Sounds very much like an ABS problem I have with my Primera.
There is an ABS sensor on each wheel and these can fail. Failure of only one will cause the problem you describe.
It usually manifests itself in the ABS triggering at low speed (do a test, see if it only happens below a certain speed) when the current across the faulty sensor drops and triggers the ABS with the characteristic pedal judder and noise.
What do you do about it?
Well unless you're really handy with a multimeter then you probably will have to take it to a mechanic and yes it will be expensive to fix! Unless you're really lucky and the sensor is just really dirty and not broken.
My mechanic told me not to bother about it as it wasn't dangerous ( i.e. no reduction in braking strength )and I would soon get used to it (which I have!!) and wasn't worth the expense of getting it fixed!
I'm no expert though, this just sounds like the same problem as mine.