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Inertial Navigation


1.   The navigation function forms part of the Guidance, Navigation and Control (GNC) system and consists of calculating a platform's location and velocity (also known as the state vector), as well as its orientation (or attitude). Navigation relies on input from a variety of sensors and subsystems.

2.   The output of the navigation function is the input for the control system, which in turn commands deflections of the control surfaces and values for other controls such as the engine.

Figure 1. Inertial Navigation system.



3.   Inertial navigation depends only on input from sensors directly contained within the platform and that have no reference to external, artificial input (e.g. GPS) and so is not susceptible to tampering or hacking.

4.   Aim.   The aim of inertial navigation, also known as dead reckoning, is therefore to determine the position, velocity and attitude of the platform by using onboard inertial sensors.

5.   Basic Components.   The essential components of an Inertial Navigation System (INS) and their setup are as follows:

  • Inertial sensors: to acquire the data.

  • Position: placement of the sensors on the platform in order to determine the trihedral of reference.

  • Computer: to make calculations within the chosen coordinate system.

6.   Main Concepts:

6.1. Inertial Measure Unit (IMU).   This device is able to measure and report attitude (roll, pitch and yaw), velocity, changes in altitude and gravitational forces acting on an aircraft. An IMU is typically composed of:

  • Accelerometers: measure the gravitational forces in a fixed coordinate system. For example, an accelerometer at rest on the surface of the Earth will measure '-1g', or -9.8 m/s2. When the platform is in motion the forces of inertia will be added. For this reason, accelerometers are often said to provide a 'noisy' signal.

  • Gyroscopes: measure angular velocity. A mechanical gyroscope includes a spinning wheel or disc. Thanks to conservation of angular momentum any change in the orientation of the axis of the spinning wheel will be registered by the sensor; the change in orientation of the platform may therefore be calculated. Different technologies and physical principles are used in the construction of gyroscopes. These include the most precise Fiber Optic Gyroscopes (FOG) based on the Sagnac effect and also the less precise Micro Electro-Mechanical (MEMS) units which are based on calculation of the Coriolis force by means of tiny vibratory structures. Gyroscopes are essential for calculation of orientation, but may suffer from drift - even when static. FOGS gyros are generally much more accurate than MEMS units.

  • Magnetometers: measure magnetism. A simple type of magnetometer is a compass, which measures the direction of the Earth's magnetic field in 2D. In recent years, magnetometers have been miniaturized (e.g. MEMS sensors). The Earth's magnetic field is a 3-dimensional vector that, like gravity, can be used to determine long-term orientation.

The IMU intelligently compensates for the disadvantages of some sensors by fuzing input from others less affected, thus obtaining an output with reduced noise and less drift. The main problem with IMUs is that they naturally accumulate error during the process of integration of both angular and linear velocity.

6.2. Air Data System/Air Data Unit (ADS/ADU).   This system (or subsystem) measures ambient atmospheric conditions. It may include some or all of the following sensors:

  • Barometer: measures static pressure. As explained in the Introduction to altimeters, altitude may be derived from air pressure.

  • Static-pitot system:  The pitot tube measures total air pressure, equal to the sum of incidental air and static port pressure. This system is used to measure airspeed.

  • Thermometer: Through different principles it can measure the temperature. The temperature is necessary to estimate the density of the surrounding air. The density is used to calculate the TAS from the IAS.

6.3. Attitude and Heading Reference System (AHRS).    Consists of sensors (gyroscopes, accelerometers and magnetometers) that provide attitude information for the platform. The difference between an IMU and an AHRS is the post processing system. The IMU reports data to an additional device that computes attitude and heading. These computers usually use Kalman filters to estimate. The AHRS can typically be found within an Electronic Flight Instrument System (EFIS) as used in many manned aircraft cockpits. When an AHRS also provides air, altitude or external temperature information it is known as an Air Data Attitude & Heading Reference System (ADAHRS).

Figure 2. AHRS Scheme.

6.4. Attitude Indicator.   Shows the orientation of the aircraft in relation to the Earth's horizon. The attitude indicator helps the pilot to fly under low visibility conditions.

6.5. Inertial Navigation System (INS).   Estimates the position, velocity and orientation of the aircraft without having to rely on external references. 

Figure 3. INS Scheme.

7.   Data processing and the intelligent fuzing of information from a variety of sensors is a core strength of the UAV Navigation AHRS and sets it apart from other, inferior products which may fail to compensate for false readings, out of range readings or the lack of input in a particular environment (e.g. flying in a GPS-denied environment). The UAV Navigation system allows the execution of accurate, robust and reliable flight control under highly dynamic conditions, as well as in degraded environments.



8.   The technology behind the sensors involved in inertial navigation has improved over the last few years, with precision increasing whilst both size and cost have reduced. Aside from these benefits, inertial sensors are a popular choice for system developers due to the fact that they are largely immune to jamming because they do not depend on outside elements such as a Global Navigation Satellite System (GNSS) system or VHF Omni-Directional Range (VOR) system.

9.   Inertial Sensor Quality.   Depending on the application, the following qualities of sensor may be identified:

9.1. Sub-Inertial or Tactical Quality.   Used in short-term navigation and the drift is normally compensated using GNSS:

  • Gyroscope drift: 1º/hour

  • Accelerometer drift: 10-3 g

9.2. Inertial or Navigation Quality.   Used in long-term and high-precision applications.

  • Gyroscope drift: <10-2 º/hour

  • Accelerometer drift: <10-4 g.

Brief History

10. As explained in the Inertial Navigation section, inertial navigation requires a continuous update of position based on readings acquired from different sensors: accelerometers, gyroscopes etc.

11. First Steps in Inertial Navigation.   The Space Inertial Reference Earth (SPIRE) was the first inertial navigation system created in 1953 as part of the navigation system of a B-29 bomber for a flight from Boston to Los Angeles. It used gyroscopes and accelerometers to determine position without relying on the transmission or reception of external signals that might reveal the aircraft's position or make it vulnerable to enemy interference. It was the first truly successful demonstration of inertial navigation. However, it was a massive piece of equipment (1.5 m diameter and 1200 kg):


Figure 4. SPIRE - Ref: INS/GPS Technology Trends. (George T. Schmidt)

12. Inertial Navigation for Submarines.   Inertial navigation is vital underwater as the GNSS satellite signals cannot penetrate water and therefore any form of GNSS navigation is unavailable when the submarine is completely submerged. In 1954 an underwater version of SPIRE was released: the Shipboard Inertial Navigation System (SINS). Since then extremely accurate inertial navigation systems have been developed for submarines to allow very accurate navigation underwater for long periods of time.

13. Inertial Navigation in Space.   Another significant historical moment for inertial navigation was the APOLLO guidance computer which safely landed the Lunar Module on the Moon in 1968. Again, inertial navigation is of vital importance during space missions where it is not possible to use traditional GNSS constellations.

14. Missile Systems.   The most precise inertial navigation sensors have been designed for use in nuclear submarines and intercontinental missiles. The most precise sensor unit was the Advanced Inertial Reference Sphere (AIRS), installed in ballistic missiles in the 70's.  It has a drift rate of 1.5 x 10-5 º/ hour. However, AIRS features about 19,000 components and was extremely expensive to produce.

15. Unsurprisingly, the general line of development over the years has been to miniaturize and improve the sensors from the type used in SPIRE to a small cube that took humankind to the moon. Nowadays, inertial sensors are tiny chips that can be integrated into many consumer devices.

16. The progress of the technology has meant a reduction of components, less maintenance, lower costs, and more reliability. A visual representation of these trends can be seen in the following chart:

Figure 5. Number of components trend

17. This reduction in size and weight has been exploited to the full in the aeronautical industry, where sensor manufacturers produce units that can be integrated in UAV flight control systems.

Types of Sensor

18. Mechanical.   Work on different mechanical principles: conservation of angular momentum for gyroscopes or Newton's second law for accelerometers. They include:

  • RIG: Rate-integrating gyroscopes
  • DTG: Dynamically tuned-rotor
  • FLEX gyroscope
  • DART: Dual-axis rate transducer.

19. Vibration.   Measure the change in heading based on the effect of the Coriolis acceleration in a vibrating mass.

20. Optical.   Based on the Sagnac-effect. This is the detection of the change in wavelength of light rays propagated in a circular path. They include:

  • RLG: Ring Laser Gyros.
  • FOG: Fiber-Optic Gyroscope.
  • Cold atom sensors: Very high precision (still under development).

21. MEMS.   Microelectromechanical systems are based on integrated circuits. They incorporate miniature mechanical mechanisms at a very reduced scale, such as the following examples:

Figure 6. MEMS Chips - Ref: Inertial Navigation Sensors (Neil M. Barbour)

22.   Pros and Cons.   A brief comparison between the main types of sensor is as follows:





Proven technology

Very precise

Subject to errors introduced by vibrations and accelerations

Long startup time

Relatively expensive

High maintenance




Extremely accurate

Wide dynamic range

More robust than mechanical sensors

Immediate start up

High unit cost

Although smaller than equivalent mechanical units, they are still large by comparison to MEMS units

Relatively fragile

Higher power consumption than MEMS




Extremely robust

Low power consumption

Immediate start up


23. Bias Stability.


Figure 7. Current gyro (right) and accelerometers (left) technology applications - Ref: Navigation sensors and systems in GNSS degraded and denied environments. (George T. Schmidt)

24. UAV Navigation products are currently based on MEMS technology, although the company is able to integrate high precision optical sensors for specific applications. MEMS technology has been chosen as the most suitable technology because high levels of navigation accuracy can be achieved for most UAV applications, within the budgets demanded by system integrators and UAV manufacturers. The key to UAV Navigation's success in this field, and what sets it apart from competitors, is the robustness of its Estimation software and the ability to extract the maximum precision from MEMS based products. This makes the company's products the ideal choice for the most demanding UAV applications.