Method and system for air-fuel ratio control

An engine method, comprising:

• during a deceleration fuel shut-off (DFSO) condition, with purge enabled,
• injecting and combusting consecutive first and second fuel pulses of differing pulse widths, the consecutive first and second fuel pulses injected from an injector into a cylinder;
• learning an error for the injector based on an actual change in lambda between the first and second fuel pulses relative to an expected change in lambda, the change between a minimum reading and a reading immediately adjacent the minimum reading;
• and
• adjusting fueling from the injector based on the learned error following termination of the DFSO condition.

A method for an engine, comprising:

• while operating an engine at a maximum lean air-fuel ratio with all cylinders disabled,
• selectively enabling an injector of a cylinder;
• injecting and combusting each of a first, longer fuel pulse and a second, shorter fuel pulse from the injector into the cylinder;
• learning a first air-fuel ratio deviation from a maximum lean air-fuel ratio following the first fuel pulse and a second air-fuel ratio deviation from the maximum lean air-fuel ratio following the second fuel pulse;
• and
• learning an injector error based on an actual difference between the first deviation and the second deviation relative to an expected difference.