Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks

Robust Positioning Algorithms for DistributedAd-Hoc Wireless Sensor Networks ECE 7360 FISP(Optimal and Robust Control) Anisha Arora anishaarora@cc.usu.edu Nov 24, 2003

Presentation Outline • Background • Why I chose this topic • The Positioning Problem within Ad-hoc Sensor Networks • Geometric interpretation • Two phase algorithm • Terrain algorithm • Hop Terrain algorithm • Refinement algorithm • Simulation Results • Obstacles to Accuracy • Areas for future improvement • Conclusion • Papers Reviewed • Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks by Chris Savarese

Plume Detection using wireless sensor networks.

Presentation Outline • Background • Why I chose this topic • The Positioning Problem within Ad-hoc Sensor Networks • Geometric interpretation • Two phase algorithm • Terrain algorithm • Hop Terrain algorithm • Refinement algorithm • Simulation Results • Obstacles to Accuracy • Areas for future improvement • Conclusion. • Papers Reviewed • Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks by Chris Savarese

Positioning Problem: Ad-hoc Sensor Networks • lack of infrastructure inherent to ad hoc networks. • all nodes are considered equal, making it difficult to rely on centralized computation to solve network wide problems, such as positioning. • there must exist within this network a minimum of four anchor nodes. • all nodes being considered in an instance of the positioning algorithm must be included in the same connected network.

Two most essential problems… At least I think they are… • RANGE ERROR PROBLEM • SPARSE ANCHOR NODE PROBLEM

Geometric Interpretation • Goal of these algorithms • To determine a specific node’s location within a given global coordinate system. • Done using Triangulation • Triangulation • Geometric technique • Uses edges between objects to determine position • Unique position of an object in a two-dimensional space: triangle • Ties between objects, in the form of measured distances and angles

Geometric Interpretation

The Two-Phase Algorithm • Split in two parts • Start up phase • Addresses the sparse anchor node problem • Awareness of the anchor nodes’ positions throughout the network • Allowing all nodes to arrive at initial position estimates • Refinement phase • Uses the results of the start-up phase • Improves upon initial position estimates • Range error problem is addressed • End goal • To deliver reliable position estimates to other parts of the system

The Two-Phase Algorithm • Start up phase algorithm #1 • TERRAIN ALGORITHM • Triangulation via extended range and redundant associated of intermediate node • Each node makes several independent maps one map for each anchor node • Once a node is included in sufficient number of maps then it aligns itself in the global co ordinate system • Suppose the node makes three maps with respect to three anchor nodes then it can use the triangulation method to find its position

TERRAIN ALGORITHM Example

Pros and Cons of TERRAIN • Pros • Helps to position a node globally without complicated arithmetic deductions • Easy to covert from a two dimensional positioning to a three dimensional positional system • Cons • Unacceptably high tendency to exponentially intensify error levels • Final position estimates are too noisy to be useful

The Two-Phase Algorithm • Start up phase algorithm #2 • HOP TERRAIN ALGORITHM • Finds number of routing hops from a node to each of anchor nodes in a network • Multiplies the number of routing hops by a shared metric (average hop distance) • Estimates range between node and each anchor node • Use these computed ranges to find positions using the triangulation method • Each anchor node initializes this algorithm by broadcasting it’s location and a hop count of zero

The Two-Phase Algorithm • The neighbors who hear this broadcast then broadcast this further just changing the hop count to 1 • This procedure continues till it reaches the normal node whose position we are trying to determine

Pros and Cons • Pros • Reduces network traffic • Simplistic approach • Does not use the magnitude of range measured • Checks to see if communication is established. • Does not iteratively compound errors • More robust • Yields more accurate and consistent positions

Possible Error In Hop Terrain Algorithm • strange or difficult topologies may cause strange positioning errors in the Hop Terrain algorithm

Possible Error In Hop Terrain Algorithm • Nodes that are physically close to each other, but separated by the obstacle, will receive hop counts that are artificially large from having had to travel around the obstacle • Distort the estimated ranges used to compute positions, thus distorting the positions themselves • The best solution to this warping effect would be to add more anchor nodes in key locations to mitigate the distortion created by the obstacle

The Refinement Algorithm • Objective • Obtain more accurate positions using the estimated ranges between nodes • Algorithm • A node broadcasts its position estimate • Receives the positions and corresponding range estimates from its neighbors • Computes a least squares triangulation solution to determine its new position

Refinement Algorithm • Refinement revealed two important error causes • Errors propagate fast throughout the whole network. If the network has a diameter d, then an error introduced by a node in step s has (indirectly) affected every node in the network by step s+d because of the triangulate-hop-triangulate-hop… pattern • Some network topologies are inherently hard, or even impossible to locate. For example, a cluster of n nodes (no anchors) connected by a single link to the main network can be simply rotated around the ‘entry’-point into the network while keeping the exact same intra-node ranges.

Refinement Algorithm • To mitigate error propagation the Refinement algorithm was modified to include a confidence metric associated with each node’s position • Confidence metrics (between 0 and 1) are used to weigh the equations when solving the system of linear equations • Anchors immediately start off with confidence value of 1 • Unknown nodes start off at a low value (0.1) and may raise their confidence after subsequent Refinement iterations • A node performs a successful triangulation it sets its confidence level to the average of its neighbors’ confidence levels • Triangulations sometimes fail or the new position is rejected on other grounds. In these cases the confidence is set to 0, so neighbors will not use erroneous information of the inconsistent node in the next iteration

Average Position Error After Hop - TERRAIN (5% Range Errors)

Fraction Of Located Nodes(2% Anchors, 5% Range Error)

Range Error Sensitivity Of Hop - TERRAIN And TERRAIN

Obstacles to Accuracy • Poor topology • Exaggerated range errors • Excessive node mobility • Stationary obstacles, such as walls, could be a large problem for Hop-TERRAIN due to the falsely inflated hop counts that result • Obstacles artificially create poor topologies, leading to inaccurately estimated extended ranges • obstacles create sections of the network that have low connectivity levels, another example of poor topology • some objects may move through a network

Areas for Improvement and Future Study • Improve the engine that drives both of these algorithms:Use the least squares triangulation method instead of the triangulation method • Attempt to alleviate the shortcomings of Refinement in the presence of high range errors is introduced

In Conclusion… • Would use Hop-TERRAIN Algorithm • More robust • Less sensitive to error • Second phase use the refinement algorithm

References: • http://bwrc.eecs.berkeley.edu/Publications/2002/thesis/robst_pstng_algrthms_dstrbtd_adhoc/Savarese_MS_Thesis_FINAL.pdf • http://mas-net.ece.usu.edu/

Any Questions ??? Thanks for your patience…

Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks