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.
Non-Linear Least Squares
Mathematical Fit
Mathematical optimization techniques estimate the parameters of non-linear models by minimizing the sum of squared differences between observed values and model predictions. Using non-linear least squares allows for the calibration of sensors whose outputs are non-linearly related to the physical inputs. This optimization handles the complex cross-axis sensitivities and high-order errors found in precision accelerometers.
The process stops when the change in parameter values falls below the numerical tolerance.
Residual Minimization
Minimizing the difference between the modeled acceleration and the raw sensor data yields the calibrated parameters. In the non-linear least squares framework, the objective function is iteratively updated using numerical derivatives. The algorithm requires a good starting point to prevent it from converging to a local minimum.
These initial values are often derived from a simplified linear model of the sensor.
Parameter Estimation
Model validation requires analyzing the residuals after the optimization converges to ensure no systematic patterns remain. When using non-linear least squares, the remaining errors should resemble white noise if the model is correct. If the residuals show a quadratic or cubic trend, it indicates that the sensor model is incomplete and needs additional parameters to capture the behavior.
This error analysis is performed on a separate validation dataset to avoid over-fitting. The resulting parameters are written directly to the non-volatile memory of the sensor chip.
Sourcing Verification
Automated test equipment executes these algorithms during the final verification stage of the sensor module. Since non-linear least squares requires significant processing power, the test bench computer performs the calculations and uploads the resulting trim values to the device. This split architecture keeps the onboard sensor processor simple and inexpensive.