Fusion

https://github.com/xiotechnologies/fusion
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Fusion is a sensor fusion library for Inertial Measurement Units (IMUs) optimized for embedded...
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### Install imufusion library

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Use pip to install the imufusion package.

```bash
pip install imufusion
```

--------------------------------

### Preset BiasSettings configurations

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Examples of different BiasSettings configurations for varying convergence speeds.

```python
# Fast convergence (frequent stationary periods)
fast = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=2.0,
    stationary_period=1.0
)

# Balanced (typical)
balanced = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3.0,
    stationary_period=3.0
)

# Slow convergence (rarely stationary)
slow = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=5.0,
    stationary_period=10.0
)
```

--------------------------------

### Initialize AHRS and Bias instances

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Required setup for orientation and gyroscope bias estimation. Configure settings using the respective settings classes before starting the processing loop.

```python
import imufusion
import numpy as np

# Create instances
ahrs = imufusion.Ahrs()
bias = imufusion.Bias()

# Configure
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))
bias.set_settings(imufusion.BiasSettings(sample_rate=100))
```

--------------------------------

### Initialize AHRS and Bias Objects

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Setup algorithm instances and apply configuration settings with a specified sample rate.

```python
import imufusion
import numpy as np

# Create algorithm instances
ahrs = imufusion.Ahrs()
bias = imufusion.Bias()

# Configure settings
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))
bias.set_settings(imufusion.BiasSettings(sample_rate=100))
```

--------------------------------

### Calculate Recovery Samples

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Example calculation for setting the recovery period based on the sample rate.

```python
recovery_samples = sample_rate * 5  # 5 seconds at given rate

# 50 Hz: 250 samples
# 100 Hz: 500 samples
# 200 Hz: 1000 samples
```

--------------------------------

### Check Library Version

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Verifies the installed version of the imufusion library.

```python
# Check library version
import imufusion
print(imufusion.__version__)  # Should be "1.3.0" or compatible
```

--------------------------------

### Complete configuration and processing workflow

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

A comprehensive example integrating bias estimation, AHRS configuration, and sensor stream processing.

```python
import imufusion
import numpy as np

# Create instances
bias = imufusion.Bias()
ahrs = imufusion.Ahrs()

# Configure bias algorithm
bias_settings = imufusion.BiasSettings(
    sample_rate=100,           # 100 Hz sensor
    stationary_threshold=3.0,  # 3 deg/s is stationary
    stationary_period=3.0      # 3 second stationary window
)
bias.set_settings(bias_settings)

# Restore gyro offset from previous session if available
try:
    saved_offset = load_from_nvram('gyro_offset')
    bias.set_offset(np.array(saved_offset))
except:
    pass  # Will estimate from scratch

# Configure AHRS algorithm
ahrs_settings = imufusion.AhrsSettings(
    sample_rate=100,
    convention=imufusion.CONVENTION_NWU,
    gain=0.5,
    gyroscope_range=2000,
    acceleration_rejection=10,
    magnetic_rejection=10,
    recovery_trigger_period=500  # 5 seconds at 100 Hz
)
ahrs.set_settings(ahrs_settings)

# Process sensor stream
for sample in sensor_data:
    # Update sample period if available (compensates for clock errors)
    ahrs.set_sample_period(sample['delta_time'])
    
    # Estimate and correct gyroscope bias
    gyro_corrected = bias.update(sample['raw_gyro'])
    
    # Apply other corrections (calibration, remapping, etc.)
    # ... (as needed)
    
    # Update AHRS
    ahrs.update(gyro_corrected, sample['accel'], sample['mag'])
    
    # Get results
    q = ahrs.get_quaternion()
euler = imufusion.quaternion_to_euler(q)
    flags = ahrs.get_flags()
    states = ahrs.get_internal_states()
    
    # Process results...

# Save gyro offset for next session
final_offset = bias.get_offset()
save_to_nvram('gyro_offset', final_offset.tolist())
```

--------------------------------

### Configure Fusion Project CMake

Source: https://github.com/xiotechnologies/fusion/blob/main/CMakeLists.txt

Sets the project requirements and includes subdirectories for the library and examples. The Python bindings are conditionally included based on the build type.

```cmake
cmake_minimum_required(VERSION 3.15)
project(Fusion)

add_subdirectory("Fusion")
add_subdirectory("Examples/C/Advanced")
add_subdirectory("Examples/C/Simple")
if(CMAKE_BUILD_TYPE STREQUAL "Debug")
    add_subdirectory("Python/imufusion") # do not include when run by CI
endif()
```

--------------------------------

### Access Python RemapAlignment Constants

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

Examples of accessing the alignment constants in the Python API.

```python
imufusion.ALIGNMENT_PXPYPZ  # +X+Y+Z (identity)
imufusion.ALIGNMENT_PXPZNY  # +X+Z-Y
imufusion.ALIGNMENT_PXNZPY  # +X-Z+Y
# ... etc
```

--------------------------------

### Define preset AHRS configurations

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Examples of common configuration profiles for different sensor-fusion performance requirements.

```python
# Conservative (gyroscope-focused)
conservative = imufusion.AhrsSettings(
    sample_rate=100,
    gain=0.25,
    acceleration_rejection=15,
    magnetic_rejection=15
)

# Balanced (typical)
balanced = imufusion.AhrsSettings(
    sample_rate=100,
    gain=0.5,
    acceleration_rejection=10,
    magnetic_rejection=10
)

# Aggressive (sensor-focused)
aggressive = imufusion.AhrsSettings(
    sample_rate=100,
    gain=1.0,
    acceleration_rejection=5,
    magnetic_rejection=5
)
```

--------------------------------

### Configure AHRS Settings with Convention

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

Python usage example for setting the coordinate convention in AhrsSettings.

```python
settings = imufusion.AhrsSettings(
    convention=imufusion.CONVENTION_NWU
)
```

--------------------------------

### Get internal algorithm states

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Retrieves diagnostic information regarding sensor errors and recovery triggers.

```python
states = ahrs.get_internal_states()
print(f"Acceleration error: {states.acceleration_error}°")
print(f"Accelerometer ignored: {states.accelerometer_ignored}")
```

--------------------------------

### Remap sensor data in a processing loop

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/utility-functions.md

Example of applying a specific alignment to multiple sensor data streams before updating the AHRS.

```python
# Sensor mounted perpendicular to body Z-axis
alignment = imufusion.ALIGNMENT_PXPZNY  # Body X=Sensor X, Body Y=Sensor Z, Body Z=-Sensor Y

for sample in sensor_data:
    gyro_remapped = imufusion.remap(sample['raw_gyro'], alignment)
    accel_remapped = imufusion.remap(sample['raw_accel'], alignment)
    mag_remapped = imufusion.remap(sample['raw_mag'], alignment)
    
    ahrs.update(gyro_remapped, accel_remapped, mag_remapped)
```

--------------------------------

### Basic BiasSettings usage

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Shows how to instantiate BiasSettings with default or custom values and apply them to a Bias object.

```python
import imufusion

# Create with defaults
settings = imufusion.BiasSettings()

# Create with custom values
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=2,
    stationary_period=2
)

# Apply to Bias
bias = imufusion.Bias()
bias.set_settings(settings)
```

--------------------------------

### Get linear acceleration

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Retrieves the accelerometer measurement with the gravity component removed.

```python
linear_accel = ahrs.get_linear_acceleration()
# Returns: [x, y, z] acceleration without gravity component
```

--------------------------------

### Get gravity vector

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Retrieves the gravity component in the sensor coordinate frame.

```python
gravity = ahrs.get_gravity()
# Returns: 3D vector in sensor frame
```

--------------------------------

### Initialize Bias Settings in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

Constructor usage for configuring bias estimation settings in the Python interface.

```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3.0,
    stationary_period=3.0
)
```

--------------------------------

### Import Fusion Module

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Initializes the imufusion library for use in Python scripts.

```python
import imufusion
```

--------------------------------

### Retrieve gyroscope offset

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Get the current estimated gyroscope offset in degrees per second.

```python
offset = bias.get_offset()
# Returns: [x_offset, y_offset, z_offset] in deg/s
```

--------------------------------

### Vector and Quaternion Math in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Demonstrates quaternion conversion, vector rotation, and standard linear algebra operations using imufusion and numpy.

```python
import numpy as np
from scipy.spatial.transform import Rotation
import imufusion

# Get quaternion from AHRS
q = ahrs.get_quaternion()

# Convert to Euler angles
euler = imufusion.quaternion_to_euler(q)
roll, pitch, yaw = euler
print(f"Euler: Roll={roll:.1f}°, Pitch={pitch:.1f}°, Yaw={yaw:.1f}°")

# Convert to rotation matrix
matrix = imufusion.quaternion_to_matrix(q)

# Rotate a vector from sensor frame to Earth frame
v_sensor = np.array([1.0, 0.0, 0.0])
v_earth = matrix @ v_sensor
print(f"Vector in Earth frame: {v_earth}")

# Perform vector operations
v1 = np.array([1.0, 2.0, 3.0])
v2 = np.array([4.0, 5.0, 6.0])

# Magnitude
mag = np.linalg.norm(v1)
print(f"Magnitude: {mag:.3f}")

# Normalized
v1_norm = v1 / np.linalg.norm(v1)
print(f"Normalized: {v1_norm}")

# Dot product
dot = np.dot(v1, v2)
print(f"Dot product: {dot}")

# Cross product
cross = np.cross(v1, v2)
print(f"Cross product: {cross}")

# Angle between vectors
cos_angle = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
angle_rad = np.arccos(np.clip(cos_angle, -1.0, 1.0))
angle_deg = np.degrees(angle_rad)
print(f"Angle: {angle_deg:.1f}°")
```

--------------------------------

### Initialize BiasSettings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Create a new BiasSettings instance and apply it to the bias object.

```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3,
    stationary_period=3
)

bias.set_settings(settings)
```

--------------------------------

### Get Earth frame acceleration

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Retrieves the accelerometer measurement in the Earth coordinate frame with gravity removed.

```python
earth_accel = ahrs.get_earth_acceleration()
```

--------------------------------

### Initialize and process sensor data with imufusion

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/README.md

Demonstrates the standard workflow for initializing AHRS and bias correction objects, updating them with sensor data, and converting the resulting quaternion to Euler angles.

```python
import imufusion
import numpy as np

# Initialize algorithms
ahrs = imufusion.Ahrs()
bias = imufusion.Bias()

# Configure
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))
bias.set_settings(imufusion.BiasSettings(sample_rate=100))

# Process sensor data
for sample in sensor_stream:
    # Correct gyroscope bias
    gyro = bias.update(sample['raw_gyroscope'])
    
    # Update AHRS
ahrs.set_sample_period(sample['delta_time'])
    ahrs.update(gyro, sample['accelerometer'], sample['magnetometer'])
    
    # Get orientation
    quaternion = ahrs.get_quaternion()
    euler = imufusion.quaternion_to_euler(quaternion)
    print(f"Roll: {euler[0]:.1f}°, Pitch: {euler[1]:.1f}°, Yaw: {euler[2]:.1f}°")
```

--------------------------------

### Initialize and Update AHRS in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Demonstrates initializing the AHRS object, configuring settings, and processing sensor data in a loop.

```python
import imufusion
import numpy as np

# Initialize AHRS
ahrs = imufusion.Ahrs()

# Configure settings
settings = imufusion.AhrsSettings(
    sample_rate=100,              # 100 Hz
    convention=imufusion.CONVENTION_NWU,
    gain=0.5,
    gyroscope_range=2000,         # degrees/second
    acceleration_rejection=10,    # degrees
    magnetic_rejection=10,        # degrees
    recovery_trigger_period=500   # samples
)
ahrs.set_settings(settings)

# Process sensor data
for sample in sensor_data:
    ahrs.set_sample_period(sample['delta_time'])
    ahrs.update(
        sample['gyroscope'],
        sample['accelerometer'],
        sample['magnetometer']
    )
    
    # Get results
    quaternion = ahrs.get_quaternion()
    euler = imufusion.quaternion_to_euler(quaternion)
    flags = ahrs.get_flags()
    
    print(f"Roll: {euler[0]:.1f}°, Pitch: {euler[1]:.1f}°, Yaw: {euler[2]:.1f}°")
    print(f"Startup: {flags.startup}")
```

--------------------------------

### Access AHRS Flags in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

Example of checking AHRS status flags returned by the get_flags method.

```python
flags = ahrs.get_flags()

if flags.startup:
    print("Initializing...")
if flags.angular_rate_recovery:
    print("Fast rotation detected - restarting")
if flags.acceleration_recovery:
    print("Acceleration in progress - reducing accel influence")
if flags.magnetic_recovery:
    print("Magnetic distortion detected - reducing mag influence")
```

--------------------------------

### Initialize and Update Bias Estimator

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Demonstrates configuring the bias estimator and integrating it into a sensor processing loop with AHRS.

```python
import imufusion
import numpy as np

# Initialize bias estimator
bias = imufusion.Bias()

# Configure for 100 Hz sampling
bias.set_settings(imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3.0,
    stationary_period=3.0
))

# Initialize AHRS
ahrs = imufusion.Ahrs()
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))

# Process sensor data
offset_history = []

for sample in sensor_data:
    # Estimate and apply gyroscope bias correction
    gyroscope_corrected = bias.update(sample['gyroscope'])
    
    # Pass corrected gyroscope to AHRS
    ahrs.update(gyroscope_corrected, sample['accelerometer'], sample['magnetometer'])
    
    # Optional: Log offset for diagnostics
    offset = bias.get_offset()
    offset_history.append(offset)

# Save offset for next session
final_offset = bias.get_offset()
save_to_nvram(final_offset)
```

--------------------------------

### Get algorithm status flags

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Retrieves boolean flags indicating the current operational mode of the AHRS algorithm.

```python
flags = ahrs.get_flags()
if flags.startup:
    print("Algorithm is in startup mode")
if flags.acceleration_recovery:
    print("Acceleration recovery is active")
```

--------------------------------

### Initialize Bias settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Creates a new BiasSettings object with specific sample rate and stationary detection parameters.

```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3,
    stationary_period=3
)
```

--------------------------------

### Initialize Bias instance

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Create a new instance of the Bias estimator.

```python
bias = imufusion.Bias()
```

--------------------------------

### Configure Fusion Library with CMake

Source: https://github.com/xiotechnologies/fusion/blob/main/Fusion/CMakeLists.txt

Defines the library target, includes source files recursively, and sets up platform-specific dependencies.

```cmake
file(GLOB_RECURSE files "*.c")

add_library(Fusion ${files})

target_include_directories(Fusion PUBLIC .)

if(UNIX AND NOT APPLE)
    target_link_libraries(Fusion m) # link math library for Linux
endif()
```

--------------------------------

### Access and Modify Properties

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Read current settings or update parameters after initialization.

```python
settings = imufusion.BiasSettings(sample_rate=100)

# Read properties
print(f"Sample rate: {settings.sample_rate} Hz")
print(f"Threshold: {settings.stationary_threshold} deg/s")
print(f"Period: {settings.stationary_period} seconds")

# Modify properties
settings.stationary_threshold = 5.0
bias.set_settings(settings)
```

--------------------------------

### Ahrs()

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Initializes a new AHRS instance with default settings.

```APIDOC
## Ahrs()

### Description
Initializes a new AHRS instance with default settings.

### Returns
- **Ahrs** - A new instance of the Ahrs class.
```

--------------------------------

### restart()

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Restarts the algorithm, resetting internal state and triggering the startup sequence.

```APIDOC
## restart()

### Description
Restarts the algorithm, resetting internal state and triggering startup sequence.

### Returns
- **None**
```

--------------------------------

### Bias Configuration Presets

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Common configuration patterns for different operational environments and sampling requirements.

```python
settings = imufusion.BiasSettings(sample_rate=100)
```

```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=2.0,    # More sensitive to motion
    stationary_period=1.0        # Faster updates
)
```

```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=5.0,    # Less sensitive
    stationary_period=10.0       # Longer period
)
```

```python
settings = imufusion.BiasSettings(
    sample_rate=500,
    stationary_threshold=3,
    stationary_period=3
)
```

--------------------------------

### Initialize and process sensor data

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Demonstrates initializing the AHRS algorithm, processing sensor inputs, and converting the resulting quaternion to Euler angles.

```python
import imufusion
import numpy as np

# Initialize algorithms
ahrs = imufusion.Ahrs()
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))

# Process sample data
gyro = np.array([0.1, -0.2, 0.05])
accel = np.array([0.0, 0.0, 1.0])
mag = np.array([20.0, 0.0, -30.0])

ahrs.update(gyro, accel, mag)

# Get orientation
q = ahrs.get_quaternion()
euler = imufusion.quaternion_to_euler(q)

print(f"Roll: {euler[0]:.2f}°, Pitch: {euler[1]:.2f}°, Yaw: {euler[2]:.2f}°")
```

--------------------------------

### Initialize AhrsSettings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Create a new AHRS settings object with custom parameters.

```python
settings = imufusion.AhrsSettings(
    sample_rate=100,
    convention=imufusion.CONVENTION_NWU,
    gain=0.5,
    gyroscope_range=2000,
    acceleration_rejection=10,
    magnetic_rejection=10,
    recovery_trigger_period=500
)
```

--------------------------------

### Project Documentation Directory Structure

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/README.md

Visual representation of the documentation file hierarchy.

```text
output/
├── README.md                           # This file
├── module-overview.md                  # Entry point - overview of library
├── quick-reference.md                  # Quick lookup guide
├── types.md                            # All type definitions
├── configuration.md                    # Configuration parameters
└── api-reference/
    ├── ahrs.md                         # AHRS class API
    ├── bias.md                         # Bias class API
    ├── settings-classes.md             # Settings objects
    ├── utility-functions.md            # Standalone functions
    └── math-operations.md              # Low-level math
```

--------------------------------

### Utility Functions

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Helper functions for coordinate conversions, sensor calibration, remapping, and heading calculation.

```python
# Conversions
euler = imufusion.quaternion_to_euler(quaternion)  # [roll, pitch, yaw] in degrees
matrix = imufusion.quaternion_to_matrix(quaternion)  # 3x3 rotation matrix

# Calibration
gyro_cal = imufusion.model_inertial(gyro_raw,
                                     misalignment=M,
                                     sensitivity=s,
                                     offset=b)
mag_cal = imufusion.model_magnetic(mag_raw,
                                    soft_iron_matrix=S,
                                    hard_iron_offset=h)

# Remapping
remapped = imufusion.remap(sensor, imufusion.ALIGNMENT_PXPYPZ)

# Heading
heading = imufusion.compass(accel, mag, imufusion.CONVENTION_NWU)
```

--------------------------------

### Access and Modify Settings Properties

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Read or update individual configuration properties after initialization.

```python
settings = imufusion.AhrsSettings(sample_rate=100)

# Read properties
print(f"Sample rate: {settings.sample_rate} Hz")
print(f"Gain: {settings.gain}")
print(f"Gyro range: {settings.gyroscope_range} deg/s")

# Modify properties
settings.gain = 0.75
settings.acceleration_rejection = 15
ahrs.set_settings(settings)
```

--------------------------------

### Configure Bias settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Define detection thresholds and sample rate for the bias algorithm.

```python
settings = imufusion.BiasSettings(
    sample_rate=100,           # Hz
    stationary_threshold=3,    # degrees/second
    stationary_period=3        # seconds
)
bias.set_settings(settings)
```

--------------------------------

### Complete Processing Pipeline

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/utility-functions.md

A full workflow for initializing AHRS, applying sensor calibration, remapping axes, and processing raw sensor data into orientation estimates.

```python
import imufusion
import numpy as np

# Initialize algorithms
bias = imufusion.Bias()
ahrs = imufusion.Ahrs()

# Configure
bias.set_settings(imufusion.BiasSettings(sample_rate=100))
ahrs.set_settings(imufusion.AhrsSettings(
    sample_rate=100,
    convention=imufusion.CONVENTION_NWU,
    gain=0.5,
    gyroscope_range=2000,
    acceleration_rejection=10,
    magnetic_rejection=10,
    recovery_trigger_period=500
))

# Calibration parameters (from prior calibration)
gyro_offset = np.array([0.05, -0.02, 0.01])
gyro_sensitivity = np.array([1.0, 1.01, 0.99])
gyro_misalignment = np.eye(3)

accel_offset = np.array([0.01, -0.01, 0.0])
accel_sensitivity = np.array([1.0, 1.0, 1.0])
accel_misalignment = np.eye(3)

mag_hard_iron = np.array([2.5, -1.3, 1.8])
mag_soft_iron = np.array([
    [0.99, 0.01, 0.00],
    [0.01, 1.01, -0.02],
    [0.00, -0.02, 0.98]
])

# Sensor mount alignment
sensor_alignment = imufusion.ALIGNMENT_PXPYPZ

# Process sensor data
results = []
for sample in sensor_data:
    # Step 1: Remap sensor axes
    gyro = imufusion.remap(sample['raw_gyro'], sensor_alignment)
    accel = imufusion.remap(sample['raw_accel'], sensor_alignment)
    mag = imufusion.remap(sample['raw_mag'], sensor_alignment)
    
    # Step 2: Apply calibration
    gyro = imufusion.model_inertial(gyro, gyro_misalignment, gyro_sensitivity, gyro_offset)
    accel = imufusion.model_inertial(accel, accel_misalignment, accel_sensitivity, accel_offset)
    mag = imufusion.model_magnetic(mag, mag_soft_iron, mag_hard_iron)
    
    # Step 3: Estimate and correct gyroscope bias
    gyro = bias.update(gyro)
    
    # Step 4: Update AHRS
    ahrs.set_sample_period(sample['delta_time'])
    ahrs.update(gyro, accel, mag)
    
    # Step 5: Extract results
    q = ahrs.get_quaternion()
euler = imufusion.quaternion_to_euler(q)
    
    results.append({
        'timestamp': sample['timestamp'],
        'euler': euler,
        'quaternion': q,
        'gravity': ahrs.get_gravity(),
        'linear_accel': ahrs.get_linear_acceleration(),
        'flags': ahrs.get_flags(),
        'states': ahrs.get_internal_states()
    })

print(f"Processed {len(results)} samples")
```

--------------------------------

### Enable Standard Square Root in C

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Define this macro to use the standard sqrt() function instead of the default fast inverse square root algorithm. Requires recompilation of the library.

```c
#define FUSION_USE_NORMAL_SQRT
```

--------------------------------

### Access Quaternion Components

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Demonstrates how to access quaternion elements using array indexing or struct members in C, and array indexing in Python.

```c
FusionQuaternion q;
q.array[0];   // w (scalar)
q.array[1];   // x
q.array[2];   // y
q.array[3];   // z

q.element.w;  // scalar
q.element.x;  // x
q.element.y;  // y
q.element.z;  // z
```

```python
q = np.array([w, x, y, z])

w = q[0]
x = q[1]
y = q[2]
z = q[3]
```

--------------------------------

### Basic Orientation Tracking with Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Initializes an AHRS instance and processes sensor data without magnetometer input to calculate Euler angles.

```python
ahrs = imufusion.Ahrs()
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))

for sample in sensor_data:
    ahrs.update_no_magnetometer(sample['gyro'], sample['accel'])
    euler = imufusion.quaternion_to_euler(ahrs.get_quaternion())
```

--------------------------------

### Configure Bias Settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Set parameters for stationary detection to calibrate sensor bias.

```python
bias_settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3.0,
    stationary_period=3.0
)
```

--------------------------------

### Access Vector Components

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Demonstrates accessing vector components via array indexing or structured fields in C and NumPy arrays in Python.

```c
FusionVector v;
v.array[0];  // x-component
v.array[1];  // y-component
v.array[2];  // z-component

v.axis.x;    // x-component
v.axis.y;    // y-component
v.axis.z;    // z-component
```

```python
import numpy as np

# Create vector
v = np.array([1.0, 2.0, 3.0])

# Array indexing
x = v[0]
y = v[1]
z = v[2]

# Unpacking
x, y, z = v
```

--------------------------------

### set_settings(settings)

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Configures the bias algorithm with detection thresholds and sample rate.

```APIDOC
## set_settings(settings)

### Description
Configures the bias algorithm with detection thresholds and sample rate.

### Parameters
- **settings** (BiasSettings) - Required - Configuration object

### Returns
None
```

--------------------------------

### Sensor Calibration Workflow

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Applies inertial and magnetic models to raw sensor data before passing it to the bias and AHRS algorithms.

```python
for sample in sensor_data:
    gyro = imufusion.model_inertial(sample['raw_gyro'], 
                                     misalignment=gyro_mis,
                                     sensitivity=gyro_sen, 
                                     offset=gyro_off)
    accel = imufusion.model_inertial(sample['raw_accel'],
                                      misalignment=accel_mis,
                                      sensitivity=accel_sen, 
                                      offset=accel_off)
    mag = imufusion.model_magnetic(sample['raw_mag'],
                                    soft_iron_matrix=mag_si,
                                    hard_iron_offset=mag_hi)
    
    gyro = bias.update(gyro)
    ahrs.update(gyro, accel, mag)
```

--------------------------------

### Access Default Bias Settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

Use this constant to initialize bias settings with standard library defaults.

```c
extern const FusionBiasSettings fusionBiasDefaultSettings;
```

--------------------------------

### Configure AHRS Settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Initialize AHRS settings for different use cases ranging from basic tracking to high-rate motion capture.

```python
settings = imufusion.AhrsSettings(sample_rate=100)
```

```python
settings = imufusion.AhrsSettings(
    sample_rate=10,
    gain=0.1,
    gyroscope_range=250,
    acceleration_rejection=20,
    magnetic_rejection=20
)
```

```python
settings = imufusion.AhrsSettings(
    sample_rate=200,
    gain=0.75,
    gyroscope_range=1000,
    acceleration_rejection=5,
    magnetic_rejection=5
)
```

--------------------------------

### Initialize AHRS instance

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Creates a new AHRS instance using default settings.

```python
ahrs = imufusion.Ahrs()
```

--------------------------------

### Access Matrix Elements in C and Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Demonstrates row-major array access and element-wise access for FusionMatrix in C, compared to NumPy array indexing in Python.

```c
FusionMatrix m;

// Row-major: [0-2] row 0, [3-5] row 1, [6-8] row 2
m.array[0];  // m[0][0]
m.array[4];  // m[1][1] (diagonal element)

m.element.xx;  // m[0][0]
m.element.xy;  // m[0][1]
m.element.yx;  // m[1][0]
```

```python
m = np.array([
    [m00, m01, m02],
    [m10, m11, m12],
    [m20, m21, m22]
])

m[0, 0]  # m[0][0]
m[1, 1]  # m[1][1]
```

--------------------------------

### Bias()

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Initializes a new Bias estimation instance.

```APIDOC
## Bias()

### Description
Initializes a new Bias estimation instance.

### Parameters
None

### Returns
Bias instance
```

--------------------------------

### AhrsSettings Constructor

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Initializes a new AHRS settings object with configurable parameters for sensor fusion.

```APIDOC
## AhrsSettings()

### Description
Creates a new AHRS settings object with specified parameters.

### Parameters
- **sample_rate** (float) - Optional - Sample rate in Hz (Default: 100)
- **convention** (int) - Optional - Earth axes convention (Default: CONVENTION_NWU)
- **gain** (float) - Optional - Feedback gain (0.0-1.0) (Default: 0.5)
- **gyroscope_range** (float) - Optional - Maximum gyroscope range in deg/s (Default: 2000)
- **acceleration_rejection** (float) - Optional - Acceleration rejection threshold in degrees (Default: 10)
- **magnetic_rejection** (float) - Optional - Magnetic rejection threshold in degrees (Default: 10)
- **recovery_trigger_period** (unsigned int) - Optional - Recovery trigger period in samples (Default: 500)

### Returns
- **AhrsSettings** - An instance of the AhrsSettings class.
```

--------------------------------

### Access default settings in C

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Declares external references to the default settings objects provided by the C API.

```c
// In C
extern const FusionAhrsSettings fusionAhrsDefaultSettings;
extern const FusionBiasSettings fusionBiasDefaultSettings;
```

--------------------------------

### Configure North-West-Up (NWU) Convention

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Sets the coordinate frame to North-West-Up, suitable for ground-based devices.

```python
settings = imufusion.AhrsSettings(convention=imufusion.CONVENTION_NWU)
```

--------------------------------

### Manage gyroscope offset

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Shows how to load a previously saved gyroscope offset and retrieve the current estimate for persistence.

```python
# Set offset from previous session
saved_offset = np.array([0.05, -0.02, 0.01])
bias.set_offset(saved_offset)

# Later, get estimated offset for saving
final_offset = bias.get_offset()
save_to_nvram(final_offset)
```

--------------------------------

### Configure gain

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Access and modify the feedback gain to balance gyroscope and accelerometer/magnetometer influence.

```python
settings = imufusion.AhrsSettings()
print(settings.gain)  # 0.5
settings.gain = 0.75
```

--------------------------------

### Configure Variable Sample Rates

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Adjust settings to match specific input frequencies, ensuring the recovery trigger period remains consistent.

```python
# For 50 Hz input
settings_50hz = imufusion.AhrsSettings(
    sample_rate=50,
    recovery_trigger_period=250  # 5 seconds at 50 Hz
)

# For 200 Hz input
settings_200hz = imufusion.AhrsSettings(
    sample_rate=200,
    recovery_trigger_period=1000  # 5 seconds at 200 Hz
)
```

--------------------------------

### Update AHRS settings during operation

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Demonstrates how to instantiate AHRS settings and apply them to an existing AHRS object at runtime.

```python
# Create AHRS with initial settings
ahrs = imufusion.Ahrs()
initial_settings = imufusion.AhrsSettings(sample_rate=100)
ahrs.set_settings(initial_settings)

# Later, update settings
new_settings = imufusion.AhrsSettings(
    sample_rate=100,
    gain=0.75  # Increase gain
)
ahrs.set_settings(new_settings)
```

--------------------------------

### Quaternion Product

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Calculates the quaternion product for rotation composition.

```c
FusionQuaternion result = FusionQuaternionProduct(a, b);
```

--------------------------------

### Accessing and modifying sample_rate

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Demonstrates reading and updating the sample rate property of BiasSettings.

```python
settings = imufusion.BiasSettings()
print(settings.sample_rate)  # 100
settings.sample_rate = 200
```

--------------------------------

### Apply Alignment Constants

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Select from 24 orthogonal permutations to define sensor axis alignment.

```python
imufusion.ALIGNMENT_PXPYPZ   # No rotation (identity)
imufusion.ALIGNMENT_PXPZNY   # Rotate 90° around X
imufusion.ALIGNMENT_PYPZPX   # Rotate axes
imufusion.ALIGNMENT_NZPXNY   # Flip and rotate
# ... 24 total, all orthogonal permutations
```

--------------------------------

### imufusion.BiasSettings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/configuration.md

Constructor for the BiasSettings class to configure gyroscope bias estimation parameters.

```APIDOC
## imufusion.BiasSettings(sample_rate, stationary_threshold, stationary_period)

### Description
Initializes a new BiasSettings object to configure how the gyroscope bias is estimated.

### Parameters
- **sample_rate** (float) - Optional - Update frequency of input data in Hz (Default: 100).
- **stationary_threshold** (float) - Optional - Gyroscope magnitude in deg/s below which the device is considered stationary (Default: 3).
- **stationary_period** (float) - Optional - Duration in seconds the gyroscope must remain below the threshold to trigger a bias update (Default: 3).

### Usage Example
```python
settings = imufusion.BiasSettings(
    sample_rate=100,
    stationary_threshold=3,
    stationary_period=3
)
bias.set_settings(settings)
```
```

--------------------------------

### Convention Constants

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/utility-functions.md

Constants defining coordinate system conventions for sensor orientation.

```python
CONVENTION_NWU    # North-West-Up
CONVENTION_ENU    # East-North-Up
CONVENTION_NED    # North-East-Down
```

--------------------------------

### imufusion.BiasSettings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Configuration object for the Bias estimation algorithm. Users can instantiate this class to configure stationary detection parameters.

```APIDOC
## Class: imufusion.BiasSettings

### Description
Configuration object for the Bias estimation algorithm.

### Constructor
`imufusion.BiasSettings(sample_rate, stationary_threshold, stationary_period)`

### Parameters
- **sample_rate** (float) - Optional, Default: 100. Sample rate in Hz.
- **stationary_threshold** (float) - Optional, Default: 3. Stationary detection threshold in deg/s.
- **stationary_period** (float) - Optional, Default: 3. Stationary detection period in seconds.
```

--------------------------------

### Modify default settings in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Instantiates settings with default values and updates specific attributes as required.

```python
# Start with defaults
settings = imufusion.AhrsSettings()

# Modify as needed
settings.gain = 0.75
settings.sample_rate = 200
```

--------------------------------

### Configure sample_rate

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Access and modify the sample rate in Hertz.

```python
settings = imufusion.AhrsSettings()
print(settings.sample_rate)  # 100
settings.sample_rate = 200
```

--------------------------------

### set_settings(settings)

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Sets the algorithm configuration using an AhrsSettings object.

```APIDOC
## set_settings(settings)

### Description
Sets the algorithm configuration using an AhrsSettings object.

### Parameters
- **settings** (AhrsSettings) - Required - Configuration object with sample rate, gain, and rejection thresholds.

### Returns
- **None**
```

--------------------------------

### Modifying settings during operation

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Shows how to update settings and re-apply them to an existing Bias object.

```python
settings = imufusion.BiasSettings()

# Change sensitivity
settings.stationary_threshold = 4.0

# Apply updated settings
bias.set_settings(settings)
```

--------------------------------

### Utility Functions

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/DOCUMENTATION_INDEX.txt

A collection of mathematical and sensor-specific utility functions for coordinate conversion, sensor calibration, and data remapping.

```APIDOC
## Utility Functions

### Conversion Functions
- `quaternion_to_euler(q: Quaternion)`: Converts a quaternion to Euler angles.
- `quaternion_to_matrix(q: Quaternion)`: Converts a quaternion to a rotation matrix.

### Sensor Tools
- `remap(data: Vector3, alignment: RemapAlignment)`: Remaps sensor data to a different coordinate frame alignment.
- `compass(accelerometer: Vector3, magnetometer: Vector3)`: Calculates heading using accelerometer and magnetometer data.
```

--------------------------------

### Implement sensor processing loop

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Standard workflow for processing inertial and magnetic data. Includes steps for calibration, axis remapping, bias correction, and AHRS updates.

```python
for sample in sensor_data:
    # Step 1: Apply sensor calibration (if needed)
    gyro = imufusion.model_inertial(sample['raw_gyro'], ...)
    accel = imufusion.model_inertial(sample['raw_accel'], ...)
    mag = imufusion.model_magnetic(sample['raw_mag'], ...)
    
    # Step 2: Remap axes (if needed)
    gyro = imufusion.remap(gyro, imufusion.ALIGNMENT_PXPYPZ)
    
    # Step 3: Correct gyroscope bias
    gyro = bias.update(gyro)
    
    # Step 4: Update AHRS
    ahrs.set_sample_period(sample['delta_time'])
    ahrs.update(gyro, accel, mag)
    
    # Step 5: Get results
    q = ahrs.get_quaternion()
    euler = imufusion.quaternion_to_euler(q)
```

--------------------------------

### Define Coordinate Conventions

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Use these constants to specify the coordinate system orientation for IMU data.

```python
imufusion.CONVENTION_NWU  # North-West-Up (default)
imufusion.CONVENTION_ENU  # East-North-Up
imufusion.CONVENTION_NED  # North-East-Down
```

--------------------------------

### Define BiasSettings default constants in Python

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Initializes the module-level constant for Bias settings with predefined parameters.

```python
# Module-level constant
fusionBiasDefaultSettings = BiasSettings(
    sample_rate=100,
    stationary_threshold=3,
    stationary_period=3
)
```

--------------------------------

### AHRS Methods

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Methods for initializing, configuring, and updating the AHRS state, as well as retrieving orientation and processed acceleration data.

```APIDOC
## AHRS Methods

### Description
Methods to manage the AHRS state, perform sensor updates, and retrieve orientation data.

### Methods
- `ahrs.restart()`: Resets the AHRS.
- `ahrs.set_settings(settings)`: Configures AHRS settings.
- `ahrs.set_sample_period(period)`: Sets the sample period in seconds.
- `ahrs.update(gyro, accel, mag)`: Updates state using gyroscope, accelerometer, and magnetometer.
- `ahrs.update_no_magnetometer(gyro, accel)`: Updates state without magnetometer data.
- `ahrs.update_external_heading(gyro, accel, hdg)`: Updates state using external heading.
- `ahrs.get_quaternion()`: Returns orientation as [w, x, y, z].
- `ahrs.get_gravity()`: Returns gravity vector.
- `ahrs.get_linear_acceleration()`: Returns linear acceleration.
- `ahrs.get_earth_acceleration()`: Returns earth acceleration.
- `ahrs.set_quaternion(q)`: Sets initial orientation.
- `ahrs.set_heading(heading)`: Sets initial heading.
- `ahrs.get_flags()`: Returns status flags.
- `ahrs.get_internal_states()`: Returns internal state values.
```

--------------------------------

### BiasSettings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/bias.md

Configuration object for the Bias estimator.

```APIDOC
## BiasSettings(sample_rate, stationary_threshold, stationary_period)

### Description
Configuration parameters for the bias estimation algorithm.

### Parameters
- **sample_rate** (float) - Required - Sampling frequency of input data in Hz (Default: 100).
- **stationary_threshold** (float) - Required - Gyroscope magnitude in deg/s below which the device is considered stationary (Default: 3).
- **stationary_period** (float) - Required - Duration in seconds the gyroscope must remain below the threshold to trigger a bias update (Default: 3).
```

--------------------------------

### FusionModelInertial

Source: https://github.com/xiotechnologies/fusion/blob/main/README.md

Applies gyroscope or accelerometer calibration parameters using a misalignment matrix, sensitivity diagonal matrix, and offset vector.

```APIDOC
## FusionModelInertial

### Description
Applies gyroscope or accelerometer calibration parameters to uncalibrated sensor data.

### Parameters
- **uncalibrated** - Uncalibrated gyroscope or accelerometer input.
- **misalignment** - Misalignment matrix (M).
- **sensitivity** - Sensitivity diagonal matrix (s).
- **offset** - Offset vector (b).

### Returns
- **i_c** - Calibrated gyroscope or accelerometer measurement.
```

--------------------------------

### Define Bias Settings Structure

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

C structure used to configure the bias estimation algorithm parameters.

```c
typedef struct {
    float sampleRate;
    float stationaryThreshold;
    float stationaryPeriod;
} FusionBiasSettings;
```

--------------------------------

### CMake Configuration for imufusion Python Package

Source: https://github.com/xiotechnologies/fusion/blob/main/Python/imufusion/CMakeLists.txt

Defines the library source files, locates Python dependencies, and links them to the target.

```cmake
file(GLOB_RECURSE files "*.c")

add_library(imufusion-Python-Package ${files})

find_package(Python COMPONENTS Development NumPy)

target_link_libraries(imufusion-Python-Package PRIVATE Python::Python Python::NumPy)
```

--------------------------------

### Configure convention

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/settings-classes.md

Access and modify the Earth coordinate frame convention.

```python
settings = imufusion.AhrsSettings()
print(settings.convention)  # 0 (CONVENTION_NWU)
settings.convention = imufusion.CONVENTION_ENU
```

--------------------------------

### FusionFastInverseSqrt(x)

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

A high-performance approximation of the inverse square root (1/√x) used for vector and quaternion normalization. It is optimized for ARM processors and provides a significant speed improvement over standard square root functions with negligible precision loss for IMU applications.

```APIDOC
## FusionFastInverseSqrt(x)

### Description
Calculates a fast approximation of 1/√x for normalization purposes. This function is designed for performance-critical applications like IMU sensor fusion.

### Signature
`float FusionFastInverseSqrt(float x)`

### Parameters
- **x** (float) - The input value to calculate the inverse square root for.

### Usage
```c
#ifndef FUSION_USE_NORMAL_SQRT
float inv_sqrt = FusionFastInverseSqrt(x);
#endif
```

### Notes
- Performance: ~2-3x faster than standard sqrt on ARM processors.
- Precision: Negligible loss for IMU applications.
- Configuration: Define `FUSION_USE_NORMAL_SQRT` to fallback to standard `sqrt()`.
```

--------------------------------

### Sensor Remapping for Alignment

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/module-overview.md

Adjusts raw sensor data based on physical mounting orientation before processing.

```python
alignment = imufusion.ALIGNMENT_PXPZNY  # Sensor mounted rotated

for sample in sensor_data:
    gyro = imufusion.remap(sample['raw_gyro'], alignment)
    accel = imufusion.remap(sample['raw_accel'], alignment)
    mag = imufusion.remap(sample['raw_mag'], alignment)
    
    gyro = bias.update(gyro)
    ahrs.update(gyro, accel, mag)
```

--------------------------------

### Perform Minimal Sensor Fusion Update

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/quick-reference.md

Initialize the AHRS object and process a single sensor reading to obtain orientation data.

```python
import imufusion
import numpy as np

# Initialize
ahrs = imufusion.Ahrs()
ahrs.set_settings(imufusion.AhrsSettings(sample_rate=100))

# Simulate one sensor reading
gyro = np.array([0.1, -0.2, 0.05])    # deg/s
accel = np.array([0.0, 0.0, 1.0])     # g
mag = np.array([20.0, 0.0, -30.0])    # µT

# Update and get orientation
ahrs.update(gyro, accel, mag)
q = ahrs.get_quaternion()
euler = imufusion.quaternion_to_euler(q)

print(f"Orientation: {euler} degrees")
```

--------------------------------

### Configure AHRS settings

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/ahrs.md

Applies configuration parameters such as sample rate and gain using an AhrsSettings object.

```python
settings = imufusion.AhrsSettings(sample_rate=100, gain=0.5)
ahrs.set_settings(settings)
```

--------------------------------

### Define FusionConvention Enumeration

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/types.md

C enumeration defining standard Earth coordinate frame conventions.

```c
typedef enum {
    FusionConventionNwu,  // North (X), West (Y), Up (Z)
    FusionConventionEnu,  // East (X), North (Y), Up (Z)
    FusionConventionNed,  // North (X), East (Y), Down (Z)
} FusionConvention;
```

--------------------------------

### FusionQuaternionProduct(a, b)

Source: https://github.com/xiotechnologies/fusion/blob/main/_autodocs/api-reference/math-operations.md

Computes the quaternion product for rotation composition.

```APIDOC
## FusionQuaternionProduct(a, b)

### Description
Quaternion product (rotation composition): returns a * b. Note that this operation is non-commutative.

### Signature
FusionQuaternion FusionQuaternionProduct(FusionQuaternion a, FusionQuaternion b)
```
Tokens:
Raw