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:
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 + Random Vectors
- Week 5: Random Vectors + Stochastic Processes
- Week 6: Stochastic Processes + Parameter Estimation
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I do not know the Lugre friction model. But generally, there are two possibilities how to estimate state and parameters; joint estimation (estimating unknown parameters as a part of the state) and dual estimation (two concurrently running filters – one estimating stateunder assumption of known parameters; second estimating parameters under assumption of known state). Both have pros and cons. There is lot of papers freely available just google the terms, or write me, I’ll provide you some references.