1. Distributed Algorithm for a Mobile Wireless Sensor Network for Optimal Coverage of Non-stationary Signals Andrea Kulakov University Sts Cyril and Methodius Skopje, Macedonia 7. Apr. 2005 – SPASWIN, Riva del Garda

2. Motivation For the problem of optimal coverage of a wireless sensor networks with limited mobility for random signals appearing with non-stationary distributions Signals should be: Signals should be: Discrete, distinct Discrete, distinct Able to isolate and localize Able to isolate and localize Examples: footsteps, cricket, drops, … Examples: footsteps, cricket, drops, …

3. Introduction of NIMS In order to reduce sensing uncertainty which arises from limitations associated with physical configuration of sensor network nodes, physical reconfiguration in the form of a coordinated mobility of the nodes is proposed in so called Networked Info-mechanical Systems (NIMS) In order to reduce sensing uncertainty which arises from limitations associated with physical configuration of sensor network nodes, physical reconfiguration in the form of a coordinated mobility of the nodes is proposed in so called Networked Info-mechanical Systems (NIMS) http://deerhound.ats.ucla.edu

4. Artificial Neural Networks (ANNs) ANN is a computational model for information processing that represents a directed graph composed of processors (cells, nodes or neurons) and connections or links between them (synapses) ANN is a computational model for information processing that represents a directed graph composed of processors (cells, nodes or neurons) and connections or links between them (synapses) Analogy with sensor networks Analogy with sensor networks

5. Our approach Modification of an existing algorithm to distributed context Modification of an existing algorithm to distributed context Control of connectivity Control of connectivity

6. 1. Listen for the input signal x, distributed according to some distribution P(x). 2. Find the nearest sensor unit s1 and the second-nearest unit s2 among several nodes that detected the signal. 3. Increment the age of all edges (radio connections) emanating from s1. 4. Add the squared distance between the input signal and the nearest unit in input space to a local error variable: 6. Move s1 and its direct topological neighbors toward x by fractions eb and en, respectively, of the total distance: for all neighbors n of s1 7. If s1 and s2 are connected by an edge, set the age of this edge to zero. If such an edge does not exist, create it. 8. Remove edges with an age larger than amax. If this results in sensor nodes having no emanating edges, set these nodes as free. 9. If the number of input signals generated so far is an integer multiple of a parameter l, activate some free unit (node) as follows: 1. Determine the unit q with the maximum accumulated error. 2. Broadcast an order to insert a new unit r halfway between q and its neighbor f with the largest error variable: wr=0.5(wq+ wf). 3. The nearest free unit should accept the order and try to move towards the requested position. 4. Insert edges connecting the new sensor unit r with the units q and f, and remove the original edge between q and f. 5. Decrease the error variables of q and f by manipulating them with a constant a. Initialize the error variable of r with the new value of the error variable of q. 10. Decrease all local error variables by multiplying them with a constant d. 11. If a stopping criterion (e.g., network size or some performance measure like minimal overall error) is not yet fulfilled, go to step 1. Modified Fritzkes algorithm

7. Life show – fast coverage

8. Life show – keep connected

9. Results for fast coverage