An Introduction to Kalman Filter [Greg Welch and Gary Bishop, 2006]

Kalman Filter: an efficient recursive filters that estimates the state of a process by minimizing the mean squared error from a series if incomplete and noisy measurements.

1. DISCRETE KALMAN FILTER

• state estimation governed by the linear stochastic difference equation
• state eqn
  
• xk = Axk-1 + Buk-1 + wk-1
• Measurement eqn
• zk = Hxk-1 + vk-1
• Process and measurement noise with probability distribution
  
• p(w) ~ N(0,Q) , p(v) ~ N(0,R)
• priori and posteriori estimate error
  
• 
  
• priori and posteriori estimate covariance error

1. PREDICT
• 
  
2. CORRECT
   

2. EXTENDED KALMAN FILTER

• state estimation governed by the non-linear stochastic difference equation