How does GPS help reinitialize an inertial navigation system?

Inertial navigation systems rely on gyroscopes and accelerometers to track a vehicle's position and velocity. However, these systems are susceptible to minute measurement errors that can accumulate over time, leading to significant deviations from the intended trajectory.12

To maintain accuracy, these systems must be reinitialized at frequent intervals using an independent navigation source, such as the Global Positioning System (GPS). By providing an external, highly accurate position and velocity fix, GPS allows the system's computer to correct the drift inherent in inertial sensors. In many modern applications, this process is optimized using Kalman filtering, a technique that weights data from multiple sources—such as inertial outputs and GPS—based on their expected quality to determine the most accurate estimate of the vehicle's current position and velocity.123