Kalman filter

A discrete random time-evolution model defined by $x_k=F_k{x}_{k-1}+B_k{u}_k+w_k$, where

• $k\in {\mathbb{Z}}^{+}$ is the time
• $x_k$ is the state of the model
• $F_k$ is a Random variable dependent on the state at the previous time $x_{k-1}$.
• $u_k$ defines our chosen controls over the system.
• $B_k$ is the control-input model.
• $w_k$ is the system’s noise.