The Kalman filter does not require adding noise. The noise is a product of whatever phenomenon you are estimating. Normally we use noise in a model to cover up some behavior that is far to complicated to include in a more rigorous way. A classic example is the origin of Brownian motion. This probabilistic model came about to describe the motion of a large particle in a fluid of a smaller particles (e.g. a spec of dust in water). You could do physics and model every particle in the fluid and its collisions but that’s not tractable. Thus, the insight was to just model the large particle and turn the effects of collisions with the smaller ones into random disturbances.