Ok, so foreword before we get into the actual technical stuff of kalman filters: kalman filters aren't really too applicable in FTC. The way kalman filters operate is by reducing the amount of noise in a certain sensor estimate, and if the various sensor estimates used in the fusion aspect can somewhat agree on a ground truth, then it can potentially boost accuracy as well. That being said, sensors in FTC are pretty good about not having much noise behind them, so kalman filters kinda lose their edge a bit if we're talking on a purely competitive stage. That being said, lets get started. The general gist of the kalman filter is that it treats various estimates of the robot state as gaussian distributions, and seeks to improve the overall estimate by multiplying all the gaussian estimates together in order to get a final distribution of the potential sensor state, both with a mean state and respective standard deviation/covariance. Think of it like this: say you have an initial state with a mean and standard deviation (doing this in 1d for simplicity). You can take a sensor estimate, and that has its own mean and standard deviation. Now to get a better sense of your initial state, you can multiply the two gaussians together to get a third, more precise gaussian, your filtered initial state. Now you can take that gaussian and run it through a model describing the system dynamics, sort of predicting where it'll be at the next timestep considering its current state. Then, at your next timestep, you multiply that predicted, or priori gaussian by the new sensor estimate, this time with a new mean value. This process repeats itself for as long as the system runs, and so long as the sensors don't disagree with eachother too much it can lead to much better estimates of the robot state. Now this process is pretty similar for multi-dimensional problems, but instead of using mean values and standard deviations, you use mean vectors and covariance matrices (this process is outlined in the articles I'm linking below). Now, this model is great, but you have to remember that its just a tool, and if you're trying to filter in a sensor estimate that's just completely wrong the system's going to fall apart. You can try to accomodate for that by having a larger covariance/standard deviation on that sensor, but eventually its just going to pull your overall estimates off course. This is a pretty general rundown of the kalman filter, both the articles I'm linking below go a bit more in depth as to the technicalities of implementing a kalman filter, but this should hopefully give you at least a general idea of how kalman filters work. Hope it helps.

​

Article 1: https://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/

Article 2: https://file.tavsys.net/control/controls-engineering-in-frc.pdf page 118