L 3 f N DA 3 max A 5 Dinvasion. A 3 56 2018/3/18

DRLS (cont. ) Refinement Dmovei : the moving vector caused by the farther anchor DRLS (cont. ) Refinement Dmovei : the moving vector caused by the farther anchor i Vi, j : the unit vector in the A 4 direction from the farther anchor i towards the initial estimative Dinvasion location j Dmove. A 5 A 2 Dmove. A 3 n asio Dmovei = Vi, j˙Di N’ N Dinv A 4 A 3 A 1 A 3 Dmove. A 4 Dinvasion. A 5 estimative region 57 2018/3/18

DRLS (cont. ) Refinement Dmove: the final moving vector Dmove = Σ Dmovei A DRLS (cont. ) Refinement Dmove: the final moving vector Dmove = Σ Dmovei A 4 A 2 A 3 A 1 Dmove N’ N’N A 5 58 2018/3/18

IMCL Improved MCL Localization Scheme Improvements 59 Dynamic number of samples According to the IMCL Improved MCL Localization Scheme Improvements 59 Dynamic number of samples According to the overlapping region of anchor constraints Restricted samples Anchor constraints The estimative locations of neighboring normal nodes Predicted moving direction of the normal node Be used to increase the localization accuracy 2018/3/18

IMCL (cont. ) Phase 2 - Neighbor Constraints Exchange Phase 60 Phase 1 - IMCL (cont. ) Phase 2 - Neighbor Constraints Exchange Phase 60 Phase 1 - Sample Selection Phase 3 - Refinement Phase 2018/3/18

IMCL (cont. ) Sample Selection Phase Dynamic sample number Sampling Region The overlapping region IMCL (cont. ) Sample Selection Phase Dynamic sample number Sampling Region The overlapping region of anchor constraints Difficult to calculate Estimative Region (ER) A rectangle surrounding the sampling region R R A 3 R N A 1 A 2 ER 61 2018/3/18

IMCL (cont. ) Sample Selection Phase The number of samples ( k ) R IMCL (cont. ) Sample Selection Phase The number of samples ( k ) R R k ≦ Max_Num R k= A 1 A 3 N A 2 ER • ERArea — the area of ER • ERThreshold — the threshold value • Max_Num — the upper bound of sample number In our simulations, ERThreshold = 4 R 2 62 2018/3/18

IMCL (cont. ) Sample Selection Phase Using the prediction and filtering phase of MCL IMCL (cont. ) Sample Selection Phase Using the prediction and filtering phase of MCL 63 Samples are randomly selected from the region extended Vmax from previous samples Filter new samples Near anchor constraints Farther anchor constraints 2018/3/18

IMCL (cont. ) Effective Location Estimation An additional normal nodes constraint Samples must locate IMCL (cont. ) Effective Location Estimation An additional normal nodes constraint Samples must locate on the communication region of neighboring normal nodes The localization error may increase Send the possible location region to neighbors instead of the estimative position EN 1 EN 2 N 3 64 2018/3/18

IMCL (cont. ) Neighbor Constraints Exchange Phase The possible location region The distribution of IMCL (cont. ) Neighbor Constraints Exchange Phase The possible location region The distribution of samples are selected in phase I 135° 180° 90° (Cx , Cy) 225° 45° 0° Step 1: Sensor A constructs a coordinate axis and uses (Cx , Cy) as origin Step 2: The coordinate axis is separated into eight directions 315° 270° 65 Central position in phase 1 2018/3/18

IMCL (cont. ) Neighbor Constraints Exchange Phase 135° Step 3: The samples are also IMCL (cont. ) Neighbor Constraints Exchange Phase 135° Step 3: The samples are also divided into eight groups according to the angle θ with (Cx , Cy) 90° 45° θ 180° (Cx , Cy) 225° (Sx , Sy) 0° 315° 270° Valid samples in current time slot 66 Central position in phase 1 2018/3/18

IMCL (cont. ) Neighbor Constraints Exchange Phase 135° 90° 180° 45° Step 4: Using IMCL (cont. ) Neighbor Constraints Exchange Phase 135° 90° 180° 45° Step 4: Using the longest distance within group as radius to perform sector 0° 225° 315° 270° the possible location region described by eight sectors and (Cx , C y) Sample in the this time slot 67 Central position in phase 1 2018/3/18

IMCL (cont. ) Neighbor Constraints Exchange Phase Neighbor constraint Extend R from the possible IMCL (cont. ) Neighbor Constraints Exchange Phase Neighbor constraint Extend R from the possible located region 90° 45° 135° Each sensor broadcasts its neighbor constraint region once R 180° (Cx , Cy) Neighbor constraint 315° 225° 68 0° 270° 2018/3/18

IMCL (cont. ) Refinement Phase Samples are filtered When sample is not satisfy the IMCL (cont. ) Refinement Phase Samples are filtered When sample is not satisfy the constraints 69 Neighbor constraints Receive from neighboring normal nodes Moving constraint Predict the possible moving direction Normal node generates a valid sample to replace it 2018/3/18

IMCL (cont. ) Refinement Phase Neighbor constraints 70 Sample S 1 is a valid IMCL (cont. ) Refinement Phase Neighbor constraints 70 Sample S 1 is a valid sample Satisfied both neighbor constraints of N 2 and N 3 Sample S 2 is a invalid sample Only satisfied the neighbor constraint of N 3 S 2 S 1 2018/3/18

IMCL (cont. ) Refinement Phase Moving constraint The prediction of nodes moving direction is IMCL (cont. ) Refinement Phase Moving constraint The prediction of nodes moving direction is [θ±ΔΦ ] In time slot t if (Cx , Cy) is located in {θ±ΔΦ} from Et-2 Prediction is right Δ Φ θ Et-2 71 Et-1 (Cx , Cy) if (Cx , Cy) is located outside of {θ±ΔΦ} from Et-2 Δ Φ Prediction is wrong Thus, we do not adopt the moving (Cx , Cy) constraint! 2018/3/18

IMCL (cont. ) Refinement Phase Sample 1 Sample 2 Δ Φ θ Et-1 If IMCL (cont. ) Refinement Phase Sample 1 Sample 2 Δ Φ θ Et-1 If prediction is right, sample must be located in {θ±ΔΦ} from Et-2 Sample 1 satisfies moving constraint Sample 2 does not satisfy moving constraint (Cx , Cy) Δ Φ Et-2 72 2018/3/18

IMCL (cont. ) Estimative Position Normal node calculates the estimative position Et (Ex , IMCL (cont. ) Estimative Position Normal node calculates the estimative position Et (Ex , Ey) of samples 73 Ex = Ey = 2018/3/18

Conclusions Determining location or position is a really important function in WSN, but fraught Conclusions Determining location or position is a really important function in WSN, but fraught with many errors and shortcomings 74 Range estimates often not sufficiently accurate Many anchors are needed for acceptable results Anchors might need external position sources (GPS) 2018/3/18

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References 76 N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost Outdoor Localization References 76 N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost Outdoor Localization For Very Small Devices, ” IEEE Personal Communications Magazine, 7(5): 28– 34, 2000. C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks, ” In Proceedings of the Annual USENIX Technical Conference, Monterey, CA, 2002. A. Savvides, C. -C. Han, and M. Srivastava. “Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors, ” Proceedings of the 7 th Annual International Conference on Mobile Computing and Networking, pages 166– 179. ACM press, Rome, Italy, July 2001. S. Simic and S. Sastry, “Distributed localization in wireless ad hoc networks, ” UC Berkeley, Tech. rep. UCB/ERL M 02/26, 2002. D. Niculescu and B. Nath. “Ad Hoc Positioning System (APS)”. In Proceedings of IEEE Globe. Com, San Antonio, AZ, November 2001. C. Savarese, J. M. Rabaey, and J. Beutel. “Locationing in Distributed Ad-Hoc Wireless Sensor Networks”. In Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP 2001), Salt Lake City, Utah, May 2001. 2018/3/18

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