Strapdown Inertial Navigation System Simulation Using Quaternion Method

In strapdown inertial navigation system (SINS) simulation, the quaternion method is widely adopted for attitude resolution due to its computational efficiency and ability to avoid singularities. This article presents a quaternion-based SINS simulation approach, performing one-minute navigation solutions using simulated gyroscope and accelerometer data.

Core Methodology: Quaternion-based Attitude Update The attitude update employs quaternion differential equations, integrating angular velocity data from gyroscopes to compute the current attitude quaternion. This approach avoids gimbal lock issues associated with Euler angles while requiring less computational overhead compared to direction cosine matrices. In code implementation, this typically involves solving dq/dt = 0.5*q⊗ω using numerical integration methods like Runge-Kutta.

Accelerometer Data Processing Accelerometers provide specific force measurements, which are transformed from body frame to navigation frame using the attitude matrix (derived from quaternions). Velocity and position calculations incorporate gravity compensation. The transformation can be implemented using quaternion rotation operations: a_nav = q⊗a_body⊗q_conjugate.

Simulation Data Generation Gyroscope data simulates angular velocity variations of the vehicle, while accelerometer data replicates specific force inputs during motion. Sensor noise and drift effects must be included in the simulation to approximate real-world conditions. Code implementation typically involves adding Gaussian white noise and bias terms to ideal sensor outputs.

Error Analysis and Correction Integration operations accumulate errors over time, requiring appropriate error suppression techniques during simulation. Periodic heading alignment or integrated navigation corrections with reference systems (like GPS) should be considered. Algorithm implementation might include error state Kalman filters for continuous error estimation.

Extended Considerations: For practical applications, Kalman Filter (KF) or Particle Filter (PF) algorithms can be incorporated to enhance navigation solution accuracy. Quaternion normalization is essential to prevent error accumulation from numerical computations, typically implemented by periodically scaling quaternion components to maintain unit magnitude.

This simulation methodology validates the effectiveness of quaternion methods in SINS applications and provides reference for subsequent algorithm optimization and engineering implementation.