**Course introduction and syllabus.**[PDF]**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.
**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.
**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.
**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.
**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.
**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.
**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.
**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.
**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.
**Kalman filter applications.**[PDF]**Linear algebra (matrix) review.**[PDF]