Methods and apparatus for operating an internal combustion engine are provided. The engine has an engine block defining a cylinder accommodating a reciprocating piston coupled to rotate a crankshaft, a fuel injector for injecting fuel inside the cylinder, and a crank position sensor positioned proximal to the crankshaft. A method includes commanding the fuel injector to perform a test fuel injection with a predetermined energizing time and using the crank position sensor to determine a crankshaft acceleration signal during the test fuel injection. The crankshaft acceleration signal is filtered and a value of an amplitude of a fundamental frequency component of the filtered crankshaft acceleration signal is determined. A correction factor of the predetermined energizing time is determined based on a difference between the determined value of the amplitude and a preset value thereof. The correction factor is used to correct an energizing time of subsequent fuel injections.