A method of operating a cleaning process on a filter in a vehicle air intake includes passing air through the filter from an upstream side to a downstream side, and providing an exhaust duct having an inlet end adjacent the upstream side of the filter and an outlet end adjacent a cooling fan or other air-extraction device of the vehicle arranged to draw air through the exhaust duct from the inlet end to the outlet end. In a periodic cleaning subroutine, the rotational speed of the fan is increased from a first speed to a second speed, while a pulse of pressurized fluid is applied to a downstream side of the filter. The exhaust duct carries away material dislodged from the upstream side of the filter by the applied pulse, and the rotational speed of the fan is reduced to its original level.