April 2019

This week, I finally start talking about the Kalman filter! In particular, in Chapter 4, I present the classic filter formulations (discrete-time and continuous-time), while, in Chapter 5, I address some computational issues and show some tools to overcome them. Material: Chapter 4: Kalman Filter Chapter 5: Computational Aspects of the Kalman Filter Computational Exercise #2 Previous post of this course: Week 1: Syllabus + Introduction Week 2: Linear Algebra + Linear Systems Week 3: Set + Probability + Random Variables Week 4: Random Variables Continue→

This week, I finish Chapter 3 (about parameter estimation) initiated in Week 6 and start presenting Chapter 4 (about state estimation). Regarding Chapter 3, I particularly present the two remaining estimation criterion: maximum a posteriori probability (MAP) and minimum mean square error (MMSE). On the other hand, regarding Chapter 4, I define the linear-Gaussian state estimation problem and start to present its exact solution (which is the well-known Kalman filter!). Material: Chapter 3: Parameter Estimation Chapter 4: Kalman Filter Previous post of this course: Week Continue→

This week, I finish Section 2.7 (about stochastic processes) initiated in Week 5 and fully present Chapter 3, which is about parameter estimation. This chapter is very important, since the notation and estimation criteria adopted here (particularly the Bayesian ones) will be almost directly applied to the formulation of optimal filters from Chapter 4 on. Material: Section 2.7: Stochastic Processes Chapter 3: Parameter Estimation Computational Exercise #1 Previous post of this course: Week 1: Syllabus + Introduction Week 2: Linear Algebra + Linear Systems Week Continue→