Suppose you’re tracking some object based on its initial position

x_{0}and initial velocityv_{0}. The initial position and initial velocity are estimated from normal distributions with standard deviations σ_{x}and σ_{v}. (To keep things simple, let’s assume our object is moving in only one dimension and that the distributions around initial position and velocity are independent.)The confidence region for the object flares out over time, something like the bell of a trumpet.

Read on for the explanation.