Application of Unscented Kalman Filter in Inertial Navigation Systems

The Unscented Kalman Filter (UKF) is a state estimation algorithm suitable for nonlinear systems. Compared to the traditional Extended Kalman Filter (EKF), UKF employs the Unscented Transform (UT) to avoid complex Jacobian matrix calculations, thereby improving estimation accuracy and stability. In Inertial Navigation Systems (INS), UKF can effectively estimate and compensate for navigation errors, enhancing positioning precision.

### Problem Background Inertial Navigation Systems measure vehicle motion using accelerometers and gyroscopes. However, due to sensor noise, drift, and initial alignment errors, navigation information accumulates errors over time. Traditional Kalman filtering relies on linearized models, but under high-dynamic or strongly nonlinear conditions, EKF may fail. UKF approximates nonlinear distributions through sigma points sampling, making it more suitable for handling nonlinear error models in INS.

### Implementation Approach of UKF in INS State Variable Selection: Typically includes position, velocity, attitude errors, and sensor biases. Unscented Transform Implementation: Selects a set of sigma points, propagates them through the system's nonlinear model, and computes the mean and covariance. Measurement Update: Integrates GPS or other external observation data to correct state estimates. Error Compensation: Feeds estimated errors back into navigation calculations to suppress error accumulation.

### Advantages and Challenges Advantages: No linearization required, higher accuracy; less sensitive to initial errors and noise statistics. Challenges: Slightly higher computational cost than EKF; requires careful design of sigma point sampling strategy.

UKF provides a robust state estimation method for inertial navigation, particularly effective in extending autonomous navigation duration during GPS-denied environments. Future developments could integrate deep learning techniques to further optimize noise modeling and parameter adaptive adjustment.