Inertial Guidance

The theoretical basis for inertial navigation

Inertial guidance is a navigation technology that monitors changes in location by measuring cumulative acceleration. In inertial guidance, the motion of the object in three-dimensional space is measured continuously by an on-board device. This enables a computer to provide related real-time information about velocity (speed) and location.

An inertial navigation system (INS) does not use information from an external reference once it has been placed in operation, in contrast to less-sophisticated navigation techniques. Gyrocompasses, older navigation aids that are dependent on the position of the stars or sun for guidance, are internally self sufficient, relying on precision gyroscopes for direction reference. However, gyrocompasses will drift with time as a result of slow, friction-induced gyrations and must be readjusted occasionally. Radiolocation navigation systems use precisely timed radio signals from distant transmitters or satellites. Radar mapping and optical terrain matching navigation require interaction with Earth’s surface.

In contrast to these navigation tools, inertial navigation systems need only sense the inertial force that results from changing velocity. These forces are not dependent upon external references, but can be measured by accelerometers in a sealed, shielded container.

Inertial navigation was first applied for military uses—guiding deeply submerged submarines, ballistic missiles, and airplanes. Inertial navigation gave results that were more accurate than could be obtained with conventional navigation. An inertial navigation system is effectively immune to deliberate interference, an obvious advantage in wartime.

In addition, inertial navigation functions as well near Earth’s poles as it does at the equator. This feature is in marked contrast to the limitations imposed by a magnetic compass’s unreliable performance in the Arctic or Antarctic regions of Earth. Magnetic compasses are also undependable in Earth’s polar regions because of day-to-day variations in Earth’s magnetic field strength and direction. Magnetic storms caused by solar disturbances that affect Earth are particularly troublesome near the magnetic poles.

The theoretical basis for inertial navigation

Inertial navigation obtains its information from the same type of inertial forces one experiences riding in an automobile when turning corners at high speed, accelerating away from a stop sign, or braking. An accelerometer measures these forces continually, and this information is processed by a computer.

An inertial navigation system makes independent measurements along each of the three principal geometric axes, which is collected by a computer. The result is real-time information about velocity and distance traveled.

Inertial guidance utilizes a family of relationships from kinematics, the description of motion. The connections between the principal formulas describing acceleration, velocity, and displacement are used. Each of these three aspects of motion contains information about the other two. An inertial navigation system continuously measures acceleration along each of the three dimensions, and then calculates the corresponding instantaneous velocity. This can be used to determine the total distance traveled. By measuring acceleration as a function of time, an inertial guidance system calculates instantaneous speed and location without the need to for outside reference.

Inertial navigation and flight

Planes flying over the oceans often rely on inertial navigation to stay on their course. Even in the early 1970s, some of the first 747 jets were designed to carry several inertial guidance systems. When more than one inertial navigation system is in use, each can monitor the plane’s position independently for improved reliability.

On long flights, as from the United States to Japan, an inertial guidance system can control a plane automatically by providing instructions to the autopilot. At the start of the journey the intended flight path is divided into a succession of short segments, perhaps a half dozen. The pilot enters the coordinates of the end points of each of these short flights into a computer. The inertial guidance system flies the plane to each of these waypoints in turn. The overall route is closely approximated by the series of nearly straight-line segments. The inertial navigation system’s computer knows where the plane is located and its velocity because acceleration is measured continuously. These systems are so accurate that a plane can fly non-stop from San Francisco to Japan under the control of an inertial navigation system, arriving with a location uncertainty of about 10 ft (3 m).

For longer journeys over the surface of Earth, interpreting inertial navigation data is more complicated. The computer must project the measured acceleration onto the spherical surface of Earth to determine

KEY TERMS

747 —Early jumbo-jet plane still in commercial service.

Geomagnetic —Related to Earth’s magnetic field.

Gyroscope —A device similar to a top, which maintains rotation about an axis while maintaining a constant orientation of that axis in space.

Precession —Wobbling of a gyroscope’s axis due to an external torque.

Real time —Happening when events actually occur.

instantaneous position relative to Earth’s coordinate system of latitude and longitude. There is an additional complication resulting from the rotation of Earth. It is not enough to know the direction of a destination when a plane takes off. As Earth rotates, the direction of the planned destination may seem to change. Navigation must continually correct for a plane’s tendency to drift off course because of Earth’s rotational acceleration, a consequence of the so-called Coriolis force. The inertial navigation system’s computer compensates for these challenges accurately and quickly.

With the advent of the newer global positioning system, inertial navigation may be less significant in the future—at least for non-military applications. (Missiles are most reliable if independent of all outside systems.) For the near future, navigation by INS will continue to make a valuable contribution to transportation safety and a backup to GPS-guided systems.