GPS-Denied Dead-Reckoning Drift Estimator

Estimate how far position error grows during a GPS outage, based on IMU grade and speed — and how long you can navigate before estimated drift exceeds the selected position-error threshold.

A free, interactive calculator for autonomous vehicle and robotics engineers. Input your LiDAR’s angular resolution, range, and scan rate — get point cloud density estimates instantly. Built by Dr. Dilip Kumar Limbu, former A*STAR scientist and co-founder of Moovita, Singapore’s first autonomous vehicle company. No signup required. No paywall.

UDHY Tools / GPS-denied dead-reckoning drift estimator

GPS-denied dead-reckoning drift estimator

Estimate how far position error grows during a GPS outage, based on your IMU grade and vehicle speed — and how long you can navigate before drift exceeds typical GPS accuracy.

IMU configuration

IMU grade preset

Gyro bias instability (deg/hr)

Accelerometer bias (mg)

Scenario

Vehicle/robot speed: 5 m/s

Time since last GPS fix: 2 min

Estimated position drift

Cross-track (heading drift)

vs. typical GPS accuracy (~3m)

—

Drift growth over timedashed line = typical GPS accuracy (3m)

Simplified model using dominant error terms only: heading-drift-induced cross-track error (velocity × gyro bias × t²/2) combined via root-sum-square with accelerometer-bias-induced error (bias × t²/2). Ignores scale factor errors, misalignment, and noise. For planning and sensor comparison only — not a certified navigation error budget.

Why this matters

GPS-denied navigation — tunnels, urban canyons, indoor spaces, underwater — forces a robot or vehicle to rely on its IMU alone to estimate position. Unlike GPS, inertial dead reckoning has no external correction, so small sensor biases compound over time into position error that grows roughly with the square of the elapsed time. Knowing how long your specific IMU grade can “coast” before drift exceeds a usable threshold is a core input into localization architecture — it determines how aggressively you need loop closure, wheel odometry fusion, or visual-inertial correction.

Built by Dr. Dilip Kumar Limbu, Co-Founder of MooVita · Former Principal Scientist, A*STAR · UDHY.com

Model Assumptions

This estimator provides a simplified analytical estimate of inertial drift. It does not model all error sources present in a production inertial-navigation system, including scale-factor error, misalignment, noise density, temperature effects, vibration, Earth rotation, lever-arm effects, vehicle dynamics, or estimator feedback

FAQs on GPS-denied dead-reckoning drift estimator

1. What is dead reckoning in GPS-denied navigation?

Dead reckoning is a method of estimating current position using only a robot or vehicle’s IMU (inertial measurement unit) — accelerometers and gyroscopes — without any external reference like GPS. It’s used when GPS is unavailable, such as in tunnels, indoor spaces, or dense urban canyons.

2. Why does dead-reckoning position error grow over time?

Every IMU has small sensor biases in its gyroscope and accelerometer readings. Without GPS to correct them, these biases compound through integration — gyro bias causes heading error, which grows into cross-track position error, while accelerometer bias directly integrates into position error. Both grow roughly with the square of elapsed time.

3. How accurate is IMU-only dead reckoning?

Accuracy depends heavily on IMU grade. Consumer-grade MEMS sensors (phone/hobby grade) can drift several meters within a minute or two, while navigation-grade sensors (fiber-optic or ring-laser gyros) can maintain sub-meter accuracy for tens of minutes. There’s roughly a 100-500x difference in gyro bias between consumer and navigation-grade IMUs.

4. How long can a robot navigate without GPS before drift becomes a problem?

This depends on IMU grade and speed, but a common practical threshold is when drift exceeds typical GPS accuracy (~3 meters) — beyond that point, dead reckoning is no longer more accurate than GPS would have been. Consumer-grade IMUs typically cross this threshold within 1-3 minutes at moderate speed; industrial-grade sensors can often hold under a minute longer before comparable drift.

5. How can dead-reckoning drift be reduced?

The most common approaches are sensor fusion with wheel odometry, visual-inertial odometry (VIO), or SLAM-based loop closure, which correct accumulated drift using additional reference points rather than relying on the IMU alone. Higher-grade IMUs also reduce drift rate but at significantly higher cost.

6. What’s the difference between consumer, industrial, and navigation-grade IMUs?

The main difference is gyro bias instability — consumer MEMS IMUs typically drift around 10-100°/hour, industrial/tactical-grade MEMS around 1-10°/hour, and navigation-grade fiber-optic or ring-laser gyros around 0.01-1°/hour. Lower bias means slower error accumulation and longer usable GPS-denied navigation time.