Systems and methods for correcting non-sinusoidal signals generated from non-circular couplers

A sensor system comprising:

• a coupler;
• a sensor spaced apart from the coupler to form a gap, the sensor comprising a transmitter coil adapted to be energized by a high frequency current source and at least two receiving coils generating a non-sinusoidal output signals, one of the receiver coils generates a sine-like function upon rotation of the coupler and the other of the receiver coils generates a cosine-like function upon rotation of the coupler;
• a memory module operable to compensate for the non-sinusoidal output signal caused by a plurality of geometric errors and the gap between the coupler and the at least two receiving coils;
• a processor module communicatively coupled to the memory module, the processor module configured to process the non-sinusoidal output signal from both the first and second receiver coils, the processor module also generates a corrected output signal representative of the rotational position of the coupler, the processor module configured to:
• compute an arctangent of the output signals from the first and second receiver coils;
• correct at least one error of the plurality of geometric errors from an electrical angle of the arctangent;
• apply a scaling factor at different operating points of the gap;
• calculate a slope and an offset parameters that when added equal a value for each of the scaling factors at the different operating points of the gap
• store the value as a corrected value;
• compensate the at least one of the plurality of geometric errors in the output signal by the corrected value.