Estimation Crash Course I: Statistics and Estimators
Statistics and Estimators: definitions of statisics and an introduction to the concepts of bias and variance of an estimator; several examples.
Mathematix
Reading Vershynin's HDP II: Subgaussianity
We study the class of sub-Gaussian random variables: those random variables whose tails are dominated by a Gaussian. Such random variables satisfy Hoeffding-type bounds and possess several interesting properties. We also define the sub-Gaussian norm and study its properties.
Reading Vershynin's HDP I: Markov, Chernoff, Hoeffding
A result on the convergence of sample mean and notes on some standard concentration inequalities such as the Markov, Chernoff, Hoeffding, and Chernoff’s bounds
Projection on the epigraph of the squared Euclidean norm
How to project on the epigraph of the squared Euclidean norm
Beyond the Kalman Filter II: Moving horizon estimation
Moving horizon estimation
Beyond the Kalman Filter I: Extended Kalman Filter
The extended Kalman filter with an application to position estimation
Projections on epigraphs
How to project on the epigraph of a convex function
The Kalman Filter VIII: QR-based square root form
Square root form of the Kalman filter
The Kalman Filter VII: Recursive maximum a posteriori
We show that the Kalman filter is a recursive maximum a posteriori estimator. This
The Kalman Filter VI: Further examples
Further examples using the Kalman filter in Python