Splitting the Linear Least Squares Problem for Precise Localization in Geosensor Networks

Large amounts of cheap and easily deployable wireless sensors enable area-wide monitoring of both urban environments and inhospitable terrain. Due to the random deployment of these sensor nodes, one of the key issues is their position determination. Noisy distance measurements and the highly limited resources of every sensor node, due to tiny hardware and small battery capacity, demand the development of robust, energy aware, and precise localization algorithms. We believe this can be achieved by appropriately distributing the complex localization task between all participating nodes. Therefore, we use a linearization tool to linearize the arising non-linear system of equations into a linear form that can be solved by a distributed least squares method. It is shown in this paper that we can save with this new approach more than 47% of computation cost whilst maintaining a low network traffic. Additionally, we describe memory optimizations to process the complex matrix operations with only a few kilobyte of memory on the sensor node.