An engine control system includes: a normalization module configured to normalize, to within a predetermined range of values, a spark timing of an engine and at least one other parameter of the engine, thereby producing a normalized spark timing and at least one normalized other parameter, respectively; a processing module configured to generate a sigmoidal spark timing by applying, to the normalized spark timing, one of (a) a sigmoidal function and a sinusoidal function; and an estimation module configured to estimate a torque output of the engine based on the normalized spark timing and the at least one normalized other parameter using a mathematical model.