BMW E46 330d: Fuel Pre-Pump Error Troubleshooting

BMW 330d car with a common rail diesel engine and 200 horsepower.

"The error code 'low pre-injection pressure' is stored. When the error is present, the vehicle jerks around 3000 RPM. At that point, the pressure drops below 2 bar. There is no jerking or error code above that RPM. At idle, I have a pressure of 4 bar when it's working correctly."

Which pump is faulty, the one in the tank or the one on the left undercarriage?
Has anyone had experience with this?

As the name suggests: the pre-lift pump! First, replace the fuel liter .

I changed the fuel filter today; we'll see if it works.

Is the pre-pump referring to the one located on the undercarriage?

The pump in the tank certainly isn't producing 4 bar; according to my documentation, it's 0.5 bar.
However, if the initial amount is too low, the pre-lift pump (underbody) may not be able to generate enough pressure.

No! It should be a vane pump or a gear pump, positioned near the high-pressure pump on the engine block. If, as described, the fuel filter and fuel lines are in good condition, then a new pre-pump should be installed. Best regards.

Since I changed the fuel filter, it seems to be working.