What is the Kalman filter?

Kalman filter makes you overcome noises caused in the real environments when you use sensor to control system or find location of system. How can Kalman filter make it possible?
There is one assumption : a noise conforms with (is to be) a Gaussian distribution.
By using the assumption, you can predict next situation from last state. And then from many predicted state, you can take(estimate) one optimal state.

Some basic notation

x(k+1|k)  means the state estimate at time k+1(next situation) given k(last state).
Covariance matrix P = E[(x-x)(x-x)^t], E(x)=x (x is mean value )
-Sorry I cannot write upper bar notation in the google blog. If you know a method to use mathematical notation in the blog, please inform me. -


To be continued.....