Error Analysis of Inertial Navigation Systems (Gyroscopes and Accelerometers)

Inertial Navigation Systems (INS) represent an autonomous navigation technology that relies on gyroscopes and accelerometers to measure angular velocity and linear acceleration. However, due to inherent sensor error characteristics, navigation accuracy can be significantly compromised. Implementing error analysis using MATLAB enables quantification of these error impacts and optimization of system performance.

Primary Error Sources Gyroscope Errors: Include bias, scale factor errors, and random noise (such as white noise and random walk). Bias causes cumulative angular drift over time, while scale factor errors affect the linearity of angular velocity measurements. Accelerometer Errors: Similarly exhibit bias, scale factor errors, and random noise. Additionally, accelerometers are susceptible to external disturbances like vibration, leading to additional measurement errors. Installation Errors: Misalignment between gyroscope and accelerometer installations introduces cross-coupling errors.

MATLAB Implementation Analysis Error Modeling: Develop error models for gyroscopes and accelerometers in MATLAB, incorporating deterministic errors (bias and scale factors) and stochastic errors (Gaussian noise and random walk). Key functions include creating state-space representations using ss() or defining noise parameters with randn() for Gaussian distributions. Simulation Verification: Generate simulated sensor data by combining ideal motion trajectories with error models, then compare true values against measurements using functions like plot() for visualization and norm() for error quantification. This evaluates error impacts on navigation solutions. Kalman Filter Optimization: Design Extended Kalman Filters (EKF) or Particle Filters (PF) using MATLAB's Control System Toolbox or custom algorithms. Implement state estimation with functions like kalman() for error compensation, enhancing navigation accuracy through real-time correction of bias and noise components.

Through MATLAB simulation analysis, cumulative error effects can be visually observed, and the effectiveness of various compensation algorithms validated, providing valuable references for optimizing practical systems.