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1 Structures for In-Network Moving Object Tracking inWireless Sensor Networks Chih-Yu Lin and Yu-Chee Tseng Broadband Wireless Networking Symp. (BroadNet), 2004.

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2 Outlines Introduction Tree construction algorithms DAT (Deviation-Avoidance Tree) Z-DAT (Zone-based DAT) Simulation Results Conclusion

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3 Introduction message-pruning tree a logical weighted tree such that the total communication cost is as low as possible weight of edge (a, b) : wT(a,b) the minimum hop count between a and b in G event rate the frequency of objects traveling from one sensor to another in statistics detected list : DLa = (L0, L1,..., Lk) each node a in T maintains a detected list DLa L0 is the set of objects currently inside the coverage of sensor a itself

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5 Introduction(Cont.) departure event : dep(o, a, b) arrival event : arv(o, b, a) par(u, v) : the root of the minimum subtree in T that includes both u and v. distT (x, y) : the sum of weights of the edges on the path connecting x and y in T. distT (F,K) = wT (F, I) + wT (I, J) + wT (J,K) = 3, although the minimum hop count between F and K is 2 in G.

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6 cost function of T by counting the number of events transmitted

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7 STUN-Scalable Tracking Using Networked Sensors Hierarchically record information about the presence of the objects. Leaves : sensors Root : query point others : communication nodes. Key action : Message pruning

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8 DAB-Drain-And-Balance Goal : building efficient tracking hierarchies In a bottom-up fashion from leaves to root. Draining threshold : event rate thresholds. Balance : merge the adjacent tree. Method : high rate subsets of leaves merge first. Input : a sensor graph G(V G,E G,l G,w) Out : a hierarchy tree T = (V T,E T,l T ) Draining threshold : H = {h 1,h 2, …,h k }

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9 DAB - Example

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11 Figure 4. Four possible message-pruning trees with the corresponding graph shown in Fig. 1(b). Those trees in (a), (c), and (d) are deviation-avoidance trees.

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12 message-pruning trees The tree in (b) is not a deviation avoidance tree (DAT), since distT(E,A) is 3 and distG(E,A) is 2. The average values of distT (u, par(u, v)) + distT (v, par(u, v)) for each (u, v) ∈ EG are 3.591, 2.864, and in (a), (c), and (d) respectively.

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13 2 message-pruning tree structures DAT (Deviation-Avoidance Tree) a greedy approach based on a deviation- avoidance idea Z-DAT (Zone-based DAT) a grid zone-based approach

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14 DAT To find a tree T that incurs a low C(T), from Eq. 1 and Eq. 2,we would expect T is deviation-free u deviates from its shortest path to the sink each sensor ’ s parent is its neighbor Only the tree shown in Fig. 4(d) satisfies this observation an edge (u, v) with a higher wG(u, v) should be merged into T early and par(u, v) should be either u or v

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15 DAT(Cont1.) edge(u, v) will be included into T only if u and v belong to different subtrees in T. edge(u, v) will be included into T only if at least one of them is a root of a subtree and the other node is on a shortest path in G from the former node to the sink A link passing these checking will then be included into T

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16 DAT(Cont2.) As a result of our construction,T is always a subgraph of G and wT (u, v) = 1 for all (u, v) ∈ ET Theorem 2 : If G is connected, then the T constructed by the DAT algorithm is connected, deviation-free, and is a shortest path tree rooted at the sink.

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18 Z-DAT (Zone-based DAT) Assumes the sensing field to be a square area and takes two input parameters α and δ T is constructed in an iterative manner. Partition the sensing field horizontally and vertically into α strips. for each boundary between strips, it is allowed to move up and down no more than a distance of δ from its original position Totally partitioned into α × α square-like zones, α2 subtrees.

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19 Figure 9. An example of ZDA algorithm with α = 4. (a) In the first iteration, we divide the field into α×α zones and adjust the boundary according to δ. (b) In the second iteration, we divide α by 2 until a single tree is obtained.

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21 Simulation deploy 4096 sensors in a 64 × 64 grid network, one in each grid. a 256 × 256 grid network, 4096 sensors are randomly deployed. the sensing field to be a square of size r × r level-1 regions : divides the sensing field into four sub-regions probability p1 : leave its current leavel-1 region probability 1 − p1 : stay in its current leavel-1 region

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22 Simulation(Cont1.) level-2 regions : each level-1 region is recursively divided into four smaller sub-regions probability p2 : leave its current leavel-2 region probability 1 − p2 : stay in its current leavel-2 region Level-i region : an exponential probability C is a positive constant d is the total number of levels a higher C will exhibit higher locality in movement

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23 Simulation(Cont2.) consider two performance metrics updating cost C(T) querying cost Q(T) : the cost spent on transmitting querying requests and replies when objects ’ locations are inquired from the sink only count the numbers of messages without considering message sizes

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24 Simulation(Cont3.) Compare 2 scheme non-message-pruning tree scheme always sends all location updates to the sink through the shortest path the sink always has the most up-to-date information has no querying cost, but may incur high updating cost

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25 Simulation(Cont4.) DAB assumes that all sensors are leaf nodes of the message-pruning tree there is a logical tree to connect these leaf nodes assume that whenever a new subtree is formed by DAB, the sensor that is closest to the sink will be the root of the subtree

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26 Results compare the updating costs C(T) generate 64 objects and adopt the 5-step DAB tree construction Z-DAT, we set α = 20 and δ = 1 grid. Fig. 10(a) (b) (c) (d) A larger C, i.e. a higher moving locality, leads to lower updating cost. The non-message-pruning scheme has the highest cost because each movement will incur a lot of update messages.

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28 Results(Cont1.) compare the querying cost Q(T) Fig. 11 The querying cost generally increases linearly with the querying rate. There is no querying cost for the non-message- pruning scheme. The querying costs for DAT and Z-DAT schemes are always the same because querying messages are always transmitted along shortest paths Not using shortest paths, DAB has higher Q(T) that depends on the tree structure in DAB.

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30 Results(Cont2.) combined updating and querying costs Fig. 12 as the querying rate becomes higher, using message-pruning tree will gradually lose its advantage because non-message-pruning scheme has no querying cost as C becomes smaller, objects will move more frequently, thus leading to more saving in using DAB/DAT/Z-DAT

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31 Figure 12. Comparison of combined (updating plus querying) costs in a 64 × 64 grid: (a) sink at a corner and C = 1.0, (b) sink at the center and C = 1.0, (c) sink at a corner and C = 0.1, and (d) sink at the center and C = 0.1.

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32 Conclusion Present 2 message-pruning structures for moving object tracking in a sensor network.

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