Does this mean that it's possible to develop a filter based on the raw data or do I still need a function that will describe the data? Because if it's the latter, then what I would suggest to the original poster is to first find a function that will describe your data, let's say you used least squares regression in order to come up with a function. And then from that function, you can apply it using the filter.
I'm still in the process of understanding the Kalman filter myself, so if there's another way to develop a filter without knowing the state equation, then I'd like to know how as well.