Multi-variate gyroscope offset temperature coefficient compensation

A system for calibrating micro-electro-mechanical system (MEMS) gyroscopes, the system comprising:

• a processor;
• and
• a chip testing interface,
• wherein the processor is configured to:
• during a characterization phase:
• a) control a first subset of the MEMS gyroscopes to vibrate masses of the first subset of the MEMS gyroscopes;
• b) determine a plurality of variates including quadrature and inphase values from output data of the first subset of the MEMS gyroscopes;
• c) determine offset temperature coefficients to minimize erroneous output data of the first subset of the MEMS gyroscopes over temperature variation;
• d) compute a linear regression using the quadrature and inphase values and the offset temperature coefficients determined for the first subset of the MEMS gyroscopes to determine linear regression variate coefficients for predicting the offset temperature coefficient based on the quadrature and inphase values;
• and
• during a production factory trim phase:
• e) control a second subset of the MEMS gyroscopes to vibrate masses of the second subset of the MEMS gyroscopes;
• f) determine a plurality of variates including quadrature and inphase values from output data of the second subset of the MEMS gyroscopes;
• g) determine a predicted offset temperature coefficient based on the quadrature and inphase values and the linear regression variate coefficients;
• and
• h) program the second subset of the MEMS gyroscopes to use the predicted offset temperature coefficient to adjust the output data during operation.

A calibrated micro-electro-mechanical system (MEMS) gyroscope, comprising:

• a mass driven by an electrical drive signal to vibrate;
• a detection electrode for detecting inphase and quadrature movement of the mass;
• a memory device storing an offset temperature coefficient for minimizing erroneous output data of the MEMS gyroscope, wherein the offset temperature coefficient is predicted by applying linear regression variate coefficients determined from a linear regression to variates including quadrature and inphase values of the output data measured while a plurality of MEMS gyroscopes are driven and are maintained in a static position;
• and
• a circuit that uses the offset temperature coefficient to compensate for a bias in the output data of the MEMS gyroscope during operation.

A method for determining linear regression variate coefficients for determining an offset temperature coefficient for micro-electro-mechanical system (MEMS) gyroscopes, the method comprising:

• a) controlling a plurality of MEMS gyroscopes from a batch of MEMS gyroscopes to vibrate respective masses;
• b) determining a plurality of variates including quadrature and inphase values from an output data of each of the plurality of MEMS gyroscopes;
• c) determining offset temperature coefficients of each of the MEMS gyroscopes;
• d) computing a multi-variate linear regression using the quadrature and inphase values and the offset temperature coefficients determined for the MEMS gyroscopes to determine the linear regression variate coefficients for predicting the offset temperature coefficient based on the quadrature and inphase values;
• and
• e) programing all the MEMS gyroscopes in the batch to use a respective predicted offset temperature coefficient in order to adjust the output data of the MEMS gyroscopes during operation, the respective predicted offset temperature coefficient being determined by applying the linear regression variate coefficients from the linear regression to the respective variates of each of the MEMS gyroscopes.