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Sensor networks Exposure analysis Baptiste Prêtre Betreuer: Kay Römer Baptiste Prêtre June 11, 2005 - p. 1/22

What’s coming up Introduction What’s coming up Specs Location discovery What I will try: Everyday utility ❏ Introduction to sensor networks. Exposure ❏ Exposure problem. Sensor networks ❏ Algorithms for finding minimal exposure path in a network. Conclusion Philippe: Adaptive sampling. Baptiste Prêtre June 11, 2005 - p. 2/22

Specs ❏ No fixed infrastructure. Introduction What’s coming up ❏ Fragile - flexible. Specs Location discovery ❏ Low computing power. Everyday utility Exposure ❏ Low battery life. Sensor networks ❏ Cheap. Conclusion ❏ Distributed. Revolutions: ❏ Connection to the internet. ❏ MEMS sensors. Baptiste Prêtre June 11, 2005 - p. 3/22

Location discovery ❏ Dterministic placement. Introduction What’s coming up ❏ GPS. Specs Location discovery ❏ Trilateration. Everyday utility Exposure Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 4/22

Location discovery ❏ Dterministic placement. Introduction What’s coming up ❏ GPS. Specs Location discovery ❏ Trilateration. Everyday utility Exposure Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 4/22

Everyday utility Real life examples: Introduction What’s coming up ❏ Monitoring (enviromental, ...) Specs Location discovery ❏ Robotics. Everyday utility ❏ Industrial automation. Exposure ❏ Military applications (smart dust). Sensor networks ❏ Surveillance (mother-in-law detection, ...) Conclusion Baptiste Prêtre June 11, 2005 - p. 5/22

The problem Let’s say we have deployed a Introduction sensor network. Exposure The problem Why? Voronoi diagram ❏ How good is it? Sensibility Intensity Exposure ❏ Efficient correction? Simple example ❍ adding least sensors Sensor networks ❍ getting best result Conclusion Exposure helps us answer such questions. Baptiste Prêtre June 11, 2005 - p. 6/22

Why? Exposure is directly related to coverage in that it is an integral Introduction measure of how well the sensor network can observe an Exposure The problem object, moving on an arbitrary path, over a period of time. Why? Voronoi diagram Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 7/22

Why? The minimal exposure path provides valuable information Introduction about the worst case exposure-based coverage in sensor Exposure The problem networks. Why? Voronoi diagram Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 7/22

Voronoi diagram Introduction Exposure The problem Intuition: Why? Voronoi diagram if sensors can sense you then stay away! Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 8/22

Voronoi diagram Introduction Exposure The problem Intuition: Why? Voronoi diagram if sensors can sense you then stay away! Sensibility Intensity Exposure Simple example In 2D, the Voronoi diagram of a set of discrete sites (points) Sensor networks partitions the plane into a set of convex polygons such that all Conclusion points inside a polygon are closest to only one site. Baptiste Prêtre June 11, 2005 - p. 8/22

Voronoi diagram Introduction Exposure The problem Why? Voronoi diagram Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 8/22

Voronoi diagram Introduction Exposure The problem Why? Voronoi diagram Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 8/22

Sensibility ❏ Point p Definition: Introduction ❏ Sensor s Exposure λ The problem S ( s, p ) = ❏ d ( s, p ) Euclidean distance Why? [ d ( s, p )] k Voronoi diagram ❏ λ and k sensor parameters Sensibility Intensity Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 9/22

Intensity Definition: All-Sensor Field Intensity I A ( F, p ) for a point p in Introduction the field F is defined as the effective sensing measures at Exposure The problem point p from all sensors in F . Why? Voronoi diagram n Sensibility � Intensity I A ( F, p ) = S ( s i , p ) Exposure Simple example i =1 Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 10/22

Intensity Definition: Closest-Sensor Field Intensity I C ( F, p ) for a point p Introduction in the field F is defined as the sensing measure at point p from Exposure The problem the closest sensor in F , i.e. the sensor that has the smallest Why? Voronoi diagram Euclidean distance from point p . Sensibility Intensity I C ( F, p ) = S ( s min , p ) Exposure Simple example Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 10/22

Exposure Definition: The exposure for an object in the sensor field Introduction during the interval [ t 1 , t 2 ] along the path p ( t ) is defined as Exposure The problem Why? Voronoi diagram � t 2 Sensibility � � dp ( t ) Intensity � � E ( p ( t ) , t 1 , t 2) = I ( F, p ( t )) � dp Exposure � � dt Simple example � t 1 Sensor networks Conclusion where the sensor field intensity I ( F, p ( t )) can either be � � � dp ( t ) I A ( F, p ( t )) or I C ( F, p ( t )) and � is the element of arc � � dt length. Baptiste Prêtre June 11, 2005 - p. 11/22

Exposure Definition: The exposure for an object in the sensor field Introduction during the interval [ t 1 , t 2 ] along the path p ( t ) is defined as Exposure The problem Why? Voronoi diagram � t 2 Sensibility � � dp ( t ) Intensity � � E ( p ( t ) , t 1 , t 2) = I ( F, p ( t )) � dp Exposure � � dt Simple example � t 1 Sensor networks Conclusion where the sensor field intensity I ( F, p ( t )) can either be � � � dp ( t ) I A ( F, p ( t )) or I C ( F, p ( t )) and � is the element of arc � � dt length. Baptiste Prêtre June 11, 2005 - p. 11/22

Exposure Definition: The exposure for an object in the sensor field Introduction during the interval [ t 1 , t 2 ] along the path p ( t ) is defined as Exposure The problem Why? Voronoi diagram � t 2 Sensibility � � dp ( t ) Intensity � � E ( p ( t ) , t 1 , t 2) = I ( F, p ( t )) � dp Exposure � � dt Simple example � t 1 Sensor networks Conclusion where the sensor field intensity I ( F, p ( t )) can either be � � � dp ( t ) I A ( F, p ( t )) or I C ( F, p ( t )) and � is the element of arc � � dt length. Baptiste Prêtre June 11, 2005 - p. 11/22

Exposure Definition: The exposure for an object in the sensor field Introduction during the interval [ t 1 , t 2 ] along the path p ( t ) is defined as Exposure The problem Why? Voronoi diagram � t 2 Sensibility � � dp ( t ) Intensity � � E ( p ( t ) , t 1 , t 2) = I ( F, p ( t )) � dp Exposure � � dt Simple example � t 1 Sensor networks Conclusion where the sensor field intensity I ( F, p ( t )) can either be � � � dp ( t ) I A ( F, p ( t )) or I C ( F, p ( t )) and � is the element of arc � � dt length. Baptiste Prêtre June 11, 2005 - p. 11/22

Exposure Definition: The exposure for an object in the sensor field Introduction during the interval [ t 1 , t 2 ] along the path p ( t ) is defined as Exposure The problem Why? Voronoi diagram � t 2 Sensibility � � dp ( t ) Intensity � � E ( p ( t ) , t 1 , t 2) = I ( F, p ( t )) � dp Exposure � � dt Simple example � t 1 Sensor networks Conclusion where the sensor field intensity I ( F, p ( t )) can either be � � � dp ( t ) I A ( F, p ( t )) or I C ( F, p ( t )) and � is the element of arc � � dt length. Baptiste Prêtre June 11, 2005 - p. 11/22

Simple example Introduction Exposure The problem How simple is the Exposure? Why? Voronoi diagram Sensibility Intensity What is the minimal ex- Exposure Simple example posure path from p to q ? Sensor networks Let us test if the Voronoi Conclusion diagram approach is suffi- cient. Baptiste Prêtre June 11, 2005 - p. 12/22

Simple example Introduction Exposure The problem Why? Voronoi diagram Sensibility The Voronoi diagram ap- Intensity Exposure proach would suggest stick- Simple example ing to the edges of the graph. Sensor networks Conclusion Baptiste Prêtre June 11, 2005 - p. 12/22

Simple example Introduction Exposure The problem ❏ step closer to sensor Why? Voronoi diagram BUT Sensibility Intensity ❏ reduced sensing time Exposure Simple example ❏ reduced path length Sensor networks ❏ overall exposure reduced Conclusion Baptiste Prêtre June 11, 2005 - p. 12/22

First algorithm ❏ Generate grid. Introduction ❏ Transfrom grid into edge-weighted graph. Exposure ❏ Find minimal exposure path using Dijkstra’s Sensor networks First algorithm Single-Source-Shortest-Path algorithm. A few examples Local knowledge Flooding Greedy More examples More local algorithms? Conclusion Baptiste Prêtre June 11, 2005 - p. 13/22