Repeated Bayesian inference to track a time-varying parameter online I have trouble finding the name of the problem (and algorithms to solve it) where one needs to repeatedly estimate the value of a continuous, time-varying parameter online based on incoming observations, without knowing the dynamics of the parameter changes, (which could even be random). This seems like a trivial Bayesian inference problem, but I get lost in the literature.
If the observation model is linear and the parameter normal-distributed, what would be an algorithm that computes the maximum a posteriori probability estimate? I thought this would be the Kalman filter without system dynamics, but I am not sure since this would still involve a process noise, which I don't know how to define.

After more reading, particularly the book by West and Harrison (1997), it seems that it is called a Bayesian forecasting or filtering problem.
If you don't wish to model the dynamics (or can't), the model you could use is then that of a random walk. If the variables are normally-distributed, the Kalman filter would give you the maximum a-posteriori estimate.
