Nice discussion from Fundamentals of Kalman Filtering: A Practical Approach by Paul Zarchan and Howard Musoff:
Often the hardest part in Kalman filtering is the subject that no one talks about—setting up the problem. This is analogous to the quote from the recent engineering graduate who, upon arriving in industry, enthusiastically says, “Here I am, present me with your differential equations!” As the naive engineering graduate soon found out, problems in the real world are frequently not clear and are subject to many interpretations. Real problems are seldom presented in the form of differential equations, and they usually do not have unique solutions.
Whether it’s Kalman filters, dynamical systems, or anything else, setting up the problem is the hard part, or at least a hard part.
On the other hand, it’s about as impractical to only be able to set up problems as it is to only be able to solve them. You have to know what kinds of problems can be solved, and how accurately, so you can formulate a problem in a tractable way. There’s a feedback loop: provisional problem formulation, attempted solution, revised formulation, etc. It’s ideal when one person can set up and solve a problem, but it’s enough for the formulators and solvers to communicate well and have some common ground.
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