Terrain-referenced navigation, image matching, map matching, gravity gradiometry, and stellar navigation.
Terrain-Referenced Navigation (TRN) determines position by comparing measured terrain features with a stored database. It is a form of position fixing — instead of dead-reckoning from a starting point, TRN asks: "Where on this map does my measured terrain profile match?"
The most common form uses a radar altimeter to measure height above the terrain, then compares this with a terrain elevation database. The key measurement is the terrain clearance:
where ĥb is the estimated height, ht,D is the database terrain height at the estimated horizontal position, and lbf is the lever arm to the radar altimeter antenna.
The radar altimeter measures the actual terrain clearance. The difference between the measured and predicted terrain clearance is the measurement innovation. If the estimated position is correct, this innovation is near zero. If the estimated position is wrong, the predicted terrain height will differ from the true terrain height, producing a non-zero innovation.
Sequential TRN processes each terrain clearance measurement one at a time using a Kalman filter (typically an EKF). The state vector includes the position errors of the host navigation system:
The measurement matrix depends on the terrain gradients:
These gradients determine how much a position error affects the predicted terrain clearance. If the terrain is steep, a small position error causes a large terrain clearance mismatch, making the measurement highly informative.
The key limitation: The terrain gradient is computed at the estimated position, not the true position. If the position error is large enough that the terrain slope at the estimated position differs significantly from that at the true position, the EKF can diverge — pushing the estimated position further from the truth instead of closer.
Solutions to divergence:
• Non-linear filters: Replace the EKF with a particle filter, point-mass filter, or Viterbi algorithm. These represent multiple position hypotheses simultaneously, avoiding the single-point linearization problem. Computationally expensive.
• Acquisition/tracking modes: Use a batch processing algorithm (Chapter 2) or a bank of parallel EKFs (MMAE filter bank) for initial acquisition when the position uncertainty is large. Switch to a single EKF for tracking once the position is well-determined.
Batch TRN processes a sequence of terrain clearance measurements together, using the shape of the measured terrain profile to find the best match in the database. This is more robust to large initial position errors than sequential processing.
TERCOM (TERrain COntour Matching): The classic batch algorithm. A sequence of terrain clearance measurements is collected along the flight path. This sequence is then correlated against terrain profiles extracted from the database for a grid of candidate positions. The candidate with the best match gives the position fix.
The matching criterion is typically the mean absolute difference (MAD) or root-mean-square (RMS) between the measured and database profiles:
The candidate position (x, y) that minimizes this is selected as the fix.
TERCOM requires:
• A sufficiently long terrain profile (typically 30–60 seconds of flight)
• Terrain variation along the flight path
• Accurate knowledge of the relative position changes during the profile (from INS dead reckoning)
• A terrain database with adequate resolution and accuracy
Performance: TERCOM achieves position accuracies of 50–200 m, depending on terrain roughness, database quality, and profile length. It was famously used by the Tomahawk cruise missile for autonomous navigation over enemy territory.
Different TRN sensors suit different environments:
| Sensor | Environment | Resolution | Accuracy |
|---|---|---|---|
| Radar altimeter | Airborne, over land | ~350 m footprint | 50–200 m position |
| Laser (LIDAR) | Airborne, low altitude | ~1 m footprint | 5–50 m position |
| Barometric | Airborne, over land | Single point | 100–500 m position |
| Sonar | Submarine/AUV, seabed | Varies with depth | 50–200 m position |
Laser TRN: A downward-pointing laser scanner produces a high-resolution terrain profile with a footprint of ~1 m. This enables much better terrain matching than a radar altimeter, achieving position accuracy of 5–50 m. However, laser TRN requires low altitude (typically <500 m), clear air, and a high-resolution terrain database.
Barometric TRN: Uses a barometric altimeter instead of a radar altimeter. The barometric height measurement is compared with the sum of the terrain height from the database and the estimated clearance. Less accurate than radar TRN but works at any altitude and without specialized hardware. Requires accurate atmospheric pressure calibration.
Sonar TRN: For submarines and AUVs, the seabed profile is measured by sonar and matched against a bathymetric database. The principles are identical to airborne TRN. The main challenges are the lower resolution of sonar compared to radar, and the limited availability of high-resolution bathymetric databases.
Image matching determines position by comparing a captured image with stored reference imagery. Two main approaches:
Scene Matching by Area Correlation (SMAC): Also known as DSMAC. A camera captures a downward-looking image, which is cross-correlated with a reference image stored in a database. The position of the correlation peak gives the position offset between the estimated and true positions.
The correlation score at offset (Δx, Δy):
SMAC can achieve position accuracy of 5–20 m when the reference imagery is high quality and the scene has not changed significantly. It was used alongside TERCOM in early cruise missiles. The main challenges are illumination changes (day/night, weather, shadows) and seasonal variations (snow cover, vegetation changes).
Continuous visual navigation: Instead of matching against a stored database, visual odometry tracks features across successive camera frames to estimate the camera's motion. This is a form of dead reckoning and accumulates drift over time, but provides smooth, high-rate velocity and heading estimates.
Visual SLAM (Simultaneous Localization and Mapping): Builds a map of the environment while simultaneously tracking the camera's position within it. SLAM eliminates the need for a pre-stored database but is computationally expensive and can fail in environments with few visual features.
Map matching constrains a navigation solution to a road or rail network. If we know the vehicle is traveling on a road, the position must lie on that road. This is perhaps the simplest and most effective form of feature matching for land vehicles.
How it works:
• Point-to-curve matching: The estimated position is projected onto the nearest road segment in a digital road map. This corrects the cross-track position error.
• Topological matching: The sequence of turns made by the vehicle is compared with the road network topology to identify which road the vehicle is on. This resolves ambiguities when multiple roads are nearby.
• Probabilistic matching: Multiple candidate roads are maintained with probabilities, updated as new information (turns, road curvature, speed limits) becomes available.
Benefits:
• Eliminates cross-track position error when correctly matched
• No additional sensors required (uses existing navigation solution)
• Constrains the heading to the road direction
• Prevents physically impossible solutions (position in a river, on a building)
Challenges: Incorrect matching to a parallel or nearby road introduces a systematic position error. This is most likely at complex junctions, in areas of dense road networks, and when the navigation solution error exceeds the road spacing. Tunnels and multi-level roads add further ambiguity.
Several less common but important feature-matching techniques exploit natural physical fields for position fixing:
Stellar navigation: Measuring the angles to known stars determines attitude precisely (arcsecond accuracy) and can also provide latitude and longitude. Star trackers have been used for maritime navigation for centuries and remain important for spacecraft attitude determination. They require a clear view of the sky and are typically combined with a gyroscope between star sightings.
Gravity gradiometry: The gravity gradient tensor — the spatial derivatives of the gravitational acceleration — varies with the subsurface mass distribution. By measuring this tensor with a gravity gradiometer and matching it against a database, position can be determined. This technique works underwater and underground, where GNSS is unavailable.
The gravity gradient tensor is a 3×3 symmetric matrix with five independent components (since it is trace-free). It is measured by differencing the outputs of pairs of accelerometers on a rotating platform.
Magnetic field variation: The Earth's magnetic field varies spatially due to subsurface geological structures. By measuring the total field intensity or its vector components with a sensitive magnetometer and matching against a magnetic anomaly database, position can be determined. This technique is mainly applicable to submarine navigation, where GNSS is unavailable and the magnetic field can be measured without the interference from ferromagnetic structures that plagues surface vehicles.
This simulation shows terrain-referenced navigation. A terrain profile (green) is generated, and an aircraft flies over it measuring terrain clearance. Watch how the measured profile is correlated against the database to find the position.