Say I want to use Kalman filters for predicting the price of items at a supermarket. I have a Kalman filter for each item (apple/beef/brooms/etc). I notice that some items are sort of related, like apple with orange, beef with pork.
My question is how can I make these Kalman filters interact with each other? For example let's say I get observations about the price of beef and they show that they are going up. I want to tell the Kalman filter for pork somehow that it should also update. How can I do this?
Any literature or examples of this usage will be greatly appreciated, thanks
I am actually trying to ask this question in the general sense, but I wanted to frame the problem in a way that would be simpler for others to understand. So I understand that the Kalman filter uses observations to update its state. Suppose I want to incorporate observations for some Kalman filter into another, is there an accepted way of 'transforming' these observations? Or is it more of an art?