Probability Grid: A Location Estimation Scheme for Wireless Sensor Networks Presented by cychen Date ： 3/7 In Secon (Sensor and Ad Hoc Communications and Networks) 2004Sensor and Ad Hoc Communications and Networks

Outline  Introduction  The Probability Grid Localization Scheme  The Localization Scheme  Performance Evaluation  System Implementation And Evaluation

Introduction  Propose a location estimation scheme completely decentralized not require special location or range finding infrastructure uses a probabilistic approach makes use of additional knowledge of topology deployment

Introduction  Assume a sensor network is deployed in a controlled manner The goal is to form a grid topology. The deployment is not completely random  an approximation to a uniform or even grid distribution

 The anchor nodes only a small percentage either equipped with GPS or can acquire their location information through other means. do not have any increased communication range  The remaining sensor nodes are unaware of their location The sensor nodes

The Probability Grid Localization Scheme  Assumption ： the nodes are deployed in a grid topology the unit length of the grid is known to all the nodes in the network  allow small errors in the true positioning of nodes around the vertexes of a grid.  Our localization problem To identify the correct position in the grid for each sensor node.  The localization error leave for future research

Parameter Definitions  M x N ： the dimensions of the grid topology  S ： the set of all the nodes  A ： the set of all the anchors Both sets, S and A, are sets of ordered pairs (i,j) representing the grid points where the nodes are located.  ： hop-count vector the hop count from each of the anchors in the set A to the node ‘ k ’ is the hop count from anchor 1 to node k.

The Probability Grid Matrix  ： the probability of node ‘ k ’, positioned at (i, j), to be hops from the l-th anchor. observe that is a discrete random variable that represents the number of hops for a particular Euclidian distance

The Probability Grid Matrix  The main features that the distribution function needs to exhibit are: ： the distance between the node and one anchor  ： the number of hops existent between the node and the anchor

The Probability Grid Matrix  Narrow and skewed positively for small values of λ For smaller values of λ  τ has a limited range of possible values with higher and higher values being less and less probable (positively skewed).  Become broader and relatively symmetric for larger values of λ. λ increases, the number of possibilities for the hop count (τ) increases and the distribution becomes bell-shaped

The Probability Grid Matrix  Through simulations, a Poisson distribution is a good approximation  Define

The Probability Grid Matrix  Obtain the Probability Grid Matrix  Let The position of node k in the grid ： The location of node k ：

The Localization Scheme  Our localization protocol is similar to the DV-Hop scheme  But it improves upon it by exploiting deployment information.

Phase 1 - Flooding  The anchors flood the network with packets containing their IDs, their location and a hop count, initially set to zero. global flooding or controlled flooding (all nodes are expected to hear from at least three anchors).  During the flooding period, sensor nodes keep track of the shortest distance (number of hops) to each of the anchors they heard from.

Phase 2 - Compute the correction factor  Correction factor ： an estimation for the Euclidian distance of one hop  Anchor positioned at (x i, y i ) compute ： where is the number of hops between the current anchor, positioned at (x i, y i ), and the anchor positioned at (x j, y j ).

Phase 2 - Compute the correction factor  The correction factor is received only by the sensor nodes in the vicinity of the anchor.  Sensor node only uses the “ first ” correction factor it received to estimate its location.

Phase 3 - Invoke The Probability Grid algorithm 1.Calculate λ the distance, in hop count units, between the evaluated grid point and one anchor.  PS. is the actual hop count 2.Calculate, and the Probability Grid matrix F k to estimation the location of node k,  k S-A

Performance Evaluation  Experimental results obtained through Simulations using GloMoSim, a discrete-event simulator developed at UCLA

Localization Error versus Anchors Percentage

Localization Error versus Network Size

Localization Error versus Number of Neighbors

Localization Error versus Imprecision in Anchor Positioning

System Implementation & Evaluation  The implementation was done on MICA2 motes from Berkeley. consisted of 25 motes, positioned in a 5x5 grid, approximately 12 meters apart.

Real System Evaluation Results