A system for estimating the friction between a road surface and a tire of a vehicle includes at least one first sensor and at least one vehicle processing device containing a friction estimation algorithm which is arranged to estimate the friction between the road surface and the tire of the vehicle based on friction related measurements is provided. The vehicle processing device is arranged to: receive an estimate of the expected friction between the road surface and the tire of the vehicle from a central processing device, from a storage device in the vehicle, or from at least one second sensor in the vehicle; adapt the friction estimation algorithm based on said received estimate of the expected friction; receive at least one friction related measurement from the at least one first sensor in the vehicle; and use the adapted friction estimation algorithm to perform an estimation of the friction between the road surface and the tire of the vehicle based on the at least one friction related measurement.