Section 3 : Kalman filters

Commentary

Section Goals

• To introduce Kalman filters in the context of linear Gaussian distribution for problems with continuous random variables.

Learning Objectives

Learning Objective 1

• Describe the properties of the linear Gaussian family of distributions, and how to apply them to Kalman filters.
• Exemplify an application of Kalman filtering, and draw a simple Bayesian network structure of a Kalman filter for a linear dynamical system.
• Explain the following concepts or terms:
  • Linear Gaussian
  • Multivariate Gaussian
  • Kalman gain matrix
  • Switching Kalman filter

Objective Readings

Required readings:

Reading topics:

Kalman Filters (see Section 15.4 of AIMA3ed)

Supplemental Readings

Ma, N., Bouchard, M., and Goubran, R. A. (2006). Speech enhancement using a masking threshold constrained Kalman filter and its heuristic implementations. IEEE Transactions on Audio, Speech, and Language Processing, 14(1), 19 - 32. DOI: 10.1109/TSA.2005.858515

Objective Questions

• What do the transition model and sensor model mean in the physical application in Kalman filtering?

Objective Activities

• Explore Kalman Filter related articles from Google Scholar to see which fields host the most applications, and then compare the representation and mechanisms from those applications with the Kalman filter in this course. Report your findings in the course conference.
• Complete Exercise 15.10 of AIMA3ed.