EECI08: State Estimation and Sensor Fusion

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This lecture provides a review of key results in state estimation and sensor fusion that will be built upon in future lectures. We briefly summarize Kalman filtering and and describe how to use Kalman filters to obtain optimal sensor fusion in a centralized setting. We also discuss several variants that are of use in a computationally-rich, networked environment: information filters, moving horizon estimation and particle filters. Extensions to networked sensors and distributed sensing are discussed in the follow two lectures.

Outline Kalman Filtering Discrete-time problem setup Minimum mean square error estimation Sensor Fusion Effect of multiple sensors; inverse covariance weighting Example: terrain estimation in Alice Extensions Information Filters Moving Horizon Estimation Particle Filters

Lecture Materials Lecture slides: State Estimation and Sensor Fusion Lecture notes: NCS06, Chapter 4 - State Estimation and Sensor Fusion Additional Information Chapters 4-7 - This is a set of notes from a course on optimization-based control that covers much of the background material required for this lecture, including random processes and Kalman filters. The Kalman Filter, G. Welch and G. Bishop. A webpage with many links on Kalman filter.

Further Reading

• An Introduction to the Kalman Filter, G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.

• Wikipedia: Kalman Filter A webpage that gives a proof and some applications.

• A New Approach to Linear Filtering and Prediction Problem, R.E. Kalman. Transactions of the ASME, Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof.