Static Gravity Reference Vector Determination for Sensor Calibration
Static gravity reference determination requires site gravimetric surveying and arcsecond stage indexing to isolate true sensor bias from facility tilt errors.
Scale Factor Matrix
Sensitivity Representation
Mathematical arrays containing the conversion coefficients for each axis of a multi-axis transducer map raw digital sensor outputs to physical units of measurement. The diagonal elements of the scale factor matrix represent the primary gains of the individual sensor axes. This matrix converts the raw voltage or digital counts into units of acceleration, angular rate or magnetic field strength.
The values are established during factory calibration by exposing the sensor to known physical inputs.
Calibration Modeling
Off-diagonal elements in this array can also be used to capture and correct for cross-axis sensitivity and axis misalignment. When utilizing a scale factor matrix, the full model corrects both the gain of each axis and the mutual influence between axes in a single matrix multiplication. This integrated approach simplifies the real-time processing requirements of the sensor microcontroller.
Mathematical Compensation
Compensation of the sensor data is achieved by multiplying the raw output vector by the inverse of the calculated scale factor matrix. During the sensor operation, this correction must be applied to every incoming data sample before the values are used in navigation or control loops. If the elements of the scale factor matrix drift due to temperature or aging, the accuracy of the corrected data degrades.
To prevent this, the calibration software often adjusts the matrix coefficients using real-time temperature sensor readings. The temperature compensation coefficients are stored in the memory of the sensor module.
Performance Verification
Verification of the matrix parameters is performed by executing a multi-axis rotation test on a calibrated stage. For a sensor using the scale factor matrix, the output vector must match the reference vector across all test orientations. This check guarantees that the gain and alignment of the sensor are within specified limits across the full operating range.
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.