Introduction

In the field of probabilistic robotics and computer vision, filtering techniques play a crucial role in state estimation and noise reduction. This lecture notes covers three topics: the Discrete Bayes Filter, the Particle Filter, and Robust Loss Functions with RANSAC.

Discrete Bayes Filter

The Discrete Bayes Filter is a probabilistic method for estimating the state of a system given a sequence of observations. It operates under the Markov assumption, where the current state depends only on the previous state and the current observation. Learn more in the Discrete Bayes Filter notes.

The Particle Filter

The Particle Filter extends the principles of the Discrete Bayes Filter to continuous state spaces. By representing the posterior distribution with a set of weighted particles, this filter can approximate complex distributions and handle non-linear and non-Gaussian systems effectively. Learn more in the Particle Filter notes.

Comparison of methods

So far we explored four aproaches of state estimation: Kalman filter, Factorgraph, Particle Filter and Discrete Bayes filter. You can learn more about advantages and disatvantages of each here.

Robust loss functions and RANSAC

Robust loss functions are essential in handling outliers in data fitting problems, in our case ICP alghorithm. The RANSAC (Random Sample Consensus) algorithm is a robust estimation method that iteratively selects a subset of the data to fit a model, aiming to maximize the number of inliers. Learn more about robust loss functions and RANSAC here.

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Author: Michal Kasarda