The Extended Kalman Filter: An Interactive Tutorial for Non-Experts
Part 2: Dealing with Noise
Of course, real-world measurements like altitude are obtained from a sensor like a GPS or barometer. Such sensors offer varying degrees of accuracy.  If the sensor is off by a constant amount, we can simply add or subtract that amount to determine our altitude. Typically, though, sensor accuracy varies unpredictably from moment to moment, making the observed sensor reading a “noisy” version of the true altitude:
observed_altitudecurrent_time = altitudecurrent_time + noisecurrent_time
Try moving around the slider above to see the effect of noise on the observed altitude. The noise is represented as percentage of the range of observable altitudes.
 For example, Garmin publishes the accuracy of its barometric altimeter readout as “10 feet with proper calibration” So, for example, if the altimeter reads 1000 feet, our actual altitude could be anywhere between 990 and 1010 feet.