Martin your answer as some core elements of what happens but technical not correct .
The pressure sensor is not within the exhaust but measures the pressure remotely.
It detects when the PAF filter is getting blocked the not the Catalysis.
The level of carbon deposits in the particulate filter is constantly monitored by the engine control unit, which calculates the flow resistance of the filter via the pressure sensor.
To determine the flow resistance, the exhaust gas volume before the particulate filter is compared with the pressure difference before and after the particulate filter and recorded as a ratio.
The pressure difference of the air flow before and after the particulate filter is calculated by exhaust gas pressure sensor.
The exhaust gas volume is calculated by the engine control unit from the air mass in the exhaust manifold and the exhaust gas temperature before the particulate filter.
The mass of exhaust gas is roughly equivalent to the mass of air in the intake manifold, which is calculated by the air mass meter. The volume of exhaust gas depends on the respective temperature.
This is calculated by the temperature sender before particulate filter. Using the exhaust gas temperature reading, the engine control unit can calculate the exhaust gas volume from the mass of air in the exhaust gas.
From the flow resistance of the filter, the engine control unit can detect the level of carbon deposit in the PAF filter.
A high flow resistance indicates that the filter is in danger of becoming blocked. The engine control unit initiates regeneration , starts injecting the additive under very strict control conditions.
The systems PSA , VAG , GM and Ford use tend to be very simliar in construction and operation.
The main differance I have found tends to be how they measure how much additive has been used and how much remains in the tank. Some have a float in the tank and some record how much as been injected and subtract this from the amount put in.