Kalman Filter States: What Do They Represent?

[Guillem]

It will sound a little bit stupid, but Ill ask anyways:

I have two series systems, the second is an UKF (Uscented Kalman Filter). I was told to reduce the first system in order to that the UKF estimate less states. My question is: What exactly do the states represent? I mean, if I have a non-discrete signal as the first system's output (for example, a voltage between -5 and 5), what would be the states?

These states sound me like discrete values that the signal can achieve.

Thank you in advance!

 

[Stephen Tashi]

The definition of "states" depends on the mathematical model that is being used in the filter. Part of specifying a Kalman filter is to define a mathematical model of how the current "state variables" of a system change with time from their present values to their "next" values.

If you look at a physical situation (e.g a car race) there is no universal procedure that tells you what the "states" of that situation are. If you define certain variables to describe its "states" then you can determine whether your choices are useful by finding out whether there are mathematical equations that correctly describe how one vector of values of your chosen state variables changes to a another vector of values as time passes.

So, when you say that you "have" a Kalman filter, this means that you can, in principle, examine what mathematical model the filter implements. The variables used in the deterministic part of the model are the "state" variables.