Mitigating systematic error in gyrocompassing

A MEMS gyrocompass for mitigating systematic error in determination of a north angle, the MEMS gyrocompass comprising:

• at least one MEMS gyroscope having a sense axis within a reference plane;
• a memory;
• and
• a processing device communicatively coupled to the memory and that is configured to execute code on the memory that configures the processing device to:
• obtain samples from an output of the at least one MEMS gyroscope in at least two different angles of rotation about an axis perpendicular to the reference plane;
• fit an Earth rate response of the output as a function of a rotation angle simultaneously with individually fitting rate drift of each MEMS gyroscope of the at least one MEMS gyroscope as a function of time, wherein the processing device further determines the fittings by:
• determining one or more first fit coefficients (a0, a1;
• a0, a1, τ1;
• a0, a1, τ1, a2, τ2;
• a0, a1, a2) by fitting samples obtained from each individual MEMS gyroscope with at least one function determined as the function of time, and
• determining cosine and sine coefficients by fitting components of an Earth rotation rate projected on the reference plane based on samples obtained from each of the at least one MEMS gyroscope with at least one function determined as the function of from the rotation angle of the at least one MEMS gyroscope with respect to a reference angle;
• and
• wherein the processing device of the MEMS gyrocompass is further configured to determine the north angle as an angle between the reference angle and true north based on the cosine and sine coefficients.

A computer program product comprising a non-transitory computer readable medium storing code with instructions executable by a processing device for mitigating systematic error in north angle determined by a MEMS gyrocompass that includes at least one MEMS gyroscope having a sense axis within a reference plane, comprising:

• code for obtaining samples from an output of the at least one MEMS gyroscope in at least two different angles of rotation about an axis perpendicular to the reference plane;
• code for fitting an Earth rate response of the output as a function of a rotation angle simultaneously with individually fitting rate drift of each MEMS gyroscope of the at least one MEMS gyroscope as a function of time, wherein the fittings is performed by:
• determining one or more first fit coefficients (a0, a1;
• a0, a1, τ1;
• a0, a1, τ1, a2, τ2;
• a0, a1, a2) by fitting samples obtained from each individual MEMS gyroscope with at least one determined as the function of time, and
• determining cosine and sine coefficients by fitting components of an Earth rotation rate projected on the reference plane based on samples obtained from all of the at least one MEMS gyroscope with at least one function determined as from the rotation angle of the at least one MEMS gyroscope with respect to a reference angle;
• and
• code for determining the north angle as an angle between the reference angle and true north based on the cosine and sine coefficients.