Estimation in Large Scale Sensor Networks

A sensor network is a collection of small sensors that are equipped with sensing, processing and communication (typically wireless) capability. Due to the small size and cost of these sensors, a large number of them can be deployed in a spatially distributed fashion to sample  various points in a region.  Applications of sensor networks are envisioned in weather forcasting, forest fire monitoring, ecological habitat monitoring, intelligent and secure buildings, structural health monitoring etc.  However, several technological hurdles have to be overcome to make this vision a reality. These include estimation of locations of randomly deployed sensors, time synchronization, distributed fusion of information in networks whose topology might be  time-varying, etc. In addition, since the sensors have limited on-board energy supply, all these have to be done with an extremely limited energy budget.

Relevant Publications:

1.  Prabir Barooah and João P. Hespanha, "Estimation on Graphs from relative Measurements: Distributed Algorithms and Fundamental Limits",  IEEE Control Systems Magazine, August 2007, vol. 27, no. 4. [PDF] 
(This paper examines two important problems in sensor networks,  location estimation and time synchronization, in a common framework. It is a review article written for a broad audience that summarises technical results reported in separate papers. It describes provably correct distributed algorithms to  compute the best (minimum variance) linear unbiased estimates, and examines how the minimum achievable variance depends on the topology of the sensor network.)

2. Prabir Barooah and João P. Hespanha, "Estimation from Relative Measurements:  Electrical Analogy and Large Graphs", IEEE Transactions on Signal Processing, in press. [PDF preprint]
(This paper provides a rigorous justification for using infinite graphs as a model for large but finite graphs in the BLUE estimation problem)

3. Prabir Barooah and João P. Hespanha, "Estimation From Relative Measurements : Error Bounds from Electrical Analogy", In proceedings of the 2nd Int. Conf. on Intelligent Sensing and Information Processing, pp. 88-93, 4-7 January, 2005, Chennai, India. (Best Paper Award) [PDF]
(establishes a classification of graphs that determine the asymptotic growth rate of the minimum achievable variance with distance in infinite graphs)

Decentralized Control in Multi-Agent Systems

Use of multiple autonomous agents offer several advantages over a single one. For example, multiple satellites flying in formation can be be used to detect distant stars which would otherwise require an extremely large satellite, and several UAVs can track a target much more accurately than a single UAV can. However, tight coordination between the agents is needed to achieve these objectives, which requires the design of novel feedback control alorithms. In particular, the control laws have to be decentralized, so that the control action at a particular agent depends only on information from nearby agents. Otherwise, if information from all the agents have to be transmitted to all other agents, the communications overhead will severly limit the number of agents. I am interested in developing methods for design of decentralized controllers and analyzing of the affect of interconnection topology on the performance of the closed loop system.

Relevant publications:

1.  Prabir Barooah and João P. Hespanha, "Graph Effective Resistance and Distributed Control: Spectral Properties and Applications ", In proceedings of the 45th IEEE Conference on Decision and Control, December 13-15, 2006, San Diego, pp. 3479-3485. [PDF]
(Among other things, this paper analyzes a decentralized formation control agorithm, and examines the effect of interconnection structure on the covariance of formation errors due to noisy relative position measurements between agents)

2. Prabir Barooah, Prashant G. Mehta and João P. Hespanha, "Control of Large Vehicular Platoons: Improving Closed Loop Stability by Mistuning", In proceddings of the American Control Conference, pp. 4666-4671, 11-13 July, 2007, New York. [PDF] 
(This paper develops a PDE model for the automated platoon problem and proposes a "mistuning"-based decentralized control algorithm that improves upon existing control agorithms)

Announcement:

I'm looking for Ph.D. students with strong mathematical skills, preferably with a solid foundation in linear algebra, linear systems and probability, for the following projects. Apart from ME and Aero students, EE, CS, or Math students are also encouraged to apply.

Current research projects:
1. Distributed algorithm design for simultaneous localization of mobile robots and of targets.
2. Decentralized controller design with continuum models.
3. Time synchronization with time-varying topolgy.
4. Optimal estimation of absolute orientation in stereo-vision.