KF gives you the optimal estimate (in the sense of maximum likelihood) for a (multivariate) Gaussian model. What KF would give you in your example depends on w

KF gives you the optimal estimate (in the sense of maximum likelihood) for a (multivariate) Gaussian model. What KF would give you in your example depends on what exactly the model is. But even in the simplest scenario imaginable you'd have to specify what expected value you start with, in the same way that you would in Bayes.