[zb]

Calculating a position (and time) from the GPS data is basically a case of throwing it in a matrix and calculating the fix with the least squared error, and many receivers do just just. However, many (most?) actually use a Kalman filter, which takes into account the estimated error from the previous fix (and calculates a new estimated error to be taken into account for the next fix). So what you're suggesting is already done inside the receiver.

This is also the ideal place to add in additional data such as from an accelerometer. If you only have the calculated position (and speeds, which are useful for figuring out how far you're actually likely to have moved since the last fix) but not the error estimates to work on then you've thrown away much of the useful data.