Array Structure
Array-based frameworks for multivariable systems allow for the organized calculation of complex interactions. A matrix model describes how multiple sensor inputs relate to various physical quantities through a set of linear equations. This format simplifies the correction of cross-axis sensitivity in devices like multi-axis accelerometers or pressure transducers.
Engineers utilize these arrays to perform rapid transformations in digital signal processors.
Error Decoupling
Cross-axis interference occurs when a sensor responds to a force applied perpendicular to its primary sensitive axis. By applying a matrix model, the calculation process can remove these unwanted components from the raw data. The off-diagonal elements in the matrix represent the coupling coefficients between the different axes.
Calibration involves determining these values by rotating the sensor through known orientations in a reference field.
Linear Transformation
Combining multiple outputs into a matrix model allows for a single mathematical operation to yield the corrected vector. The multiplication of the input vector by the inverse of the calibration matrix provides the final result in the desired coordinate system. This method is highly efficient for real-time applications where latency must be minimized.
It is a standard approach in inertial navigation and robotic control.
Validation Requirement
Model accuracy is verified by comparing the predicted outputs against a set of independent measurements not used during the initial calibration. If the matrix model fails to represent the physical behavior of the sensor, the residuals will show a non-random pattern. This failure might indicate that the system is non-linear and requires a higher-order approximation.
Regular re-calibration ensures that changes in the coupling coefficients over time are corrected.
