Multivariate Kalman Filter

Overview

Multivariate Kalman filters, like one dimensional Kalman filters, work in three parts:

• Model (prior)
• Predict (prediction)
• Update (posterior)

However, this is not as simple as it sounds. Now that we're working with multiple variables, we're straying away from the more direct "multiplying gaussians" approach to math and discretizing the system using linear algebra. Everything is matrices, many of which we have to design ourselves according to what we want to put in and get out of the system. We'll go through the steps we took to set up our specific multivariate Kalman filter, but for more general information you should, as always, read this book.

General Setup

Choosing state variables

We decided to expand on our previous Kalman filter by adding velocity as a state variable, while still working with one dimensional movement.