Presented by Prashant Duhoon Localization methods Presented by Prashant Duhoon

Motivation Features. Added benefits.(track and search) Resource optimization. Environment monitoring. Mapping

Methods GPS.(expensive) Dedicated sensors. Localization methods.

Localization Localization schemes for sensor networks Saves cost. Uses seed nodes Estimates location for nodes from messaging. Saves cost. Adds computational burden. Allows for Mobility.

Problems Dependence on special hardware: measuring ranging information from: signal strength, time of arrival, time difference of arrival Increases overall cost due to additional hardware Requirement for particular network topologies: require seed nodes to be Numerous Evenly distributed.

Localization Cases: Nodes are static, seeds are moving. Nodes are moving, seeds are static. Both nodes and seeds are moving.

Discussion: Centralized localization techniques. Location is centrally computed. High communication costs. Inherent delay. Distributed localization techniques. Node determining its location with nearby nodes. range-based: signal strength, distance estimates, angle of arrival, time difference in arrival. range-free: message contents, cost effective.

Range Free: Centroid localization. (local technique) Amorphous localization. (Hop-Counting Technique) Monte-Carlo localization.

Local Technique Node estimates its location by Calculating the center of the locations of all seeds it hears. Location error can be reduced if seeds are well positioned Impractical in ad hoc deployments. Triangulation of maximum area a node will likely reside. Needs high seed density.

Hop-Counting Technique Localization in networks where seed density is low Propagate location announcements throughout the network distance vector routing. A counter denotes the minimum number of hops to each seed. Seed location announcements propagate through the network. Each node can maintains a hop-count to all seeds. Nodes calculate their position based on the received seed locations and corresponding hop count.

Monte-Carlo Localization (MCL): Inspired from Robotics. Uses prior or previously learned map. A bit of learning involved. Outperforms other proposed localization algorithms in both accuracy and computational efficiency. Uses posterior distribution of possible locations using a set of weighted samples.

MCl methods: Involves: A prediction phase An update phase In a nutshell: use new seed information to filter out irrelevant probabilities. Simulation-based solutions to estimate the posterior distribution. Represent the posterior distribution by a set of m weighted samples. Updated recursively. Uses importance sampling.

importance sampling Estimating properties of a particular distribution from samples of another distribution. Estimate the expected value of X under P, denoted E[X;P]. Eliminate trajectories with small normalized importance weights.

Location Estimation Algorithm: t be the discrete time lt be the position distribution of the node at time t ot be the observations from seed nodes received between time t-1 and time t. Transition: p(lt | lt-1) be the prediction of node’s current position based on previous position, Observation p(lt | ot) describes the likelihood of the node being at the location lt given the observations. Filtering distribution p(lt | o0, o1, …, ot) to be estimated recursively. N samples Lt represents the distribution lt Set of samples at each time step. Compute lt using only Lt-1 and ot.

Algorithm:

Prediction step A node starts from the set of possible locations computed in the previous step, Lt-1 Applies the model to each sample to get a set of new samples, Lt. Assumption: speed is less than vmax. If in previous step lit-1 is one possible position of a node Possible current positions are contained in the circular region with origin lit-1 and radius vmax. d(l1, l2) be the Euclidean distance between two points l1 and l2. Uniformly distributed in [0, vmax) Probability of current location based on previous location estimate:

Filtering step: Filters the impossible locations based on new observations. Types of seeds: Outsiders – seeds that were not heard in either the current or the previous time. Arrivers – seeds that were heard in the current time, but not in the previous one. Leavers – seeds were heard in the previous time quantum, but not in this one. Insiders – seeds that were heard in both time quanta. Arrivers and leavers provide the most useful information. Seed information can be gathered directly or via neighboring nodes.

Filtering Step Contd. p(lt | ot) is zero if the filter condition is false, evenly distributed otherwise. Fewer than N possible locations remaining after filtering. Prediction and filtering processes repeated, Union the possible points found.

ANALYSIS Weights are measured for each sample using: Re-sampling: eliminate small normalized importance weights. Calculate effective N. We can set thresholds for Neff Prediction phase Update phase Normalized phase

Questions?

Resolution limit Regions I and II are regions that can affect node’s connectivity when it moves d distance. maximum distance a sensor can move without changing connectivity is πr/12sd. The resolution limit for sd =1 is 0.26r. where sd is the seed density

Security issues: Inject bogus seeds into the network. Digital signatures and public key encryption can solve this issue but increases computation overhead. Rogue node to disrupt many node locations by advertising a false hop count. MCL more robust to above two vulnerabilities. Susceptible to replay attacks.

EVALUATION: Accuracy: nd = 10, sd = 1, vmax = smax= r

Evaluation: Impact of node speeds:

Evaluation: Impact of seed density: nd = 10, vmax = smax= .2r

Evaluation: Impact of node density: sd = 1, vmax = smax =.2r

Evaluation: Impact of irregularity (sample count): nd = 10, sd = 1, vmax = smax =.2r N=50

Conclusion: Many wireless sensor network applications depend on nodes being able to accurately determine their locations. Mobility can improve localizing. Questions?

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