| FWIW, I think I understand Kalman filters quite well, but the linked PDF is hard for me to follow, and I'd really struggle to understand it if I didn't already know what it's saying. I think the lesson there is that the Kalman filter is simpler in the "information form" where the Gaussian distribution is parameterized using the inverse of the covariance matrix. If you don't already know what that means, you likely don't get much out of that. I think the more intuitive way is to first understand the 1D case where the filter result is weighted average of the prediction and the observation where the weights are the multiplicative inverses of the respective variances (the less uncertainty/"inprecision", the more you give weight). In the multidimensional case the inverse is the matrix inverse but the logic is the same. More generally the idea is to statistically predict the next step from the previous and then balance out the prediction and the noisy observation based on the confidence you have in each. This intuition covers all Bayesian filters. The Kalman filter is a special case of the Bayesian filter where the prediction is linear and all uncertainties are Gaussian, although it was understood this way only well after Kalman invented the eponymous filter. Not sure how intuitive that's either, but don't be too worried if these things aren't obvious, because they aren't until you know all the previous steps. To implement or use a Kalman filter you don't really need this statistical understanding. If you prefer to understand things more "procedually", check out the particle filter. It's conceptually the Bayesian filter but doesn't require the mathematical analysis. That's the way I really understood the underlying logic. |