Fusion Sensor Fusion Library

The Bias algorithm provides run-time estimation of the gyroscope offset to compensate for temperature variations and fine-tune existing calibrations. It works by detecting stationary periods—when gyroscope measurements remain below a specific threshold for a set duration—and updating the offset using a high-pass filter with a low cutoff frequency. This can be used to clean gyroscope data before passing it to the AHRS algorithm.

To configure the algorithm, use the FusionBiasSettings structure with the FusionBiasSetSettings function.

The algorithm produces four primary outputs:

• quaternion: Describes the orientation of the sensor relative to the Earth. This can be converted to a rotation matrix via FusionQuaternionToMatrix or to Euler angles via FusionQuaternionToEuler.
• gravity: The direction of gravity in the sensor coordinate frame.
• linear acceleration: The accelerometer measurement with gravity removed.
• earth acceleration: The accelerometer measurement in the Earth coordinate frame with gravity removed.

The algorithm supports three Earth axes conventions: NWU (North-West-Up), ENU (East-North-Up), and NED (North-East-Down).

By default, Fusion uses a fast inverse square root algorithm for vector and quaternion normalization. If you require higher accuracy at the cost of execution speed, you can enable standard square root operations by:

1. Including the definition FUSION_USE_NORMAL_SQRT in FusionMath.h.
2. Adding FUSION_USE_NORMAL_SQRT as a preprocessor definition in your build configuration.

The Bias algorithm is configured using the FusionBiasSetSettings function and the FusionBiasSettings structure.

Algorithm settings are defined using the FusionAhrsSettings structure and applied via the FusionAhrsSetSettings function.

The FusionModelInertial function applies calibration parameters to gyroscope or accelerometer measurements using the following model:

$$\mathbf{i}_c = \mathbf{M} \mathbf{s} (\mathbf{i}_u - \mathbf{b})$$

Where:

• $\mathbf{i}_c$: Calibrated output
• $\mathbf{i}_u$: Uncalibrated input
• $\mathbf{M}$: Misalignment matrix
• $\mathbf{s}$: Sensitivity diagonal matrix
• $\mathbf{b}$: Offset vector

The FusionModelMagnetic function applies magnetometer calibration parameters using the following model:

$$\mathbf{m}_c = \mathbf{S} (\mathbf{m}_u - \mathbf{h})$$

Where:

• $\mathbf{m}_c$: Calibrated output
• $\mathbf{m}_u$: Uncalibrated input
• $\mathbf{S}$: Soft-iron matrix
• $\mathbf{h}$: Hard-iron offset vector