GNSS + IMU: How Inertial Navigation Fills the Gaps

Introduction

The integration of GNSS with an Inertial Navigation System (INS) is the most widely deployed form of sensor fusion in precision navigation. These two technologies are almost perfectly complementary: GNSS is globally referenced and drift-free but slow and vulnerable to outages, while an INS is self-contained, high-rate, and immune to signal denial but accumulates error over time. Together, they form a navigation system dramatically superior to either alone.

IMU Components and What They Measure

An Inertial Measurement Unit (IMU) combines two fundamental sensor types into a single package:

• Accelerometers: Three orthogonally mounted accelerometers measure specific force - the non-gravitational acceleration experienced by the sensor. By integrating this measurement (correcting for gravity), the INS can compute velocity and position changes over time.
• Gyroscopes: Three orthogonally mounted gyroscopes measure angular rate about each axis. Integrating gyroscope data yields attitude - the orientation of the sensor with respect to a reference frame (roll, pitch, heading/yaw).

A complete INS combines the IMU with a navigation algorithm that mechanises the measurements - integrating accelerations to velocities and positions while tracking attitude changes. Dead-reckoning from a known starting point is the result: a continuously updated position estimate that requires no external signal.

Short-Term Accuracy vs Long-Term Drift

The fundamental challenge of inertial navigation is error growth. Every real sensor has noise, bias, scale factor error, and other imperfections. When accelerometer measurements are integrated once to obtain velocity and twice to obtain position, and gyroscope measurements are integrated to obtain attitude, these small errors accumulate. For a consumer-grade MEMS IMU, position error can grow to hundreds of metres within minutes. For a tactical-grade fibre-optic gyro IMU, the same drift may take hours to reach a metre.

The Three GNSS/INS Integration Architectures

The method by which GNSS and INS data are combined defines the system architecture. Three principal approaches exist, each offering a different trade-off between complexity and performance.

Loosely Coupled Integration

In a loosely coupled system, the GNSS receiver operates entirely independently and outputs its standard position and velocity solution. These outputs feed a Kalman filter alongside the INS-derived position and velocity. The filter estimates the errors in the INS state and periodically corrects the INS solution.

Loosely coupled integration is the simplest approach. It works with any GNSS receiver that outputs position and velocity, requires no access to internal receiver data, and can be implemented as an external post-processing step. However, it requires at least four satellites for the GNSS receiver to produce a valid solution - during periods of poor satellite geometry, the GNSS update becomes unavailable.

Tightly Coupled Integration

Rather than using the GNSS receiver''s position output, a tightly coupled system feeds raw GNSS measurements - pseudoranges and pseudorange rates - directly into the Kalman filter alongside the INS state. The filter models both the INS errors and the GNSS receiver clock errors simultaneously.

The critical advantage is that tightly coupled systems can continue to provide GNSS corrections even when fewer than four satellites are visible. With just one or two satellites, the filter can still constrain INS drift in one or two dimensions. This dramatically improves performance in urban canyons, partial sky obscuration, and building-entry/exit transitions.

Deeply Coupled (Ultra-Tight) Integration

Deep integration goes further still, combining the GNSS receiver''s tracking loops directly with the inertial navigation algorithm. The INS provides predicted pseudoranges to assist the receiver''s signal tracking in weak-signal and high-dynamic environments. This architecture offers the best performance in severely challenged environments - near-jammed signals, very high dynamics, rapid satellite transitions - but requires access to the receiver''s internal signal processing and is extremely complex to implement. It is primarily found in defence and high-performance aerospace systems.

The Kalman Filter''s Role

The Extended Kalman Filter (EKF) is the mathematical engine at the heart of most GNSS/INS fusion systems. It maintains a state vector representing the estimated errors in the INS solution (position error, velocity error, attitude error, accelerometer bias, gyroscope bias - typically 15 states for a loosely coupled system, 17 for a tightly coupled system that includes receiver clock state).

The filter propagates this error estimate forward in time using the inertial measurements, then updates it whenever a GNSS measurement arrives. The ratio of process noise to measurement noise - encoded in the filter''s covariance matrices - determines how much trust is placed in each source. A well-tuned Kalman filter will correctly weight the high-rate INS data against the lower-rate but drift-free GNSS data.

Practical GNSS/INS Systems

Several commercial systems implement GNSS/INS fusion for demanding applications. The u-blox ZED-F9R integrates a high-precision GNSS receiver with a built-in sensor fusion engine that accepts external IMU data, providing robust dead-reckoning for automotive applications including tunnel traversal. The NovAtel SPAN system represents the tactical-grade end of the market, combining NovAtel''s precision GNSS receivers with high-grade IMUs for surveying, LiDAR mapping, and defence applications, achieving centimetre-level accuracy even during significant GNSS outages.