Girishkumar Sabhnani

Distributed localization using noisy distance and angle information

Localization is an important and extensively studied problem in ad-hoc wireless sensor networks. Given the connectivity graph of the sensor nodes,along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In this paper, we study the problem of localization with noisy distance and angle information. With no noise at all, the localization problem with both angle (with orientation) and distance information is trivial. However, in the presence of even a small amount of noise, we prove that the localization problem is NP hard.Localization with accurate distance information and relative angle information is also hard. These hardness results motivate our study of approximation schemes. We relax the non-convex constraints to approximating convex constraints and propose linear programs (LP) for two formulations of the resulting localization problem, which we call the weak deployment and strong deployment problems.These two formulations give upper and lower bounds on the location uncertainty respectively: No sensor is located outside its weak deployment region, and each sensor can be anywhere in its strong deployment region without violating the approximate distance and angle constraints. Though LP-based algorithms are usually solved by centralized methods, we propose distributed, iterative methods, which are provably convergent to the centralized algorithm solutions. We give simulation results for the distributed algorithms, evaluating the convergence rate, dependence on measurement noises,and robustness to link dynamics.

Dynamic Airspace Configuration Management based on Computational Geometry Techniques

New techniques for dynamic airspace configuration in the National Airspace System based on computational geometry techniques are investigated. The current airspace is subdivided into Air Route Traffic Control Centers and sectors of airspace that remain statically defined. New methods of designing airspace regions that are balanced in terms of workload per unit area over a given planning time period are presented. Configuring the airspace dynamically provides a means to change sector designs from one day to the next or within the course of a single day, to better balance controller workload. A recursive, top-down partitioning algorithm is used to subdivide a given 2D polygonal region R of airspace (e.g., a center) into sector regions. Three types of local partitioning are investigated: straight-line cuts, pie-cuts, and wheel-cuts. During each subdivision, the local partitioning balances workload among the resulting subregions, while other shape parameters, such as aspect ratio, are kept within acceptable bounds. Experiments show promising results for balancing workload. Airspace designs were shown to controllers, and their feedback regarding design considerations were summarized for use in improving our modeling approach.

Algorithmic Traffic Abstraction and its Application to NextGen Generic Airspace

We develop traffic abstraction algorithms that, given a set of 4D Trajectories (4DTs), extract the traffic structure in terms of standard flows and critical points (conflict and merge points). We demonstrate the application of our techniques to enable the NextGen generic airspace concept. We also analyze historical demand data to evaluate the level of abstraction underlying the en-route traffic within high-altitude sectors. Finally, we compare the structure of historical traffic to user preferred, wind optimal futuristic trajectories.

Distributed localization and clustering using data correlation and the Occam's razor principle

We present a distributed algorithm for computing a combined solution to three problems in sensor networks: localization, clustering, and sensor suspension. Assuming that initially only a rough approximation of the sensor positions is known, we show how one can use sensor measurements to refine the set of possible sensor locations, to group the sensors into clusters with linearly correlated measurements, and to decide which sensors may suspend transmission without jeopardizing the consistency of the collected data. Our algorithm applies the “Occams razor principle” by computing a “simplest” explanation for the data gathered from the network. We also present centralized algorithms, as well as efficient heuristics.

Effectiveness of Dynamic Airspace Configuration to Manage Airspace Capacity in Response to Highly Dynamic Changes in Traffic Demand and Weather Events

We present experimental results to gain insight into how dynamic airspace capacity management can alleviate or support Traffic Flow Management (TFM) initiatives. Through analysis of historical flight and weather data, we explore mechanisms by which Dynamic Airspace Configuration (DAC) and TFM models can interact and exchange information to provide airspace capacity where and when it is most needed by users.