That’s exactly right - new measurements (observations) or state predictions (estimates based on the assumed system model) are weighted based on the ratio of the

That’s exactly right - new measurements (observations) or state predictions (estimates based on the assumed system model) are weighted based on the ratio of the standard deviation (uncertainty) of that observation/measurement to the historical standard deviation of the model to that point in time. For the closed form equations of the KF to work, you have to assume a) all measurements and parameters in the state model can be approximated by normal distributions with known standard deviations and means b) the underlying system model is linear. If you can’t assume b), then as the author mentions you can approximate the non-linear model with a linear one by taking the Jacobian and evaluating it at each step, and use the slightly modified EKF algorithm to bring everything together into an estimate of the system’s underlying state. As an aside a nice property of particle filtering (a different approach for localization and SLAM) is that there’s no linearity assumption. A nice property of both particle filtering and the KF/EKF is that the Markov assumption holds. This simplifies the underlying mathematics, as well as benefits the implementation on a computer by reducing time and space complexity required to evaluate the algorithms at each step.