Lecture notes and recordings for ECE5550: Applied Kalman Filtering

To play any of the lecture recording files (below), QuickTime is required. This software may be downloaded (free) from http://www.apple.com/quicktime/download/. Each of the recordings is on the order of 20 to 30 minutes long, and between about 40 and 50 Mb in size.

If you are not registered at UCCS to take this course for credit, and if you wish to do so, please contact Dr. Gregory Plett using the information provided in the Section 0 notes.

This course can be taken at the graduate level as part of the Masters of Science in Electrical Engineering option in Battery Controls. See the IDEATE web site for more details.

0. Course introduction and syllabus. [PDF]
• 0: Course introduction and syllabus.
1. Introduction to Kalman filters. [PDF]
• 1.1: What does a Kalman filter do?.
• 1.2: The basic idea of the Kalman filter.
• 1.3: Examples of applications of Kalman filtering.
2. State-space dynamic systems. [PDF]
• 2.1: Introduction to state-space systems.
• 2.2: Time (dynamic) response.
• 2.3: Discrete-time state-space systems.
• 2.4: Examples of discrete-time state-space models.
• 2.5: Continuous-time observability and controllability.
• 2.6: More insight; discrete-time controllability and observability.
3. Dynamic systems with noisy inputs. [PDF]
• 3.1: Scalar random variables.
• 3.2: Vector random variables.
• 3.3: Uncorrelated versus independent.
• 3.4: Functions of a random variable.
• 3.5: Conditioning.
• 3.6: Vector random (stochastic) processes.
• 3.7: Discrete-time dynamic systems with random inputs.
• 3.8: Continuous-time dynamic systems with random inputs.
• 3.9: Relating Σ_w to S_w precisely; a little trick.
• 3.10: Shaping filters.
4. The linear Kalman filter. [PDF]
• 4.1: Introduction.
• 4.2: Developing the framework.
• 4.3: Setting up the Gaussian assumption.
• 4.4: Generic Gaussian probabilistic inference solution.
• 4.5: Optimal application to linear systems: Kalman filter.
• 4.6: Visualizing the Kalman filter.
• 4.7: MATLAB code for the Kalman filter steps.
• 4.8: Steady state: Deriving the Hamiltonian.
• 4.9: Steady state: Solving for covariances using Hamiltonian.
• 4.10*: Initializing the filter.
5. Kalman filter generalizations. [PDF]
• 5.1: Maintaining symmetry of covariance matrices.
• 5.2: Sequential processing of measurements.
• 5.3: Square-root filtering.
• 5.4: MATLAB code for the SR-KF steps.
• 5.5: Cross/auto-correlated process and measurement noises.
• 5.6: Kalman-filter prediction and smoothing.
• 5.7: Reduced-order Kalman filter.
• 5.8: Measurement validation gating.
6. Nonlinear Kalman filters. [PDF]
• 6.1: Extended Kalman filters.
• 6.2: An EKF example, with code.
• 6.3: Problems with EKF, to be improved in SPKF.
• 6.4: Sigma-point Kalman filters.
• 6.5: The SPKF steps.
• 6.6: An SPKF example, with code.
• 6.7: Efficient square-root SPKFs.
7. Particle filters. [PDF]
• 7.1: Numeric integration to solve Bayesian recursion.
• 7.2: Monte-Carlo integration and the importance density.
• 7.3: Weight normalization and impulse functions.
• 7.4: Sequential importance sampling.
• 7.5: Example.
• 7.6: How to display a marginal posterior.
• 7.7: Reducing particle degeneracy.
8. Multi-target, multi-model tracking. [PDF]
• 8.1: Introduction and a long example.
• 8.2: Data association.
• 8.3: Tracking with polar measurements and a Cartesian state.
• 8.4: The interacting-multiple-model Kalman filter.
• 8.5: Code for IMM.
9. Simultaneous state and parameter estimation using Kalman filters. [PDF]
• 9.1: Parameters versus states.
• 9.2: EKF for parameter estimation.
• 9.3: SPKF for parameter estimation.
• 9.4: Simultaneous state and parameter estimation.
• 9.5: EKF and SPKF joint and dual estimation.
10. Kalman filter applications. [PDF]
• 10.1: Examples of Kalman filters.
1. Linear algebra (matrix) review. [PDF]
• A.1: Terminology and notation.
• A.2: Matrix operations: Transpose, addition, subtraction.
• A.3: Matrix operations: Multiplication, powers, inverse.
• A.4: Linear equations and matrices.
• A.5: Interpreting y = A x.