Static Accelerometer Orientation Tumble Calibration Procedures
Static tumble calibration calculates accelerometer bias, scale factor, and cross-axis matrices by optimizing spatial vector residuals against local gravity.
Scalar Invariant Calibration
Magnitude Invariance
Multi-axis sensor calibration techniques that exploit the constancy of a physical field vector’s magnitude eliminate the need for precise orientation control during testing. Using scalar invariant calibration allows engineers to calibrate triaxial accelerometers by simply rotating the device into arbitrary positions within the Earth’s gravity field. This method relies on the principle that the sum of the squares of the three sensor outputs must always equal the square of the local gravitational acceleration.
The boundary of the calibration is defined by the stability of the local field.
Orientation Independence
Eliminating the requirement for high-precision mechanical positioning stages reduces the complexity and cost of the test setup. Since scalar invariant calibration does not depend on knowing the exact angle of the sensor during each measurement, the sensor can be held in a simple manual fixture. This independence makes the technique suitable for field calibration of completed instruments where a dedicated test bench is unavailable.
Numerical Adjustment
Computation of the sensor biases, scale factors and misalignments is performed by fitting the collected vector magnitudes to a sphere. When executing a scalar invariant calibration, the algorithm searches for the parameter set that distorts the ellipsoidal measurements of the raw sensor into a perfect sphere of radius equal to the local field magnitude. This optimization requires a minimum of nine distinct orientations to solve for all the correction factors.
If the orientations are clustered in one hemisphere, the optimization may converge to an incorrect solution. The quality of the fit is checked by analyzing the variance of the corrected vector lengths.
Reference Verification
Stability of the local reference field must be maintained during the calibration process to prevent errors in the computed parameters. For a scalar invariant calibration, the test area must be free of local magnetic or mechanical disturbances that could alter the field strength. If the local field varies during the test, the calibration algorithm will calculate incorrect scaling coefficients.