What is Dead Reckoning?
Dead reckoning navigation is a measure of change of position, or measurement of velocity and integrating the measure of velocity as an overlay on the initial position to yield a new position. The carrier coordinate system is used to measure speed or travel so further attitude parameters are also needed to determine the direction of travel based on the environment.
In 2D navigation, courses only need to be measured; In 3D navigation, we need all three elements of the attitude to be measured. With attitude changed, the smaller the step size of position calculation the better the navigation parameters. The calculation was manually done before thus making the rate of updating data very low but what happens is that now it is calculated using computers.
How Dead Reckoning Works
The Mathematical Foundation
Dead reckoning fundamental equations:
Direction Measurement
To get heading or bearing is generally obtained by:
- Magnetic compass
- Gyrocompass
- Inertial measurement units (IMUs)
- GNSS heading
Distance Measurement
The travelled distance may be measured by:
- Odometer (wheel rotations)
- Pitometer log (water speed)
- Air speed indicator
- Pedometer or step counters
- Accelerometer integration
Error Sources
The first issue with a dead reckoning is that it accumulates errors:
| Error Source | Description | Impact |
|---|---|---|
| Instrument Errors | Inaccuracies of measuring devices | Systematic drifting of position |
| Environmental Factors | Currents, wind or rough land | Unstable position deviation |
| Calculation Errors | Round off errors/Approximation errors | Tiny accumulative mistakes |
| Time Measurement | Inaccurate timekeeping | Speed and distance errors |
| Initial Position | False initial position | Bias of every estimate |
Practical Applications
Dead reckoning in navigation remains to be a necessity in most disciplines:
Maritime Navigation
It is used as the main method of navigation in places where there is no sight of land or when electronic systems malfunction.
Aviation
Critical in producing flight plans and in the event of a jamming of the GPS along the transoceanic flights.
Robotics
Dead reckoning is applied in mobile robots on indoor setting by using wheel encoders.
Wilderness Navigation
Map, compass and pacing are used by backcountry travelers in route finding.
Space Exploration
The use of spacecraft dead reckoning takes place between celestial navigation fixes.
Advantages and Limitations
Error Accumulation
The main problem of navigation by dead reckoning is that the errors tend to add on over time:
- Heading errors – The error of 1° in heading will lead to 1.7 percent distance error
- Speed errors – Proportional to the position error directly
- Time measurement – When a period is large then small timing errors are important
- Environmental factors – Actual movement is influenced by currents, wind and slip
- Instrument errors – Error in calibration accumulates over the period of time
- Human factors – Modeling errors and computational errors
Modern Enhancements
To mitigate the shortcoming of dead reckoning, the most up-to-date systems supply it together with additional technologies:
GNSS Integration
The integration of DR and GPS offers position corrections periodically to remove the drift.
Map Matching
With the use of digital maps to confine the position to potential areas on the roads or in the pathways.
Sensor Fusion
Integration between IMU data, camera or Lidar data and artificial intelligence (AI) or Kalman filter information.
Landmark Recognition
Regular resetting of the error of positions and removal of the drift by reference to known objects.
Combined Navigation Systems
In recent dead reckoning based navigational systems the dead reckoning is normally integrated with other technologies:
| System Type | DR Role | Complementary Technologies |
|---|---|---|
| Automotive Navigation | GPS outage positioning | GPS, GLONASS, Galileo, wheel sensors, map matching |
| Marine Navigation | Primary position estimation | GPS, Radar, Sonar, AIS, electronic chart systems |
| Avionics | Backup navigation system | GPS, INS, VOR, DME, radar altimeters |
| Robotics | Future of position estimation Short-term | Lidar, cameras, ultrasonic sensors, SLAM |
| Wearable Tech | Indoor Navigation and step counting | GPS, Beacons via Bluetooth, WiFi location |