Process noise ($w_t,Q_t=\mathrm{Cov}(w_t)$)

Process noise is the random contribution to a state transition in a state-space model. It represents uncertainty in how the state evolves. Measurement noise instead affects the observed value of the state. In the local-level state-space model $x_t=x_{t-1}+w_t$, $y_t=x_t+v_t$, the first disturbance changes the state itself; the second changes its measurement.