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A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks. Lei Fang (Syracuse) Wenliang (Kevin) Du (Syracuse) Peng Ning (North Carolina State). Location Discovery in WSN . Sensor nodes need to find their locations Rescue missions Geographic routing protocols
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A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks Lei Fang (Syracuse) Wenliang (Kevin) Du (Syracuse) Peng Ning (North Carolina State)
Location Discovery in WSN • Sensor nodes need to find their locations • Rescue missions • Geographic routing protocols • Many other applications • Constraints • No GPS on sensors • Cost must be low
Existing Positioning Schemes Beacon Nodes
Two Important Elements • Reference points • They must know their locations. • e.g. beacon nodes, satellites. • Relationship between nodes and reference points • Distance • Angle of arrival • Time of arrival • Time difference of arrival
The Beacon-Less Scheme • Without using beacon nodes • Beacon nodes are more expensive • They can be the main target of attacks • Nonetheless, we still have to find reference points and the corresponding relationships. • Remember: the locations of the reference points must be known.
Modeling of The Group-Based Deployment Scheme Deployment Points: Their locations are known. We still need another important element: The relationship between nodes and reference points.
Using pdf function to model the node distribution. Example: two-dimensional Gaussian Distribution. Other distribution can also be used. Modeling of the Deployment Distribution
Observation at location O See more nodes from A and D than from H and I. Observation at location P Quit different from location O. See more nodes from H and I than from A and D. Given a location, we can derive the observation. Given the observation, can we derive the location? The Idea
The Problem Formulation Observation a = (a1, a2, … an) Location Estimation Locationθ = (x, y)
A Geometric Approach • Pick the three nearest deployment points (the three highest ai values). • Estimate the distance between the sensor and these points. • MLE (Maximum Likelihood Estimation): f (Xi = ai|Z): The probability of observing ai nodes from Group i when the distance is Z. • Find Z, such that f (Xi = ai|Z)is maximized.
A More General Solution • Instead of considering only three groups, we consider all the groups. a = (a1, a2, … an): The observation. fn(a|θ): The probability of observing a at location θ. • MLE Principle:find θ, such thatfn(a|θ)is maximized.
Maximum Likelihood Estimation • Likelihood Function fn(a|θ) =Pr (X1=a1, …, Xn=an|θ) = Pr (X1=a1|θ) · · · Pr (X1=an|θ) L(θ)=logfn(a|θ) • Find θ:
Finding θ • Brute-Force Search: search all possible θ. • Small Area Search: • Find an initial point (accuracy can be low). • Conduct brute-force search around the initial point. • Gradient Descent: A standard solution.
Gradient Descent • A 2-dimensional function is represented as a surface in a 3-dimensional space • The maximum point (peak) holds a zero gradient • Find the shortest path to reach the peak. • Could be expensive
Evaluation • Setup • A square plane: 1000 meters by 1000 meters • 10 by 10 grids (each is 100m X 100m) • σ = 50 (Gaussian Distribution) • What to evaluate? • Accuracy vs. Density • Accuracy vs. Transmission Range • Boundary Effects • Computation Costs.
Effect of Density m An Improvement: Dummy Nodes m: number of sensors in each group
Conclusion and Future Work • Beacon-Less Location Discovery • Formulate the location discovery problem as an estimation problem • Use the Maximum Likelihood Estimation to solve the estimation problem • Future work • How the inaccuracy of the deployment model affect the result? • Resilience and Security: • IPDPS’05 paper (Best Paper Award in the Algorithm Track) • Google “Wenliang Du” can get the paper.