Abstract 
Networks of hundreds or thousands of sensor nodes equipped with sensing, computing and communication ability 
are conceivable with recent technological advancement. Methods are presented in this report to recover and 
visualize data from wireless sensor networks, as well as to estimate node positions. A communication system 
is assumed wherein information from sensor nodes can be transferred to a centralized computer for data processing, 
though suggestions are made for extensions to distributed computation. Specifically, this report presents four 
topics. First, the notion of using network connectivity to reconstruct node positions via linear or semidefinite 
programming is explored. Random feasible node placement and bounding methods are both found to increase in 
precision with the indiviual geographical constraints. Second, the potential effectiveness of two correlation-
based sensor data encoding schemes is reported. Blind correlation methods are found to provide meager compression 
while semi-blind correlation can effectively reduce bandwidth requirements by one-half. Third, trajectory 
reconstruction through a sparse sensor network is used to track objects with expectation-minimization techniques. 
Trajectories can be distinguished providing that sufficient spatial or temporal separation exists. Fourth, 
optical flow algorithms are used to visualize time-varying continuous flow around the network. A qualitative 
analysis of the reconstructed flow for several case studies suggests a minimal node density as related to flow 
speeds.

Summary:
This paper looks at determining the position of sensor nodes as a mathematical problem. A brief description 
on the details given follows. The hardware side of the paper has not been dealt with. A sensor network is defined 
as an undirected graph as follows:

{V,E} - where V are the vertices and E are the edges
x(i)  - gives the node position in two dimensional or 3 dimensional space
Ti    - Gives the senor reading at each node

Creation of a Sensor Network:

1. Random Seed Node Networks: A seed node is placed at the origin, A second node is placed at an selected angle 
and didstance from the first. Repeat placing the other nodes relative to any predecessor. Such a layout has a 
gaussian distribution

2. Sequential Seed Node network: A node is placed exclusively relative to its direct predecessor.
3. Subnet extraction
4. Combination of convex constraints: Nodes are placed so that they satisfy many constraints.

Knowing the position of some of the nodes, it is possible to calculate other poisiotns using LPs and SDPs. As the no. 
of nodes increase, the mean error in calculating the position decreases.

Applications of estimating node position:
1. Tracking through the sensor network: This simplifies to the case of one unknown. - one unknown node position 
and m known node position
2. Hierarchical solution for large networks: Solve for smaller subnetworks. Abstract the centroids of these 
subnetworks to nodes in a larger network and repeat.

This paper primarily deals with how node positions can be calcutlate as mathematical problems involving several 
unknowns depending upon a set of constraints.