A method of controlling an internal combustion engine, the engine capable of operating both in a rich mode where an air:fuel ratio supplied to a combustion chamber of the engine is below stoichiometric, and in a lean mode where the air:fuel ratio supplied to the combustion chamber is above stoichiometric, the method comprising: determining both a first parameter value of a first engine parameter and a first sensed value of an oxygen sensor disposed in an exhaust plenum of the internal combustion engine while the engine is operating at a first air:fuel ratio point in the rich mode, wherein the first engine parameter comprises one of fuel metering rate and engine speed; characterized in that the method further comprises: determining both a second parameter value of the first engine parameter and a second sensed value of the oxygen sensor while the engine is operating at a second air:fuel ratio point in the rich mode, the second point being different from the first point; determining a reference relationship between the first engine parameter and the air:fuel ratio according to the first sensed value, the second sensed value, the first parameter value, the second parameter value, as taken in the rich mode, and extrapolating the reference relationship into the lean mode; thereafter, switching operation of the engine to the lean mode and controlling operation of the engine in the lean mode, using a current value of the first engine parameter, by: estimating a target parameter value of the first engine parameter to achieve a target air:fuel ratio according to the determined reference relationship; and controlling the engine so that the first engine parameter assumes the target parameter value. wherein the oxygen sensor is a resistive-based oxygen sensor having a resistance which is uncorrelated with oxygen content when the engine is in the lean mode, and wherein the first sensed value and the second sensed value of the oxygen sensor comprise a resistance of the oxygen sensor. determining both a first parameter value of a first engine parameter and a first sensed value of an oxygen sensor disposed in an exhaust plenum of the internal combustion engine while the engine is operating at a first air:fuel ratio point in the rich mode, wherein the first engine parameter comprises one of fuel metering rate and engine speed; characterized in that the method further comprises: determining both a second parameter value of the first engine parameter and a second sensed value of the oxygen sensor while the engine is operating at a second air:fuel ratio point in the rich mode, the second point being different from the first point; determining a reference relationship between the first engine parameter and the air:fuel ratio according to the first sensed value, the second sensed value, the first parameter value, the second parameter value, as taken in the rich mode, and extrapolating the reference relationship into the lean mode; thereafter, switching operation of the engine to the lean mode and controlling operation of the engine in the lean mode, using a current value of the first engine parameter, by: estimating a target parameter value of the first engine parameter to achieve a target air:fuel ratio according to the determined reference relationship; and controlling the engine so that the first engine parameter assumes the target parameter value. wherein the oxygen sensor is a resistive-based oxygen sensor having a resistance which is uncorrelated with oxygen content when the engine is in the lean mode, and wherein the first sensed value and the second sensed value of the oxygen sensor comprise a resistance of the oxygen sensor. determining both a second parameter value of the first engine parameter and a second sensed value of the oxygen sensor while the engine is operating at a second air:fuel ratio point in the rich mode, the second point being different from the first point; determining a reference relationship between the first engine parameter and the air:fuel ratio according to the first sensed value, the second sensed value, the first parameter value, the second parameter value, as taken in the rich mode, and extrapolating the reference relationship into the lean mode; thereafter, switching operation of the engine to the lean mode and controlling operation of the engine in the lean mode, using a current value of the first engine parameter, by: estimating a target parameter value of the first engine parameter to achieve a target air:fuel ratio according to the determined reference relationship; and controlling the engine so that the first engine parameter assumes the target parameter value. estimating a target parameter value of the first engine parameter to achieve a target air:fuel ratio according to the determined reference relationship; and controlling the engine so that the first engine parameter assumes the target parameter value. wherein the oxygen sensor is a resistive-based oxygen sensor having a resistance which is uncorrelated with oxygen content when the engine is in the lean mode, and wherein the first sensed value and the second sensed value of the oxygen sensor comprise a resistance of the oxygen sensor.