1. Chapter 7 Localization & Positioning
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2. 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
Anchor nodes that know their position
Directly adjacent nodes
Over multiple hops
本篇的大綱主要是使用節點定出實體位置的座標或是表示性的位置(例如:客廳)
通常以下列參數來協助計算:
錨節點來得知他們的位置
鄰近節點
透過多次的傳送
以距離或角度的方式來定位
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3. Outline 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
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4. 7.1 Properties of localization and positioning procedures
Physical position versus logical location
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, …)
在定位的基礎下,我們通常需要取得的資訊為實體位置或邏輯的位置
座標系統: 方位
參考位置: 位置
若需要取得絕對座標,必須要有錨節點 (兩點可定出位置)
計算節點資訊的方式分為兩種,集中式或是分散式計算
範圍有很多種,大致上分為室內,室外以及全區域,但是在不同區域又有不同的限制
像是使用GPS的情況,由於室內無法接收到衛星的訊號,所以無法在室內使用
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5. 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
Costs, energy consumption, …
在定位上我們常會考量的分析大致分為三類:
正確性
評估的位置離實際位置的差距,透過計算的方式可以評估出大致上的位置
精確度
重複的定位,是否能在最短的時間達到正確的位置,直到越來越精確為止
成本,能量消耗
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6. 7.2 Possible approaches 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
Angulation: when angles between nodes are used
Scene analysis
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
to bound the possible positions of a node
常見的方法:
計算鄰近值: 節點透過anchor來決定鄰近的位置,藉由anchor與節點之間的距離或角度來計算
點定位或是角定位:
透過節點彼此的距離來定位
透過節點彼此的角度來定位
影像分析法: 透過鏡頭所捕捉到的影像來做定位,ex:RADAR,類似雷達圖形的方式來評估出距離與大致位置
Bounding box : 與多點定位法類似,不過將“圓半徑”改為方形的邊長
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7. 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)
鄰近點
使用鄰近捷點的相關資訊來計算
使用鄰近節點的資訊
利用有限範圍的通訊
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8. Trilateration and triangulation (range-based approach)
(Tri-/Multi-)lateration and angulation
Using geometric properties
Lateration: distances between entities are used
Angulation: angle between nodes are used
多點定位法(邊)
點定位或是角定位:
透過節點彼此的距離來定位
透過節點彼此的角度來定位
圖1: 三個節點發送出廣播,中間的交會點則會有交集區得知目標位置
圖2:透過節點發出的有向性訊號來得知與目標之間的夾角,藉此計算出位置
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9. Trilateration and triangulation (cont.) Determining distances
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 (ToA), and Time Difference of Arrival (TDoA).
使用多點定位的方法時,錨節點需要距離來評估位置
利用已存在的無線節點來做定位,是最好的方式
常見的方法為,RSSI,ToA,TDoA
1.RSSI大致上是使用訊號強度來評估出距離
2.ToA則是使用無線電波發送訊號,以到達目標並且傳回訊號的”時間”做為評估距離的資訊
3.TDoA則是與ToA類似,但不同的部分則是以多種不同的無線波(ex:超音波,無線電波),並藉此計算出更精準的資訊
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10. Distance estimation RSSI (Received Signal Strength Indicator)
Send out signal of known strength, use received signal strength and path loss coefficient to estimate distance
使用傳送出去的訊號強度,並透過回傳的訊號強度與路徑損耗的係數來評估距離
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11. Distance estimation RSSI (cont.)
Problem: Highly error-prone process :
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!
RSSI容易發生的錯誤
有易錯的問題
問題1: 在移動性高的環境中,容易訊號衰弱
解決方法: 持續的做測量並且過濾出錯誤的數值
相對的,所花費的時間相對提高
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12. Distance estimation RSSI (cont.)
Signal strength
PDF
PDF(機率密度函數) 特性: a. 總和為1 b.單一機率不大於1
PDF of distances in a given RSSI value
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13. Distance estimation ToA (Time of arrival )
Use
time of transmission,
propagation speed
Problem: Exact time synchronization
Usually, sound wave is used
But propagation speed of sound depends on temperature or humidity
ToA:使用無線電波發送訊號,以到達目標並且傳回訊號的”時間”做為評估距離的資訊
使用 1. 傳輸的時間 2.散佈的速度 來評估距離
問題: 確切的時間同步性
通常使用超音波
但是聲波廣播的速度會受溫溼度所影響
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14. Distance estimation TDoA (Time Difference of Arrival )
Use two different signals with different propagation speeds
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
TDoA
使用兩種不同的訊號來取得不同的廣播速度
計算兩種方法的ToA來計算距離
例如: 超音波與無線電波
超音波與無線電波的傳送時間可以忽略
問題:昂貴,需要高度能量的硬體設備
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15. Scene analysis
RADAR system: Comparing the received signal characteristics from multiple anchors with premeasured and stored characteristics values.
Radio environment has characteristic “fingerprints”
The necessary off-line deployment for measuring the signal landscape cannot always be accommodated in practical systems.
Scene analysis:
分析影像中的特徵內容來取得實際的位置並且透過節點來測量位置
利用監視器拍攝並利用影像處理的方法，尋找出移動或使用者之位置
Ex:RADAR為透過此方法做為架構的定位演算法,使用雷達圖的方式來評估出以發送訊號的anchor為中心,計算出與anchor相對關係與距離
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16. Bounding Box
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 2di (where d is the estimated distance) and with coordinates (xi –di, yi–di) and (xi+di, yi+di).
Bounding box
BB的方法提出以正方形來取代圓形的通訊半徑
來圍出可能節點的位置
參考節點 i ,以節點的通訊半徑di 的兩倍來定出正方形的邊長
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17. Bounding Box (cont.)
Using range to anchors to determine a bounding box
Use center of box as
position estimate B C
使用錨來範圍出定義的Bounding Box
原本是使用圓形,現在則改成使用正方形的方式,如此一來則較方便計算之間的距離
在使用ER的時候也更方便將中心區域分割成小區域(計算交疊次數算權重值) d A
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18. References
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 7th 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 M02/26, 2002.
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19. 7.3 Mathematical basics for the lateration problem
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20. Solution with three anchors and correct distance values
Assuming distances to three points with known location are exactly given
Solve system of equations (Pythagoras!)
(xi , yi) : coordinates of anchor point i,
ri : distance to anchor i
(xu, yu) : unknown coordinates of node
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21. Solution with three anchors and correct distance values (cont.)
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22. Trilateration as matrix equation
Rewriting as a matrix equation:
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23. 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,
i.e,
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24. 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 0
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25. 7.4 Positioning in multi-hop environments
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26. Connectivity in a multi-hop network
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
假設已經知道n anchors的位置，以及m nodes放置完成
任意兩個節點在R範圍內，則具有通訊能力
事實上，任兩節點的通訊帶出了限制的可行性問題
兩個連接的節點，則放置位置不能超過R的範圍
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27. Multi-hop range estimation
How to estimate range to a node to which no direct radio communication exists?
No RSSI, TDoA, …
But: Multi-hop communication is possible
如何評估無指向性的無線通訊中的節點?
不使用RRSI與TDoA這類的指向性方法
但是,可以使用多點傳輸的方式來實行
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28. Multi-hop range estimation (cont.)
Idea 1: (DV-Hop) Start by counting hops between anchors then divide known distance
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.
方法1:
計數hops的數量，假設一個hop的距離長度是已知的
計數anchors之間的hops，並且劃分節點之間的距離
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29. DV Hop So do L2 and L3 : L1 calculates average hope length :
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.
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30. DV-Distance
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.
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31. Multi-hop range estimation (cont.) 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
在密集的網路中，使用最短路徑的hop
來計算出趨近於兩點間的距離
缺點 : 需要大量的通訊
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32. Discussion Number of anchors Uniformly distributed network
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
Uniformly distributed network
Distance vector methods perform less well in non-uniformly networks
Euclidean method is not very sensitive to this effect
Anchor的數量
Euclidean method 隨著anchor的數量上升以增加準確性
distance vector 的方法，較合適數量較少的anchors
平均分散網路
Distance vector methods在非等向的網路中是不盡理想的
Euclidean method並沒有顯著的結果
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33. 7.5 Positioning assisted by anchors
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34. 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:
inquire all its neighbors about their distance to the given three corner anchors
使用單純的連通性資訊
想法:使用任意三個anchor圍成三角形來決定所要定位的節點在內部還是外部
無論如何,移動的一個發送節點比較沒辦法有效率的去定出他的位置
解決方法: 確認所有鄰近節點彼此的位置後,大約在角落的地方給定三個anchor節點
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35. 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 C B M
APIT使用AoA的方式來做
三角形內部
無論節點移動至哪個方向,該節點必須靠近至少一個角落
透過接近的程度來決定出離哪一個anchor節點較近
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36. APIT (cont.) Outside a triangle:
There is at least one direction for which the node’s distance to all corners increases M A B C
若M點在三角形之外的情況
若移動到三角形之外後,另外會有新的三個anchor節點來定位它
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37. APIT (cont.)
Approximation: Normal nodes test only directions towards neighbors
比較RSSI值大小
只要neighbor中有一個是同時遠離三角形的三個頂點, 就是out
Propositions I: If M is inside triangle ΔABC, when M is shifted in
any direction, the new position must be nearer to ( further from)
at least one anchor A, B or C. (Figure 2A)
Proposition II: If M is outside triangle ΔABC, when M is shifted,
there must exist a direction in which the position of M is further
from or closer to all three anchors A, B and C. (Figure 2B).
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38. APIT (cont.) Grid-Based Aggregation
Narrow down the area where the normal node can potentially reside 2 1
先把三邊經過的格子都加1, 再把中間區域加1
為何不在三角形中要減1-可能還有另一個正的三角形區域與它重疊
可講scan整個網路? no
A node’s presence inside or outside of these triangular regions allows a node to narrow down
the area in which it can potentially reside.
anchor node
normal node
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39. 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 two- hop neighbors
Notation
R - communication range
以下介紹一個用在mobile sensor中的定位方法, Monte-Carlo 定位方法, 為了讓定位問題變的更簡單, 有幾項基本假設:
1. 時間分為很多個time slot.
2. 每個time slot會重複算一次自己的位置.
3. 每個time slot, node移動距離是介於 [0, Vmax] 的區間內.
4. 每個Anchor node定期廣播自己的location位置給2-hop鄰居.
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40. MCL (cont.) Each normal node maintains 50 samples in each time slot
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
在MCL中, 每個normal node 在每個time slot中　維持 50個samples,
每一個sample是一個座標位置, 代表這個normal node可能的位置.
由於normal node是持續的移動, 所以這個time slot的sample會與上一個time slot的sample 有一定的距離關係, 因此sample選擇的位置, 與上一個time slot的sample有關.
這些sample位置必須滿足三個條件, 必須要落在anchor constraint中
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41. MCL (cont.) Anchor constraints Near anchor constraint
The communication region of one-hop anchor node ( near anchor )
Farther anchor constraint
The region within ( R , 2R ] centered on two-hop anchor ( farther anchor )
Near anchor constraint R A1 N1 R
Farther anchor constraint A1
前面有提到 anchor定期broadcast封包給兩步鄰居內的node, 當有一個normal node N1 是anchor node A1的one-hop neighbor, 我們稱 則anchor A1 為 N1的near anchor, 且Node N1位置必定在A1的通訊範圍內, 則A1的通訊範圍稱為N1的near anchor constraints, 所有的N1的 sample
都必須落在near constraint中. 同理, 假設有一個normal node 是A1的two-hop neighbor, near constraint中. 同理, 假設有一個normal node N2是A1的
two-hop neighbor, 則N2一定不會落在A1的通訊範圍內, 但會落在2R範圍之內, 因此, (R, 2R ] 所為成的區域稱為farther anchor constraints, 並且
N2的sample比需落在此區域中. N1 N2
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42. MCL (cont.) Environment
Anchor node
Normal node A1 A2 A3 A4 N1
舉一個例子,
N1為想要定位的節點，
A1~A4為Global anchor，
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43. MCL (cont.) Initial Phase
Sample in the last time slot
Anchor node
Normal node N1 A1 A2 A3 A4
一開始N1會在整個field裡找出50個sample，
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44. MCL (cont.) Prediction Phase & Filtering Phase
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
Vmax R A1 A2 A3 A4 R N1
接著N1會去找附近的anchor，
先找到near anchor A2，再找到further anchor A1，
由A1和A2的範圍得到N1目前可能的位址範圍在兩個range的交會點。
接著開始預測sample的下個位置並過濾可能的sample。
假設亮綠色的sample有可能的下一個位置為淺藍色的，
此時淺藍色的這個sample並不在可能的範圍內，
因此會把他過濾掉。
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45. MCL (cont.) Prediction Phase & Filtering Phase
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
Vmax A1 A2 A3 A4
Vmax R N1 R
Vmax R
假設此時亮綠色的點下一個可能的位置在N1可能的範圍內，便會將此sample保留。
定接著把所有的sample預測完後，找到在N1可能範圍內出現的所有可能sample。
並且當可能的範圍內剩餘的sample數不足50個時會將sample補足到50個。
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46. MCL (cont.) Estimative Location
Sample in this time slot
Estimative position
the average of samples
Anchor node
Normal node A1 A2 A3 A4 N1
EN1
接著會求出所有sample的平均值，此時這個值便是N1目前可能的位置。
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47. MCL (cont.) Repeated Prediction Phase & Filter Phase
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
In the next time slot
Vmax A1 A2 A3 A4 R N1
假設N1繼續移動，他就會繼續用預測及過濾的方式，
從剛剛剩餘的sample裡面繼續過濾出剩餘的sample。
並且當sample數不足時也會繼續產生sample補足到50個sample。
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48. DRLS Distributed Range-Free Localization Scheme
There are three phases in the DRLS algorithm.
Phase 1 – Beacon exchange
Phase 2 – Using improved grid-scan algorithm to get initial estimative location
Phase 3 – Refinement
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49. DRLS (cont.) Beacon Exchange
Beacon exchange via two-hop flooding A4
Normal node
Near anchor N3
Farther anchor A3
Collect at most farther anchors inside 2r communication range
蒐集anchor的資訊,最大的通訊範圍則到2r為止,超過2r的通訊半徑則不使用
If 沒有代傳點, 蒐集不到farther anchor, depend on anchor node density A1 N2 A2 N1
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50. DRLS (cont.) Improved Grid-Scan Algorithm
Calculate the overlapping rectangle
up side
left side
right side N A3
E, F, G 為anchor node, 但不為 farther anchor
透過Bounding Box的方式將所需計算的區域框起來
以ER的方法將淡藍色區域分割 A1 A2
Anchor node
Normal node
down side
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51. DRLS (cont.) Improved Grid-Scan Algorithm
Divide the ER into small grids
The initial value of the grid is 0 A3 N
透過ER的方式將交集的區域ER切割為多個小區塊
一開始所有的小區塊初始化的數值為0
由於交疊處的次數不同繼續做累加 A1 A2
Anchor node
Normal node
Estimative location
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52. DRLS (cont.) Improved Grid-Scan Algorithm
Initial estimative location
Apply centroid formula to grids with the maximum grid value 2 3 A2 A3 A1 1 N N’
Anchor node
Normal node
Estimative location
針對交集的次數來定
由圖所示,交集次數為3的表示越重要的區域,所以以權重的方式來表示
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53. DRLS (cont.) Refinement
Repulsive virtual force (VF)
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
接下來則是使用VF(Virtual Force)虛擬力的方式來將節點移動
最多逼到角落
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54. 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
the initial estimative location
Vi,j : the unit vector in the
direction from the farther anchor
i towards the initial estimative
location j
VFi = Vi,j˙Dinvasioni
VFA4
DinvasionA4 A4
VFA3
DinvasionA3
estimative region A2
VFA5
DinvasionA5
中心位置則為目標點
不同方向的anchor則受VF的影響往目標點拉近以增加定位的精確性
藉由不同的anchor計算出新的VF之後則大致上可評估出目標移動的方向 N’ N A1 A3 A5
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55. DRLS (cont.) Refinement
Resultant Virtual Force (RVF)
RVF = ΣVFi A4
estimative region A2
RVF
合力的公式 N’ N’ N A3 A1 A5
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56. DRLS (cont.) Refinement
Di : the moving distance caused by the farther anchor i A4
DinvasionA3max
DA3max
Dimax : the maximum moving
distance caused by the farther anchor i
estimative region L3 a b c d e f A2
DinvasionA3 N’ Di N
Dinvasioni A1 A3 =
Dimax
Dinvasionimax A5
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57. DRLS (cont.) Refinement
Dmovei : the moving vector caused by the
farther anchor i
Vi,j : the unit vector in the
direction from the farther anchor
i towards the initial estimative
location j
Dmovei = Vi,j˙Di
DmoveA4
DinvasionA4 A4
DmoveA5
DinvasionA5 A2
DmoveA3
DinvasionA3 N’ N A1 A3 A5
estimative region
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58. DRLS (cont.) Refinement
Dmove: the final moving vector
Dmove = Σ Dmovei A4
estimative region A2
Dmove N’ N’ N A3 A1 A5
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59. IMCL Improved MCL Localization Scheme
Improvements
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
我們提出了一個方法叫 Improved MCL 定位方法, 主要有三項改進
Sample number 不再是固定的值, 而是會隨著anchor constraints所交集的區域所改變
Sample 受到兩個限制, 一個是anchor constraint限制, 另外一個則是鄰居的normal node的估計位置
我們也會利用預估normal node的移動方向, 增加定位精準度.
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60. IMCL (cont.) Phase 1- Sample Selection Phase
Phase 2- Neighbor Constraints Exchange Phase
Phase 3- Refinement Phase
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61. 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 A3 R N
首先先進到我們第一個phase- sample selection phase
在這我們先定義一個sample region, 也就是所有anchor constraint的交集區域,
我們希望sample number可以依照sampling region的面積動態調整
但是很顯然的, sample region呈現不規則狀態,對於一個運算能力有限的sensor而言, 計算十分困難.
因此, 我們用一個正方形區域包圍住sample region　叫Estimative Region ER,則sample number隨著ER面積而遞減 A1 A2 ER
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62. IMCL (cont.) Sample Selection Phase
The number of samples ( k ) A1 A2 A3 R ER N
k ≦ Max_Num
k =
ERArea — the area of ER
ERThreshold — the threshold value
Max_Num — the upper bound of sample number
Sample number k的公式, 我們定義三個變數
ER area 代表 ER的面積
ER threshold代表一個threshold值
Max_Num 是sample number的upper bound值
因此, 利用ER area 與 threashold的比直　我們降低sample number的個數.
為了不要讓sample number過多, 我們定義一個max_num. 則max_num是
In our simulations, ERThreshold = 4R2
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63. IMCL (cont.) Sample Selection Phase
Using the prediction and filtering phase of MCL
Samples are randomly selected from the region extended Vmax from previous samples
Filter new samples
Near anchor constraints
Farther anchor constraints
決定Sample number之後, 我們利用MCL的取sample的方法, 取出足夠的sample.
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64. 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
EN1
EN2
Send the possible location region to neighbors instead of the estimative position N1
為了增加定位精準度, 我們希望利用鄰近的normal node 來增加定位精準度,
假設這裡有三個normal node N1 N2 N3,　若 N3收到N1 N2的封包　則N3是落在兩個點的通訊範圍內的交集區域內
但是 normal自己本身有的位置是有誤差的, N1跟N2預估的位置分別在EN1與EN2, N3實際上會認為他在EN1 EN2交集區域內.
因此, 在我們的方法中, normal node不適送出自己估計的位置, 而是送出自己所在可能的範圍, 稱為possible location region. N2 N3
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65. IMCL (cont.) Neighbor Constraints Exchange Phase
The possible location region
The distribution of samples are selected in phase I
Central position in phase 1
45°
135°
225°
315°
90°
270°
180° 0°
(Cx ,Cy)
Step 1: Sensor A constructs a coordinate axis and uses (Cx ,Cy) as origin
Step 2: The coordinate axis is separated into eight directions
The possible location 就是 sample的分佈區域, 因為這塊區域是不規則的無法送出, 所以我們把sample分佈的區域
分成八個區塊送出. 以下就來介紹建立的流程. 首先, 以剛剛那個位置為原點建立一個座標系統, 並且把這麼座標系統分為
八個象限,
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66. IMCL (cont.) Neighbor Constraints Exchange Phase
Step 3: The samples are also divided into eight groups according to the angle θ with (Cx , Cy)
45°
90°
135°
180° 0°
225°
270°
315°
(Sx ,Sy) θ
(Cx ,Cy)
每個sample 利用與中心點的夾角角度為基準, 將sample分為 8個group
Valid samples in current time slot
Central position in phase 1
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67. IMCL (cont.) Neighbor Constraints Exchange Phase
45°
90°
135°
180° 0°
225°
270°
315°
Step 4: Using the longest distance within group as radius to perform sector
在每個group中, 我們挑選出距離中心點最遠的sample, 因此　我們可以挑出 8個sample, 並且以最遠距離為半進　畫一個扇形
則此節點的possible location region就是這八個扇形所為出的面積
the possible location region described by eight sectors and (Cx , Cy)
Sample in the this time slot
Central position in phase 1
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68. IMCL (cont.) Neighbor Constraints Exchange Phase
Extend R from the possible located region
90°
45°
135°
180° 0°
225°
270°
315°
(Cx ,Cy) R
Each sensor broadcasts its neighbor constraint region once
利用possible location region 八個扇形往外延伸 的範圍, 則這塊區域形成neigbor constraint, 舉例而言, 假這這塊區域是normal node N1的Neighbor constraint, 則N2, N3 為node N1的one-hop neighbor,
則node N2 N3 則會落在N1的neighbor constraint中
Neighbor constraint
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69. IMCL (cont.) Refinement Phase
Samples are filtered
Neighbor constraints
Receive from neighboring normal nodes
Moving constraint
Predict the possible moving direction
When sample is not satisfy the constraints
Normal node generates a valid sample to replace it
因此, 當收集鄰近的neighbor constraint, node 進入Refinement phase,
在這個phase中, 在phase 1中選出的sample 被檢查是否符合鄰近的neighbor constraints 與moving constraint.
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70. IMCL (cont.) Refinement Phase
Neighbor constraints
Sample S1 is a valid sample
Satisfied both neighbor constraints of N2 and N3
Sample S2 is a invalid sample
Only satisfied the neighbor constraint of N3 S2 S1
假設Node N1收到鄰近節點N2與N3的constraints, 則N1落在這兩個constraint交集中, 假設S1 與S2為N1ｋ的兩個交點, 很顯然的
只有sample S1落在交集中, 因此只有sample s1為合法的sample, S2則檢查為一個不合法的sample
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71. 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 Prediction is right
if (Cx , Cy) is located outside of {θ±ΔΦ} from Et-2 Prediction is wrong
Thus, we do not adopt the moving constraint!
第二個constraint是moving constraint, 因為在感測網路中, 一般節點的會朝同一個方向持續一段時間, 藉由此特性我們利用前兩個time slot計算的位置,
預估這個time slot可能的方向, 因此, 假設ET-1 ET-2 為time slot t-1和t-2預估的位置, 我們估計node往Et-2 E-t-1這個方向移動的機率比其他方向高但是, Et-1 Et-2是估計的位置, 所以我們放寬移動方向的條件ΔΦ, 所以我們預估node會往 θ±ΔΦ方向移動, 並且把這塊扇形區域稱為moving constraint.
為了確保我們的預估是對的, 剛剛算出的central Point 是這個time slot粗估的位置, 也就是ET粗估的位置, 因此, 若 Et 落在這個方向中, 我們才利用這個moving constraint, 若Et落在這個constraint的外面, 則不採用這個constraints. 在我們的實驗中, ΔΦ 是由實驗來決定
(Cx , Cy)
Et-1 Δ Φ θ
Et-2
(Cx , Cy)
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72. IMCL (cont.) Refinement Phase
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
Sample 1
Sample 2
假設粗估的位置central point落在moving constraint中, 則該node的sample必須符合這個moving constraint,
假設sample 1, 2分別為兩個sample, 很顯然的只有sample 1符合moving constraint, 因此sample 1為一個合法的sample, 相反的
Sample 2 是一個不合法的sample.
Et-1
(Cx , Cy) Δ Φ θ
Et-2
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73. IMCL (cont.) Estimative Position
Normal node calculates the estimative position Et (Ex , Ey) of samples
Ex =
Ey =
　結束Refine phase, node利用最後取出來的sample計算它的估計位置, 估計位置的x y值　同樣是 所有sample的平均值.
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74. Conclusions
Determining location or position is a really important function in WSN, but fraught with many errors and shortcomings
Range estimates often not sufficiently accurate
Many anchors are needed for acceptable results
Anchors might need external position sources (GPS)
結論:
定位的方法目前在WSN中占很重要的地位,但是在計算中常常會產生很多的錯誤
範圍的評估通常不會達到非常精準
大多的方法都需要有anchor的存在
Anchor在定位的時候都必須先有GPS才能做定位,這部分為成本較高的缺點
多點計算的問題,由於很多節點在計算目標位置,所以需要增加精確性
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75. References
J. Hightower and G. Borriello. “Location Systems for Ubiquitous Computing,” IEEE Computer, 34(8): 57–66, 2001.
J. Hightower and G. Borriello. “A Survey and Taxonomy of Location Systems for Ubiquitous Computing,” Technical Report UW-CSE , University of Washington, Computer Science and Engineering, Seattle, WA, August 2001.
A. Boukerche, H. Oliveira, E. Nakamura, and A. Loureiro. “Localization systems for wireless sensor networks”. IEEE Wireless Communications, December 2007.
R. Want, A. Hopper, V. Fal˜ao, and J. Gibbons. The Active Badge Location System. ACM Transactions on Information Systems, 10(1): 91–102, 1992.
A. Ward, A. Jones, and A. Hopper. A New Location Technique for the Active Office. IEEE Personal Communications, 4(5): 42–47, 1997.
P. Bahl and V. N. Padmanabhan. RADAR: An In-Building RF-Based User Location and Tracking System. In Proceedings of the IEEE INFOCOM, pages 775–784, Tel- Aviv, Israel, April 2000.
N. B. Priyantha, A. Chakraborty, and H. Balakrishnan. The Cricket Location- Support System. In Proceedings of the 6th International Conference on Mobile Computing and Networking (ACM Mobicom), Boston, MA, 2000.
2017/4/21

76. References
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,
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 7th 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 M02/26, D. Niculescu and B. Nath. “Ad Hoc Positioning System (APS)”. In Proceedings of IEEE GlobeCom, 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
2017/4/21

77. References
V. Ramadurai and M. L. Sichitiu. “Localization in Wireless Sensor Networks: A Probabilistic Approach”. In Proceedings of 2003 International Conference on Wireless Networks (ICWN 2003), pages 300–305, Las Vegas, NV, June 2003.
M. L. Sichitiu and V. Ramadurai, “Localization of Wireless Sensor Networks with A Mobile Beacon,” Proc. 1st IEEE Int’l. Conf. Mobile Ad Hoc and Sensor Sys., FL, Oct. 2004, pp. 174–83.
N.Bodhi Priyantha, H. Balakrishnan, E. Demaine, S. Teller,”Mobile-Assisted Localization in Sensor Network”, IEEE INFOCOM 2005, Miami, FL, March 2005.
T. He, C. Huang, B. M. Blum, J. A. Stankovic, and T. Abdelzaher. Range-Free Localization Schemes for Large Scale Sensor Networks. Proceedings of the 9th Annual International Conference on Mobile Computing and Networking, pages 81– 95. ACM Press, 2003.
F. Dellaert, D. Fox, W. Burgard, and S. Thrun, "Monte Carlo Localization for Mobile Robots", IEEE International Conference on Robotics and Automation (ICRA), 1999
L. Hu and D. Evans, "Localization for Mobile Sensor Networks," Proc. ACM MobiCom, pp , Sept
2017/4/21

78. References
J.-P. Sheu, P.-C. Chen, and C.-S. Hsu, “A Distributed Localization Scheme for Wireless Sensor Networks with Improved Grid-Scan and Vector-Based Refinement,” IEEE Trans. on Mobile Computing, vol. 7, no. 9, pp , Sept
Jang-Ping Sheu, Wei-Kai Hu, and Jen-Chiao Lin, "Distributed Localization Scheme for Mobile Sensor Networks," IEEE Transactions on Mobile Computing Vol. 9, No. 4, pp , April 2010.
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