MATLAB Implementation for Inertial Navigation Algorithm

Inertial navigation solving is a process that utilizes data from inertial measurement units (IMUs) such as accelerometers and gyroscopes to calculate a vehicle's position, velocity, and attitude through mathematical algorithms. Implementing inertial navigation solving in MATLAB typically involves several key steps, including initial alignment, attitude update, velocity solving, and position solving. Code implementation often begins with structuring data input interfaces for IMU measurements and defining coordinate transformation matrices.

First, the initial alignment phase determines the vehicle's initial attitude and position, generally comprising coarse alignment and fine alignment. Coarse alignment uses gravity vectors and Earth's rotation angular velocity for preliminary attitude estimation through vector matching algorithms, while fine alignment enhances accuracy using filtering algorithms like Kalman filtering. In MATLAB, this can be implemented using functions like `kalman` for state estimation and coordinate transformation functions such as `quat2dcm` for quaternion-to-direction-cosine-matrix conversions.

Next, attitude solving forms the core component. Using angular velocity measured by gyroscopes, attitude is updated via quaternions or direction cosine matrices. The quaternion method is widely adopted due to its computational efficiency, implemented using update equations like `q_{k+1} = q_k + 0.5 * Ω * q_k * Δt`. Code implementation must include quaternion normalization using `quatnormalize` to maintain solving accuracy.

Velocity solving is based on accelerometer data but requires gravity component removal and consideration of coordinate system transformation from body frame to navigation frame. Since accelerometer measurements include both vehicle motion acceleration and gravitational acceleration, implementation involves coordinate transformations using functions like `quatrotate` and integration operations through numerical methods such as trapezoidal integration. Gravity compensation is typically handled by subtracting the local gravity vector from the transformed accelerations.

Finally, position solving is obtained by integrating velocity. Due to Earth's curvature and rotation effects, navigation equations in geographic coordinate systems are typically employed for calculation, ensuring results conform to physical laws. Implementation often uses geodetic coordinate updates with functions like `lla2ecef` for coordinate conversions and considers Coriolis effects in the navigation equations. The integration process can be optimized using Runge-Kutta methods for higher accuracy.

When implementing in MATLAB, additional considerations include data preprocessing (such as filtering and noise removal using `filter` or `smoothdata` functions), error compensation (like bias calibration through least-squares fitting), and real-time optimization. By appropriately selecting solving frequencies and algorithm parameters using timing functions like `tic`/`toc` for performance measurement, computational efficiency can be improved while maintaining accuracy.