Towards a Unified View of Localization in Wireless Sensor Networks
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1 Towards a Unified View of Localization in Wireless Sensor Networks Suprakash Datta Joint work with Stuart Maclean, Masoomeh Rudafshani, Chris Klinowski and Shaker Khaleque York University, Toronto, Canada December 3, 2008 S. Datta (York Univ.) Sensor network localization December 3, / 31
2 York University CSE S. Datta (York Univ.) Sensor network localization December 3, / 31
3 Roadmap 1 Localization in sensor networks 2 Related work Algorithm MSL* Algorithm EASeL 3 Analytical results 4 Ongoing and future work S. Datta (York Univ.) Sensor network localization December 3, / 31
4 Sensor network localization Uses: Topology maintenance. Clustering. Routing. Event detection. Motion planning. Many other uses... S. Datta (York Univ.) Sensor network localization December 3, / 31
5 The localization problem Want to find locations of sensors. S. Datta (York Univ.) Sensor network localization December 3, / 31
6 The localization problem Want to find locations of sensors. Use global co-ordinates. S. Datta (York Univ.) Sensor network localization December 3, / 31
7 The localization problem Want to find locations of sensors. Use global co-ordinates. Manual entry of locations not feasible. S. Datta (York Univ.) Sensor network localization December 3, / 31
8 The localization problem Want to find locations of sensors. Use global co-ordinates. Manual entry of locations not feasible. Some nodes (seeds) can self-localize. S. Datta (York Univ.) Sensor network localization December 3, / 31
9 The localization problem Want to find locations of sensors. Use global co-ordinates. Manual entry of locations not feasible. Some nodes (seeds) can self-localize. Nodes communicate with each other. S. Datta (York Univ.) Sensor network localization December 3, / 31
10 The localization problem Want to find locations of sensors. Use global co-ordinates. Manual entry of locations not feasible. Some nodes (seeds) can self-localize. Nodes communicate with each other. Nodes may move with speeds up to v max. S. Datta (York Univ.) Sensor network localization December 3, / 31
11 The localization problem Want to find locations of sensors. Use global co-ordinates. Manual entry of locations not feasible. Some nodes (seeds) can self-localize. Nodes communicate with each other. Nodes may move with speeds up to v max. Nodes may have ranging capability. S. Datta (York Univ.) Sensor network localization December 3, / 31
12 Our model and assumptions 2-dimensional sensor field. S. Datta (York Univ.) Sensor network localization December 3, / 31
13 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. S. Datta (York Univ.) Sensor network localization December 3, / 31
14 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. S. Datta (York Univ.) Sensor network localization December 3, / 31
15 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. S. Datta (York Univ.) Sensor network localization December 3, / 31
16 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. Reliable MAC layer. S. Datta (York Univ.) Sensor network localization December 3, / 31
17 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. Reliable MAC layer. Do not know speed or direction of motion*. S. Datta (York Univ.) Sensor network localization December 3, / 31
18 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. Reliable MAC layer. Do not know speed or direction of motion*. Nodes know the radio range. S. Datta (York Univ.) Sensor network localization December 3, / 31
19 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. Reliable MAC layer. Do not know speed or direction of motion*. Nodes know the radio range. Radio range is a circle*. S. Datta (York Univ.) Sensor network localization December 3, / 31
20 Our model and assumptions 2-dimensional sensor field. A (small) fraction of nodes are seeds. No routing infrastructure available. Reasonable time synchronization available. Reliable MAC layer. Do not know speed or direction of motion*. Nodes know the radio range. Radio range is a circle*. Want distributed algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
21 Categorizing Existing Algorithms The important axes are Mobility. S. Datta (York Univ.) Sensor network localization December 3, / 31
22 Categorizing Existing Algorithms The important axes are Mobility. Ranging ability. S. Datta (York Univ.) Sensor network localization December 3, / 31
23 Categorizing Existing Algorithms The important axes are Mobility. Ranging ability. Communicating quality of location estimate. S. Datta (York Univ.) Sensor network localization December 3, / 31
24 Categorizing Existing Algorithms The important axes are Mobility. Ranging ability. Communicating quality of location estimate. ranging quality mobility S. Datta (York Univ.) Sensor network localization December 3, / 31
25 Categorizing Existing Algorithms The important axes are Mobility. Ranging ability. Communicating quality of location estimate. ranging Ranging: Nodes can measure distances to neighbors using extra hardware. Trilateration/multi-lateration; least square error fit to data. mobility quality S. Datta (York Univ.) Sensor network localization December 3, / 31
26 Categorizing Existing Algorithms The important axes are Mobility. Ranging ability. Communicating quality of location estimate. ranging mobility Ranging: Nodes can measure distances to neighbors using extra hardware. Trilateration/multi-lateration; least square error fit to data. More accurate localization in high seed densities. quality S. Datta (York Univ.) Sensor network localization December 3, / 31
27 Categorizing Existing Algorithms The important axes are quality Mobility. Ranging ability. Communicating quality of location estimate. ranging mobility Ranging: Nodes can measure distances to neighbors using extra hardware. Trilateration/multi-lateration; least square error fit to data. More accurate localization in high seed densities. Range-free algorithms: Nodes only know who its neighbors are.. S. Datta (York Univ.) Sensor network localization December 3, / 31
28 Categorizing Existing Algorithms The important axes are quality Mobility. Ranging ability. Communicating quality of location estimate. ranging mobility Ranging: Nodes can measure distances to neighbors using extra hardware. Trilateration/multi-lateration; least square error fit to data. More accurate localization in high seed densities. Range-free algorithms: Nodes only know who its neighbors are.. Less complex hardware. S. Datta (York Univ.) Sensor network localization December 3, / 31
29 Categorizing Existing Algorithms The important axes are quality Mobility. Ranging ability. Communicating quality of location estimate. ranging mobility Ranging: Nodes can measure distances to neighbors using extra hardware. Trilateration/multi-lateration; least square error fit to data. More accurate localization in high seed densities. Range-free algorithms: Nodes only know who its neighbors are.. Less complex hardware. Less affected by radio noise. S. Datta (York Univ.) Sensor network localization December 3, / 31
30 Trilateration/Multilateration Very simple idea. S. Datta (York Univ.) Sensor network localization December 3, / 31
31 Trilateration/Multilateration Very simple idea. Problem: the multi-hop case. S. Datta (York Univ.) Sensor network localization December 3, / 31
32 Trilateration/Multilateration Very simple idea. Problem: the multi-hop case. S. Datta (York Univ.) Sensor network localization December 3, / 31
33 Range-free algorithm 1 (Algorithm dv-hop/gradient) Designed for static networks Steps: 1 Seeds transmit their positions to all nodes. 2 Other nodes record their distances to seeds in hops. 3 Optional: Distances between seeds are used to compute average per hop distance. 4 The (approximate) distances to seeds are used in multilateration. Comments Rather sensitive to seed density. Needs multihop transmission of packets. With the optional phase, the algorithm is relatively slow. S. Datta (York Univ.) Sensor network localization December 3, / 31
34 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? S. Datta (York Univ.) Sensor network localization December 3, / 31
35 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? Example: range-free algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
36 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? Example: range-free algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
37 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? Example: range-free algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
38 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? Example: range-free algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
39 Uniform view of localization information Information as constraints What does it tell us? What constraints does it impose on locations? Example: range-free algorithms. S. Datta (York Univ.) Sensor network localization December 3, / 31
40 Range-free information as constraints - continued Multiple hops. Using negative information. Using non-seeds. Incorporating mobility. S. Datta (York Univ.) Sensor network localization December 3, / 31
41 Range-based information as constraints Ranging error. S. Datta (York Univ.) Sensor network localization December 3, / 31
42 Range-based information as constraints Ranging error. S. Datta (York Univ.) Sensor network localization December 3, / 31
43 Range-based information as constraints Ranging error. S. Datta (York Univ.) Sensor network localization December 3, / 31
44 Range-based information as constraints Ranging error. S. Datta (York Univ.) Sensor network localization December 3, / 31
45 Range-based information as constraints Ranging error. Multiple hops. Using negative information. Using non-seeds. Incorporating mobility. S. Datta (York Univ.) Sensor network localization December 3, / 31
46 Differences between algorithms Position on ranging axis. Range-free: MCL [Evans-HU 04], MCL-B [Baggio-Langendoen 08], dv-hop [Niculescu et al 01],polygon [Datta et al 06]; ranging: MCL-R [Dil-Havinga 06]; anywhere: MSL/MSL* [Rudafshani-Datta 07], EASeL [Maclean-Datta 08]. S. Datta (York Univ.) Sensor network localization December 3, / 31
47 Differences between algorithms Position on ranging axis. Range-free: MCL [Evans-HU 04], MCL-B [Baggio-Langendoen 08], dv-hop [Niculescu et al 01],polygon [Datta et al 06]; ranging: MCL-R [Dil-Havinga 06]; anywhere: MSL/MSL* [Rudafshani-Datta 07], EASeL [Maclean-Datta 08]. Position on mobility axis. Static: dv-hop; mobile: MCL, MCLB; anywhere: polygon, MSL/MSL*, EASeL. S. Datta (York Univ.) Sensor network localization December 3, / 31
48 Differences between algorithms Position on ranging axis. Range-free: MCL [Evans-HU 04], MCL-B [Baggio-Langendoen 08], dv-hop [Niculescu et al 01],polygon [Datta et al 06]; ranging: MCL-R [Dil-Havinga 06]; anywhere: MSL/MSL* [Rudafshani-Datta 07], EASeL [Maclean-Datta 08]. Position on mobility axis. Static: dv-hop; mobile: MCL, MCLB; anywhere: polygon, MSL/MSL*, EASeL. Maintaining error estimates. None: dv-hop. Regions: Bounding boxes [Shastri et al 99?], polygons [Datta et al 06], Curved regions [Guha et al 05], sampled points [MCL,MCL-B, MCL-R,MSL,MSL*,EASeL]. S. Datta (York Univ.) Sensor network localization December 3, / 31
49 Differences between algorithms Position on ranging axis. Range-free: MCL [Evans-HU 04], MCL-B [Baggio-Langendoen 08], dv-hop [Niculescu et al 01],polygon [Datta et al 06]; ranging: MCL-R [Dil-Havinga 06]; anywhere: MSL/MSL* [Rudafshani-Datta 07], EASeL [Maclean-Datta 08]. Position on mobility axis. Static: dv-hop; mobile: MCL, MCLB; anywhere: polygon, MSL/MSL*, EASeL. Maintaining error estimates. None: dv-hop. Regions: Bounding boxes [Shastri et al 99?], polygons [Datta et al 06], Curved regions [Guha et al 05], sampled points [MCL,MCL-B, MCL-R,MSL,MSL*,EASeL]. Use of non-seeds - exchange region [polygon], samples [MSL*] or location+error [MSL, EASeL]? S. Datta (York Univ.) Sensor network localization December 3, / 31
50 Differences between algorithms Position on ranging axis. Range-free: MCL [Evans-HU 04], MCL-B [Baggio-Langendoen 08], dv-hop [Niculescu et al 01],polygon [Datta et al 06]; ranging: MCL-R [Dil-Havinga 06]; anywhere: MSL/MSL* [Rudafshani-Datta 07], EASeL [Maclean-Datta 08]. Position on mobility axis. Static: dv-hop; mobile: MCL, MCLB; anywhere: polygon, MSL/MSL*, EASeL. Maintaining error estimates. None: dv-hop. Regions: Bounding boxes [Shastri et al 99?], polygons [Datta et al 06], Curved regions [Guha et al 05], sampled points [MCL,MCL-B, MCL-R,MSL,MSL*,EASeL]. Use of non-seeds - exchange region [polygon], samples [MSL*] or location+error [MSL, EASeL]? Use of multi-hop information. S. Datta (York Univ.) Sensor network localization December 3, / 31
51 Range-free algorithm 2: Monte Carlo Localization (MCL) Initialization: uniformly over the sensor field. S. Datta (York Univ.) Sensor network localization December 3, / 31
52 Range-free algorithm 2: Monte Carlo Localization (MCL) Initialization: uniformly over the sensor field. Sampling (prediction): for each sample location x: S. Datta (York Univ.) Sensor network localization December 3, / 31
53 Range-free algorithm 2: Monte Carlo Localization (MCL) Initialization: uniformly over the sensor field. Sampling (prediction): for each sample location x: sample uniformly over the circle radius v max, center x. S. Datta (York Univ.) Sensor network localization December 3, / 31
54 Range-free algorithm 2: Monte Carlo Localization (MCL) Initialization: uniformly over the sensor field. Sampling (prediction): for each sample location x: sample uniformly over the circle radius v max, center x. Filtering/resampling: Remove points inconsistent with distances to seeds. Resample. S. Datta (York Univ.) Sensor network localization December 3, / 31
55 Range-free algorithm 2: Monte Carlo Localization (MCL) Initialization: uniformly over the sensor field. Sampling (prediction): for each sample location x: sample uniformly over the circle radius v max, center x. Filtering/resampling: Remove points inconsistent with distances to seeds. Resample. Comments Requires mobile nodes. May take long to get a fixed number of samples. Robust. S. Datta (York Univ.) Sensor network localization December 3, / 31
56 Algorithm MSL*[Rudafshani, Datta, IPSN 2007] Mobile Sensor Network Localization Problem: Storing regions with curved boundaries is hard. S. Datta (York Univ.) Sensor network localization December 3, / 31
57 Algorithm MSL*[Rudafshani, Datta, IPSN 2007] Mobile Sensor Network Localization Problem: Storing regions with curved boundaries is hard. Idea 1: discretize circles as rectangles, regular polygons. S. Datta (York Univ.) Sensor network localization December 3, / 31
58 Algorithm MSL*[Rudafshani, Datta, IPSN 2007] Mobile Sensor Network Localization Problem: Storing regions with curved boundaries is hard. Idea 1: discretize circles as rectangles, regular polygons. Idea 2: discretize regions as sets of sampled points (like MCL). S. Datta (York Univ.) Sensor network localization December 3, / 31
59 Algorithm MSL*[Rudafshani, Datta, IPSN 2007] Mobile Sensor Network Localization Problem: Storing regions with curved boundaries is hard. Idea 1: discretize circles as rectangles, regular polygons. Idea 2: discretize regions as sets of sampled points (like MCL). MSL* stores sample sets at each timestep. Samples have weights. Samples and weights are updated at each step. S. Datta (York Univ.) Sensor network localization December 3, / 31
60 Algorithm MSL* : basic steps At each step, Seeds send location to all neighbors; nodes send samples, weights to all neighbors. S. Datta (York Univ.) Sensor network localization December 3, / 31
61 Algorithm MSL* : basic steps At each step, Seeds send location to all neighbors; nodes send samples, weights to all neighbors. Nodes recompute location estimates (samples) and weights. S. Datta (York Univ.) Sensor network localization December 3, / 31
62 Algorithm MSL* steps (for non-seeds) Initialization: uniform random samples over whole field S. Datta (York Univ.) Sensor network localization December 3, / 31
63 Algorithm MSL* steps (for non-seeds) Initialization: uniform random samples over whole field Sampling: Generate random samples from circles around each existing sample with radius v max + α. We used α = 0.1r. Sample weights: product of partial weights of each neighbor. Partial weights of seed neighbors 1 or 0, as with MCL. Partial weights of non-seed neighbors is the sum of weights of samples in radio range. S. Datta (York Univ.) Sensor network localization December 3, / 31
64 Algorithm MSL* steps (for non-seeds) Initialization: uniform random samples over whole field Sampling: Generate random samples from circles around each existing sample with radius v max + α. We used α = 0.1r. Sample weights: product of partial weights of each neighbor. Partial weights of seed neighbors 1 or 0, as with MCL. Partial weights of non-seed neighbors is the sum of weights of samples in radio range. Filtering: Reject samples with weight < β = (0.1) number of neighbors. S. Datta (York Univ.) Sensor network localization December 3, / 31
65 Algorithm MSL* steps (for non-seeds) Initialization: uniform random samples over whole field Sampling: Generate random samples from circles around each existing sample with radius v max + α. We used α = 0.1r. Sample weights: product of partial weights of each neighbor. Partial weights of seed neighbors 1 or 0, as with MCL. Partial weights of non-seed neighbors is the sum of weights of samples in radio range. Filtering: Reject samples with weight < β = (0.1) number of neighbors. Re-sampling: Choose each existing sample with probability proportional to its weight. S. Datta (York Univ.) Sensor network localization December 3, / 31
66 Algorithm MSL* steps (for non-seeds) Initialization: uniform random samples over whole field Sampling: Generate random samples from circles around each existing sample with radius v max + α. We used α = 0.1r. Sample weights: product of partial weights of each neighbor. Partial weights of seed neighbors 1 or 0, as with MCL. Partial weights of non-seed neighbors is the sum of weights of samples in radio range. Filtering: Reject samples with weight < β = (0.1) number of neighbors. Re-sampling: Choose each existing sample with probability proportional to its weight. Transmit samples to all neighbors. measure of confidence (closeness): mean weighted square deviation from weighted mean Only use samples from neighbors with LOWER closeness values S. Datta (York Univ.) Sensor network localization December 3, / 31
67 MSL*: Comments Comparison with MCL Works for static, mobile and mixed networks Improved sampling and resampling procedures; a version of MSL* that uses location information of only seeds outperforms MCL Uses much more communication and information; much higher accuracy than MCL Robustness issues Performs very well on a C shaped sensor field Graceful degradation with increasing mobility, and increasing radio range irregularity S. Datta (York Univ.) Sensor network localization December 3, / 31
68 Combining MSL*, Polygon algorithm, ranging Algorithm EASeL Uses sampling. Uses ranging when available Uses negative (non-neighborhood) constraints. Lower communication complexity than MSL*, Polygon algorithm. Very good localization accuracy. S. Datta (York Univ.) Sensor network localization December 3, / 31
69 EASeL steps Using the contraints described (1st and 2nd neighbors), compute approximate region. Sample from this region, filter using constraints. Compute center (location estimate) and radius (quality estimate/error) of the points. Exchange these numbers with neighbours. S. Datta (York Univ.) Sensor network localization December 3, / 31
70 Lower bounds on localization error Lower bounds are hard to prove. Known bounds for range free. Most use the indistinguishability argument [Nagpal et al 2003]. Assumes one node, rest seeds. All nodes Poisson distributed. Computes resolution limit: expected distance a node can move without changing neighborhood. The original bound by Nagpal et al and the extension to mobile networks by Evans-Hu are incorrect [Maclean Datta 08]. S. Datta (York Univ.) Sensor network localization December 3, / 31
71 New lower bounds on localization error Old lower bound [Nagpal et al 2003] E[Y ] = 1 4rλ New lower bound: [Maclean, Datta, 2008] [ ] E[Y ] = 1 1 4πr 2 λ e 4πr 2 λ 4πrλ 1 e 4πr 2 λ New lower bound on area: [Maclean, Datta, 2008] E[X ] π π(8λr 2 + 1) e 8λr 2 8λ 2 r 2 Assumes all seed positions known. S. Datta (York Univ.) Sensor network localization December 3, / 31
72 New lower bounds on localization error Old lower bound [Nagpal et al 2003] E[Y ] = 1 4rλ New lower bound: [Maclean, Datta, 2008] [ ] E[Y ] = 1 1 4πr 2 λ e 4πr 2 λ 4πrλ 1 e 4πr 2 λ New lower bound on area: [Maclean, Datta, 2008] E[X ] π π(8λr 2 + 1) e 8λr 2 8λ 2 r 2 Assumes all seed positions known. Derived assuming Poisson distribution of nodes. S. Datta (York Univ.) Sensor network localization December 3, / 31
73 New lower bounds on localization error Old lower bound [Nagpal et al 2003] E[Y ] = 1 4rλ New lower bound: [Maclean, Datta, 2008] [ ] E[Y ] = 1 1 4πr 2 λ e 4πr 2 λ 4πrλ 1 e 4πr 2 λ New lower bound on area: [Maclean, Datta, 2008] E[X ] π π(8λr 2 + 1) e 8λr 2 8λ 2 r 2 Assumes all seed positions known. Derived assuming Poisson distribution of nodes. Radio range is a perfect circle. S. Datta (York Univ.) Sensor network localization December 3, / 31
74 Performance evaluation Java-based simulator. Random (uniform, Poisson) deployment of sensors. A small fraction of nodes are seeds. Radio range is a small fraction of sensor field dimensions. Modified random waypoint mobility model S. Datta (York Univ.) Sensor network localization December 3, / 31
75 Results: all static nodes Expected localization error EASeL dv-hop Seed density Static nodes. S. Datta (York Univ.) Sensor network localization December 3, / 31
76 Results: all ranging nodes Expected localization error Our algorithm dv-hop Seed density Static nodes, ranging errors are truncated gaussians with σ = 0.2. S. Datta (York Univ.) Sensor network localization December 3, / 31
77 Results: all mobile nodes Expected localization error Our algorithm MCL Seed density v max = r. S. Datta (York Univ.) Sensor network localization December 3, / 31
78 Results: utility of non-neighborhood information Expected localization error Our algorithm without second neighbours Our algorithm with second neighbours lower bound seed density Static nodes, range-free. S. Datta (York Univ.) Sensor network localization December 3, / 31
79 Results: utility of using non-seeds 1 Fraction of localized nodes Seeds only All nodes seed density Static nodes, range-free. S. Datta (York Univ.) Sensor network localization December 3, / 31
80 Results: comparison with area lower bound Measured error lower bound expected area of R_i density 1.Single unlocalized node; all other nodes are seeds. 2. Lower bound uses all seeds; algorithm uses only 1st and 2nd neighbors. S. Datta (York Univ.) Sensor network localization December 3, / 31
81 Extensions Incorporate into applications using locations. S. Datta (York Univ.) Sensor network localization December 3, / 31
82 Extensions Incorporate into applications using locations. Efficiency in communication: nodes could decrease the frequency of location message transmission. adaptively determine how much data to exchange. S. Datta (York Univ.) Sensor network localization December 3, / 31
83 Extensions Incorporate into applications using locations. Efficiency in communication: nodes could decrease the frequency of location message transmission. adaptively determine how much data to exchange. Analyzing localization error. Are the lower bounds tight? Can we prove upper bounds? S. Datta (York Univ.) Sensor network localization December 3, / 31
84 Extensions Incorporate into applications using locations. Efficiency in communication: nodes could decrease the frequency of location message transmission. adaptively determine how much data to exchange. Analyzing localization error. Are the lower bounds tight? Can we prove upper bounds? Modeling mobility in analyses. S. Datta (York Univ.) Sensor network localization December 3, / 31
85 Current whereabouts (upto June 2009) Hopeman 342, extension S. Datta (York Univ.) Sensor network localization December 3, / 31
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