IKFoM Understanding

Understanding of IKFoM in-depth involves the following topics:

1. State Representation

• State manifold structure (state_ikfom)
• Error state concept
• Handling different state types (position, rotation, biases)

2. Filter Core Components

• Prediction step implementation
• Update step mechanics
• Covariance propagation
• Noise modeling and handling

3. Manifold Operations

• SO3 (3D rotation) operations
• S2 (unit sphere) operations
• Vector space operations
• State composition

4. Measurement Integration

• Dynamic share model concept
• Measurement updates
• LiDAR-IMU fusion specifics
• Innovation computation

5. Implementation Architecture

• Template metaprogramming usage
• Class structure and inheritance
• Memory management
• Optimization techniques

6. Initialization and Configuration

• State initialization
• Parameter setup
• Noise covariance configuration
• System calibration

State manifold structure (state_ikfom):

prefix understanding of SO3 (special orthogonal group in 3d):

A custom manifold structure could be something like this :

MTK_BUILD_MANIFOLD(state_ikfom,
((vect3, pos))      // 3D position
((SO3, rot))        // 3D rotation as SO(3)
((SO3, offset_R_L_I))  // LiDAR-to-IMU rotation
((vect3, offset_T_L_I)) // LiDAR-to-IMU translation
((vect3, vel))      // 3D velocity
((vect3, bg))       // Gyroscope bias
((vect3, ba))       // Accelerometer bias
((S2, grav))        // Gravity direction on unit sphere
);

MTK_BUILD_MANIFOLD(process_noise_ikfom,
((vect3, ng))  // Gyroscope noise
((vect3, na))  // Accelerometer noise
((vect3, nbg)) // Gyroscope bias noise
((vect3, nba)) // Accelerometer bias noise
);