# CDS 110b: Kalman Filters

CDS 110b | ← Schedule → | Project |

In this lecture we introduce the optimal estimation problem and describe its solution, the Kalman (Bucy) filter. We discuss the extension of Kalman filters to nonlinear systems (the EKF) as well as the Linear Quadratic Guassian (LQG) problem.

- Lecture notes (from 2007)
- PVTOL example: pvtol_lqg.m, pvtol_kf.m, pvtol.m

- HW #6 (due 27 Feb 08)

## References and Further Reading

- R. M. Murray,
*Optimization-Based Control*. Preprint, 2008: Chapter 5 - Kalman Filtering

## Frequently Asked Questions

**Q : In homework 6, problem 1, I'm having a problem with ode45. What's going wrong?**

The integrator will get confused if you are declaring a random variable in the function that is passed to ode45. To get around this, in the script that calls ode45, declare a global varible that represents the sensor noise to use in the function that is integrated. This does make the noise "static" but unknown, which is fine for this problem.

**Q : In homework 6, problem 2c, is there a mistake in the second set of eigenvalues?**

Yes, it should instead read -2 +/- 2j.

**Q (2007): you asked what the estimator for the ducted fan would show (compared to eigenvalue placement). What should we be looking at and how would we be making those guesses?**

This was not such a great question because you didn't have enough information to really make an informed guess. The main feature that is surprising about the result is that the convergence rate is much slower than eigenvalue placement.