Understanding the Statistics of Kalman Filters I

Kalman Filters uses the concept of correlation and regression. I use the following example.

Let use predict the position of car at time k on the basis of position of car at time  k-1 and velocity of the car at time k. 

So, we apply the concepts of simple linear regression. Here A is the change in the position of car at time k with a unit change in the position of car at time k-1. B is the change in the position of car at time k with a unit change in the velocity of car at time k. Further, 

As these two linear models mentioned above approximate a real life scenario some amount of error is always involved. This error is represented by wk and vk. These are independently and identically normally distributed with a mean 0.These errors are called measurements errors or white noise. This discussion will be continued in the next entries of this blog.