When mobile devices enter GPS-denied environments like underground transit tunnels, Inertial Navigation Systems (INS) estimate continuous movement vectors from internal MEMS sensors.

1. Sensor Fusion with Extended Kalman Filters (EKF)

The Kalman Filter Prediction-Update Loop

An Extended Kalman Filter combines noisy high-frequency IMU acceleration data with intermittent absolute GNSS fixes, calculating an optimal state estimate that minimizes cumulative sensor drift error.