Spherical Error Residual

Mathematical Evaluation

Optimization routines calculate the difference between the distance of each data point from the estimated center and the calculated average radius. Minimizing this spherical error residual yields the correct scaling factors and offset values for each axis of the sensor. Corrected measurements then describe a sphere centered on the origin.

This mathematical approach removes the systematic biases that skew the raw sensor output.

Calibration Sweep

Rotation of the sensor through a wide range of orientations collects data across all three dimensions. Analyzing the spherical error residual after this scan confirms the quality of the calibration process. A high residual value indicates that some axes may suffer from non-orthogonal alignment or scaling errors.

System software checks these residual values before accepting the new calibration parameters.

Operational Limit

Non-linear distortions and magnetic interference can prevent the data from forming a clean spherical pattern. If the environment contains variable local magnetic fields, the spherical error residual will remain high even after optimization. Physical sensor damage or severe temperature drifts can also create non-repeatable errors.

In these cases, the high residual warns the operator that the sensor requires repair or environmental shielding.