Kalman Filter with delayed measurements?

Hi all, sorry if this is a trivial question but I am new in this field. I have the following problem. I have a system where I need to measure some variables that are affecting the evolution of my system now, but that I can only know after gathering all pieces of information slowly during a quite long period of time. Let me make an example. Let’s say we have a complex economical system, where we have to keep the fraudulent transactions below a critical number in order to avoid the collapse of the system. The rate of fraudulent transactions is affecting the system now, but I can only know the final value of this rate many days in the future. Let’s take another example. I have a long wine pipe terminating in a barrel. The time needed by wine to rich the barrel is normally distributed around an average value. In order to avoid the wine overflow the barrel, I can control only the faucet at the beginning of this pipe. But I can only measure the velocity at the wine is filling the barrel. I think that this problem has a lot of similarities with a navigation system based on the Kalman filter that is widely used in robotics, but I can’t overcome the problem of the fact that I can only know the real value of my variable after a long period of time. Is there some specialized version of the Kalman filter that I can use to tackle this problem?

submitted by /u/Tokukawa
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