Fuel flow estimation and control system and method in a gas turbine engine

A method of estimating fuel flow through a gas turbine engine fuel supply circuit, the fuel supply circuit including a metering valve a first fuel loop disposed upstream of the metering valve, the first fuel loop being a bypass fuel line that includes a pressure regulating valve, the method comprising:

• determining a metering valve position from a metering valve position sensor;
• determining a thermally corrected metering valve position by applying the metering valve position to a first set of reference data stored in memory, the first set of reference data being thermal growth data for the metering valve position sensor;
• determining an uncorrected fuel flow across the metering valve by applying the thermally corrected metering valve position to a second set of data reference stored in memory, the second set of reference data being stroke-to-flow data for the metering valve;
• determining the flow through the bypass fuel line based in part on leakage fuel flow in a second fuel loop upstream of the metering valve, the second fuel loop being an actuation system that comprises fueldraulic engine actuators;
• determining a metering valve inlet pressure based on pressure downstream of the metering valve;
• determining a discharge pressure upstream of the bypass fuel line;
• determining a differential pressure error of the pressure regulating valve by applying the metering valve inlet pressure, the discharge pressure and flow through the bypass fuel line to a third set of reference data stored in memory, the third set of reference data being pressure regulating valve differential pressure data for the pressure regulating valve;
• determining a corrected metering valve fuel flow based on the uncorrected fuel flow and the differential pressure error;
• and
• controlling the metering valve based on the corrected metering valve fuel flow.