Inertial Navigation Systems


The aircraft attitude and the direction in which it is heading are clearly essential information for the pilot in executing a manoeuvre or flying in conditions of poor visibility, flying in clouds or at night. Accurate attitude and heading information are also required by a number of avionic subsystems which are essential for the aircraft's mission - for example, the autopilot and the navigation system and weapon aiming in the case of a military aircraft.

The attitude and heading information is provided by the inertial sensor system(s).

These comprise a set of gyros and accelerometers which measure the aircraft's angular and linear motion about the aircraft axes, together with a computing system which derives the aircraft's attitude and heading from the gyro and accelerometer outputs. Most modern attitude and heading reference systems (AHRS) use a strapped down (or body mounted) configuration of gyros and accelerometers as opposed to the earlier gimbaled systems.

The attributes of an ideal navigation and guidance system for military applications can be summarized as follows:

  • High accuracy
  • Self contained
  • Autonomous -does not depend on other systems
  • Passive - does not radiate
  • Unjammable
  • Does not require reference to the ground or outside world

In the late 1940s these attributes constituted a ‘wish list' and indicated the development of inertial navigation as the only system which could be capable of meeting all these requirements. It was thus initially developed in the early 1950s for the navigation and guidance of ballistic missiles, strategic bombers, ship and submarines [Introduction to avionics, by R.P.G. Collinson,Page 259 chapter 6.2 ISBN 0-412-48250-9]

Precision accelerometers had to be developed with bias uncertainties of less than 50 micron-g. the major task of achieving the required computational accuracies had to be solved and in fact the first digital computers operating in real time were developed for inertial navigation systems. Once these problems had been solved, however, the INS could provide:

  • Accurate position in whatever coordinates are required - eg latitude/longitude etc
  • Ground speed and track angle.
  • Euler angles: heading, pitch and roll to very high accuracy.
  • Aircraft velocity vector (in conjunction with the air data system).


The INS is initially provided with its position and velocity from another source (a human operator, a GPS satellite receiver, etc.), and thereafter computes its own updated position and velocity by integrating information received from the motion sensors. The advantage of an INS is that it requires no external references in order to determine its position, orientation, or velocity once it has been initialized.

An INS can detect a change in its geographic position (a move east or north, for example), a change in its velocity (speed and direction of movement), and a change in its orientation (rotation about an axis). It does this by measuring the linear and angular accelerations applied to the system. Since it requires no external reference (after initialization), it is immune to jamming and deception.

Gyroscope definition

A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. A Gyroscope is defined as any rotating body that exhibits two fundamental properties: gyroscopic inertia and precession. These properties are inherent in all rotating bodies, including the earth itself. The device is a spinning wheel or disk whose axle is free to take any orientation. This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin. Since external torque is minimized by mounting the device in gimbals, its orientation remains nearly fixed, regardless of any motion of the platform on which it is mounted.

Gyroscopes and accelerometers are known as inertial sensors. This is because they exploit the property of inertia, namely the resistance to a change in momentum, to sense angular motion in the case of the gyro and changes in linear motion in the case of the accelerometer. They are fundamental to the control and guidance of an aircraft. For example, in a Fly By Wire (FBW) aircraft the rate gyros and accelerometers provide the aircraft motion feedback which enables a manoeuvre command control to be achieved and an aerodynamically unstable aircraft to be stabilized by the flight control system.

They are also the essential elements of the spatial reference system or attitude/heading reference system (AHRS). The AHRS provides the vertical and directional reference information for the pilot's head up display (HUD), electronic flight instrument system (EFIS), the autopilot system and the navigation system.

The title is “Inertial Navigation Systems”. To help you get started I would

like to see you paper including Mechanical vs solid state gyros, accelerometers and how they are used in the navigation of aircraft. Errors and how they are minimised/overcome.

A good question to ask an interviewee who is interested in entering the avionics systems field is ‘How can you measure the motion of a vehicle and derive the distance it has travelled without any reference to the outside world?'

The answer is that you can sense the vehicle's acceleration (and also the gravitational vector) with accelerometers. If the vehicle's acceleration component can then be derived along a precisely known set of axes, successive integration of the acceleration components with respect to time will yield the velocities and distances travelled along these axes. This is true provided the initial conditions are known, that is the vehicle velocity and position at the start time.


Early inertial navigation systems used a gimbaled and gyro-stabilized arrangement to provide a stable platform on which the inertial sensors were located. The platform was stabilized using rate information from the gyro to drive torque motors which stabilized the platform in its original frame of axes, independently of movement of the aircraft.

Resolvers provided angular information about the aircraft in relation to the platform, and hence aircraft attitude could be determined.

The inertial platform uses a combination of gyro and accelerometers to provide a platform with a fixed reference in space. By using the combined attributes of position and rate gyros and accelerometers, a stabilized platform provides a fixe attitude reference in space and, when fitted in an aircraft, can provide information about aircraft body rates and acceleration in all three axes. Suitable computation can also provide useful information relating to velocity and distance travelled in all three axes.[CIVIL AVIONICS SYSTEMS by Ian moir and Allan seabridge ISBN 1-56347-589-8 page119 ]


The spinning rotor type of gyroscope uses the fundamental characteristic of the angular momentum of the rotor to resist changing its direction to either provide a spatial reference or to measure the rate of angular rotation.

In the first case the spinning rotor is supported in such a way that the spin axis is free to point in any arbitrary direction and provided there are zero torques acting about its axis of freedom it will stay pointing in this fixed direction in space.

In the second case the rotor spin axis is constrained to follow the rotation the gyros experiences about its axis or axes. The torque required to constrain the rotor is directly proportional to the input rate which can then be determined by measuring the torque. The first type is known as a free gyro and the second type is referred to as a rate gyro.


All inertial navigation systems suffer from integration drift: Small errors in the measurement of acceleration and angular velocity are integrated into progressively larger errors in velocity, which is compounded into still greater errors in position. This is a problem that is inherent in every open loop control system. The inaccuracy of a good-quality navigational system is normally less than 0.6 nautical miles per hour in position and on the order of tenths of a degree per hour in orientation.

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