The linear dynamical system model underlying the Kalman filter technique involves a random process $(x_{0}, v_{1}, w_{1}, x_{1}, z_{1}, v_{2}, w_{2}, x_{2}, z_{2}, \ldots)$ where $x_{k}$ represents state, $v_{k}, w_{k}$ represent measurement and process noise, and $z_{k}$ represent measurements. The wikipedia article on the topic generally uses the word "estimation" to refer to what the Kalman filter does, e.g. saying that it "produces estimates of unknown variables". Later, the article states that the Kalman filter is a "minimum mean-square error estimator".
My understanding of the term estimation in the context of statistics is that it refers to estimation of fixed, unknown parameters, and the term "prediction" applies when we attempt to make guesses about random variables (in this case, the states $x_{k}$) from others (the measurements $y_{k}$). See: What is the difference between estimation and prediction?. In light of the answer in the linked post, it would seem that there is nothing to estimate in the Kalman filter setup because all of the parameters are assumed to be known.
Question: In the context of statistics, is it better to say that the Kalman filter is performing prediction? If so, what explains the use of the word estimation in discussions of the Kalman filter. Or is there a way of seeing Kalman filtering as a statistical estimation procedure.
Note: I think this question is essentially the same as an unanswered question on the math stack exchange: https://math.stackexchange.com/questions/3452938/kalman-filter-state-estimate
