why Extended Kalman Filter represent the belief of mobile robot position by the gaussian with a mean, µ, and a covariance matrix Σ and how can this be explained in real world ?
thanks
Hi Elfituri,
The mean µ represents the most probable position of the robot, and the covariance Σ models how deviated from the most probable position it might be.
If you think in a 2D world, then you can plot Σ as an ellipse around µ. This ellipse represents the position of your robot with a certain level of confidence (i.e. your robot has a probability of a 99% of being within the bounds of an ellipse representing 3·Σ).
Not always a Kalman Filter is suitable to represent the belief of the robot position, as it assumes that the noise of your motions and sensors is Gaussian, but it is an efficient method which is suitable for most practical applications.
Regards,
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