[michaelt]

Imagine you want to know the depth of liquid in a tank you're filling up - and you've got a noisy depth gauge and a noisy flow-rate meter.

If you merely take the mean of the last 10 depth gauge readings, your smoothed depth reading will always lag behind the true depth, being about 5 readings out-of-date.

By fusing together the noisy depth gauge, and the noisy flow-rate meter, and a model saying how fast depth rises with flow, you can average out the noise without creating the same level of lag.

This is useful in applications like GPS receivers - there's noise so you do need filtering, but for driving through complex junctions, the last thing you want is a 5 second delay!