What is the Kalman Filter?

The Kalman Filter is a recursive optimal estimator that can extract data from inaccurate or uncertain observations. Various conditions must be met to use the Kalman Filter;

• The system must be linear and dynamic.
• The system being modeled must be capable of being formulated using the linear equations given in the table below.

  State Equation:	$x_{k+1} = Ax_{k} + Bu_{k} + w_{k}$
  Output Equation:	$y_{k} = Cx_{k} + z_{k}$

  
  
  (A, B, C are matrices. w and z are noise. u is an input to the system.)

• The system must contain measurement and process noise, both of which must be Gaussian.

The Kalman Filter is widely used in controlling and observing projectile motion, such as aircraft navigation, missile control and radar tracking.