CDS 270-4: Distributed Kalman Filtering

This page contains notes on a lecture that I gave in CDS 270-4, Estimation and Control over Wireless Sensor Networks in Spring 2008.

• Handwritten lecture notes

Lecture Outline

Problem setup Definitions: cooperative, distributed, decentralized Literature review: 1970s to now Dynamic consensus Introduction to consensus on graphs Static consensus to dynamic consensus

Distributed estimation and fusion Easy case: static environment Interesting case: dynamical system Extensions and open issues Optimality during convergence Effects of communication rate limits

Notes

• Ling will have already covered the information-filter formation of distributed Kalman filtering (Durrant-Whyte style)
• Possible approach: remind people of the consensus results and talk about how to do distributed estimation in this context (choose weights so that everyone converges properly). This obviously only works for static data and when the weights are selected centrally. Use this to motivate two things: handling dynamic data and doing local weighting
• Work out the simple case (same C matrix) in full detail, in particularly showing why we don't have problems with cycles in the graph leading to double counting measurements

Annotated Bibliography

There are quite a large number of papers in the area of distributed estimation and distributed Kalman filtering, dating back to the late 1970s.

• J. Speyer, "Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem", IEEE T. Automatic Control, 1979. This paper solves the LGQ problem for the case where all agents communicate with all other agents.

• Chong, 1979. I have not been able to obtain this paper, but it apparently solves the "hierarchical estimation" problem, which corresponds to the case of having a central hub and distributing the computation (I think).

• Willsky et al, "Combining and Updating of Local Estimates and Regional Maps Along Sets of One-Dimensional Tracks ", EEE T. Automatic Control, 1982. This paper considers the case of taking measurements over a spatial region and integrating these into a single fused representation. It captures as a special case the results of Chong. Assumes communication with a central fusion node.

• Rao, Durrant-Whyte and Sheen, "A Fully Decentralized Multi-Sensor System For Tracking and Surveillance", International Journal of Robotics Research, 1993. This papers makes use of the information form of the Kalman filter to formulate a Kalman filter with no central fusion node but full connectivity. It is similar in spirit to Speyer's 1979 paper, but gives a nicer (and slightly more general?) formulation.

• R. Olfati-Saber, "Distributed Kalman Filtering for Sensor Networks", Conference on Decision and Control, 2007. This paper describes the use of "consensus filters" to implement distributed estimation on a sensor network. Several approaches are presented, each of which converges to the optimal estimate at each node. The approach uses the properties of consensus filters, including their ability to work in the presence of time-varying connectivity.

Additional Resources

• EECI: Distributed Estimation and Control - notes from a lecture I gave as part of a short course on networked control systems.