Inertial Guidance

Type of physical science: Inertial Guidance, Navigation, Gyros, Classical physics

Field of study: Mechanics

Inertial guidance and navigation systems determine the positions of aircraft, spacecraft, missiles, ships, and other vehicles by using accelerometers and gyroscopes to integrate the accelerations and rotations they experience. They provide complete navigational solutions without the use of any external references.

Overview

Inertial guidance and navigation systems are used to determine the positions of the vehicles in which they are mounted. They do this without necessarily referring to any external landmark or signal but rather by sensing and tracking a vehicle's motions by using gyroscopes and accelerometers. Vehicles using such systems can navigate accurately in remote areas where no external references are available or in military situations where such references might be obscured or even falsified by enemy actions.

The "velocity" of an object is the rate at which its position changes, and the "acceleration" of an object is the rate at which its velocity changes. By continuously (or very frequently) measuring the acceleration an object experiences, it is possible to integrate these accelerations to determine the net change in velocity; similarly, it is possible to integrate a series of velocity estimates to determine the net change in the object's position. Thus if the initial position and velocity of an object are known, and its accelerations are measured, it is possible to know at all times its velocity and position.

Devices that measure acceleration are called "accelerometers." Usually, they consist of a housing and what is called a "seismic mass" or "pendulous mass" that can move back and forth within the housing in one direction only. Since the housing accelerates along with the vehicle, a force must be exerted on the seismic mass to keep it accelerating along with the housing. By Isaac Newton's second law of motion, this force will be directly proportional to the required acceleration.

The force itself can be measured readily. Some accelerometers simply employ springs, which exert a force proportional to their compression, which is then measured. Others use electrical or magnetic forces in a "feedback" loop to hold the mass in a constant position relative to the housing, and then determine the amount of force from the nical gyroscope, a rapidly rotating object with a high moment of inertia, hence high angular momentum. The seismic mass is attached to the gyroscope housing to unbalance it so that, when the housing is accelerated, the mass exerts a torque on it, causing the gyroscope's axis to change direction, or "precess." The rate of precession can then be related to the amount of acceleration.

If the vehicle moved only along a single straight line, a single accelerometer could be used to keep track of its position. For a vehicle such as an aircraft, however, which moves in three dimensions, at least three accelerometers are necessary. Sometimes more are employed for redundancy.

However, this does not completely solve the problem. Since the "attitude" (spatial orientation) of the vehicle can change, an accelerometer pointed toward its front might sometimes measure northward accelerations, and sometimes eastward, westward, or even southward. It is therefore also necessary to keep track of the orientation of the vehicle. This is done by means of gyroscopes, usually called "gyros" in this context.

The first inertial guidance systems used simple mechanical gyros--massive hoops of metal kept spinning around a single axis by an electric motor. For this use, the gyros are carefully balanced, so that the vehicle acceleration exerts no torque on them. The "angular momentum" of the gyro, an expression of its rate and direction of rotation (multiplied by its "moment of inertia," which depends on its mass and shape), can only be changed by exerting a "torque" (an off-center force) on the gyro. This means that as the vehicle rotates, a torque must be exerted on the gyro to cause it to follow that motion. This torque can be measured and used to determine the rate at which the vehicle is turning.

A more modern variation of this is the "electrostatically suspended gyro (ESG)." The rotor in an ESG is a hollow sphere with electrically conductive areas on its surface. The sphere is kept suspended in a closely fitted cavity by electrostatic forces, so there is no contact of moving parts and, hence, very little friction. Electrical currents in the cavity wall induce currents in the conductive areas on the rotor, causing it to spin. The position and motion of the rotor are monitored optically. The low friction permits such gyros to be very accurate.

Two other modern gyros are the "ring laser gyro (RLG)" and the "fiber optic gyro (FOG)." These are not true gyroscopes but are called gyros because they are also used to detect rotations. They have no moving parts but instead use light beams, relying on what is called the "Sagnac effect" after French physicist Georges S. S. Sagnac, who demonstrated it in 1913. An exact analysis of either of these devices requires the use of Albert Einstein's general theory of relativity.

The Sagnac effect is that a light beam transmitted around a closed path is shifted in frequency if the path is rotated. In a fiber-optic gyro, the closed path is created by winding a fiber-optic conduit many times around a spool. A beam of light is split in two and transmitted around this fiber-optic coil in opposite directions, creating opposite frequency shifts. The beams are then recombined. If the coil is rotating, the two beams will have undergone slight frequency shifts in the opposite directions, resulting in a phase difference between them. This can be measured, thus determining the rate of rotation. Fiber-optic gyros are simple and extremely reliable, but they suffer accuracy limitations caused by scattering along the optical path, which makes phase-shift measurements difficult.

A ring-laser gyro is a gas laser built in the form of a triangle or square, with mirrors at the corners. An electrical current is passed through the gas (usually a mixture of helium and neon), causing it to act as a very low-power laser with no outlet. It thus becomes a "cavity resonator," not unlike a microwave oven, but at optical frequencies (with helium and neon, the beam is red). A standing-wave pattern is set up within the cavity; because of the Sagnac effect, this pattern tends to remain stationary even if the cavity rotates. The peaks and valleys of the pattern can be detected optically by placing a sensor at one of the mirrors; these extremes can then be counted to determine the angular displacement as the cavity rotates.

Ring-laser gyros are thus extremely accurate, but they too suffer from limitations. First, if the mirrors are imperfect, the standing-wave pattern will tend to "lock on" to them, and at low rotational rates, the pattern will turn with the cavity rather than remaining fixed in space. This results in extremely demanding specifications for the mirrors and normally requires that the gyro be kept constantly rotating. Usually, a vibrating device on the gyro is used for this purpose. Another potential problem is that gas in the laser must be maintained at a precise mixture and pressure. This can be difficult in spacecraft applications, where the seal on the laser cavity must be maintained reliably for long periods.

There are two fundamentally different methods for implementing an inertial guidance system, depending on how the "inertial platform" to which the accelerometers and gyros are fixed is mounted. Some (including the earliest) inertial guidance and navigation systems use gimbaled inertial platforms. The platform is mounted on three motor-controlled gimbals so that it can be rotated in any direction. Output from the gyros is used as an input to the gimbals so as to result in no net rotation of the platform, which remains fixed in inertial space. Accelerometer outputs therefore can be directly integrated to produce true displacements. A potential drawback is that it is always possible to maneuver the system so that two of the gimbal axes become precisely aligned, leaving the platform with no third axis about which to turn. It is then unable to track rotations about that third axis. This is called "gimbal lock" or "dumping the platform" and is a favorite amusement of test pilots.

The alternative to this is a "strapdown inertial system," in which the inertial platform is rigidly attached to the body of the vehicle. Gyro outputs are used to determine how much the platform has rotated from its original position, and the accelerometer outputs are interpreted based on this. Strapdown systems are potentially simpler and more reliable than gimbaled systems, since they have no gimbals at all, but they have much larger computational requirements and usually have very demanding specifications on their gyros.

One interesting limitation of all inertial systems is that they cannot sense gravity directly. This is because inertial mass and gravitational mass are identical, so the force of gravity acts on the accelerometer housing and the seismic mass in the same way, producing no net force between them.

This limitation means that high-precision guidance systems must take into account the exact shape of Earth's gravitational field. The field varies with altitude, with latitude (since Earth is not a perfect sphere), and with local mass concentrations. It may be necessary for the inertial system to carry a complete map of the gravitational field so that it can be taken exactly into account.

Inertial guidance systems process their sensor data using a variation on the "Kalman filter," an optimal estimation algorithm named for Rudolf Kalman, to obtain the best possible position estimates.

Applications

Inertial guidance and navigation systems are used on many civilian and military vehicles, including aircraft, ships, submarines, missiles, spacecraft, and some military land vehicles. Most large airliners employ inertial systems as their primary means of navigation. The systems are very accurate and reliable and do not require the use of external navigational aids such as radio beacons. This facilitates journeys over water and over polar regions where radio aids are not available. It also makes more direct routes feasible, since the aircraft does not have to fly from beacon to beacon. Typically, the inertial navigation system is integrated with a computer that provides several kinds of information to the crew and to other aircraft systems. The crew enters a series of "waypoints"--latitudes and longitudes along the intended route--into the navigation system, which determines the plane's position, and also such things as the heading to the next waypoint.

Inertial guidance systems provide all these advantages to military applications, as well as immunity from enemy interference. Enemy action can jam radio signals, destroy the stations that broadcast them, or even produce false signals. During World War II, faked radio beacons were used to confuse bombers, often causing them to miss their targets. In one extreme case, a German bomber pilot was so confused by British jamming that he landed in Scotland, erroneously believing he was safe in occupied France. Because they are entirely internal, inertial systems are immune to such enemy action.

Inertial systems provide another military advantage by being passive. These systems emit nothing, so they provide no extra information to the enemy. Some radar homing missiles, for example, use nothing but inertial guidance to fly to the vicinity of their targets. Only when the missiles are close enough for final homing is the radar activated. This strategy has several advantages. First, the enemy may be unaware that a missile is coming until it is too late. Second, when the radar system is carried on the missile itself, it need only be designed to work at short range and for a short time, so it can be made smaller and cheaper. Third, when the radar signal used by the missile for homing comes from a distant ship or aircraft, that signal is only needed for a short time, thus permitting the ship or aircraft to service more missiles over any given time period.

Missile systems that are intended to attack stationary targets on the ground may use inertial guidance alone to reach their targets. This is especially true of ballistic nuclear missiles, which must be designed to defeat all possible enemy countermeasures. Extreme accuracy is also required, since some of these are designed to destroy missile silos, which are protected against anything except very close nuclear explosions. Some military land vehicles, especially self-propelled artillery pieces, may also use inertial navigation systems.

All inertial systems must be initialized. This requires not only supplying an initial position and velocity but also--and to high accuracy--an initial orientation. For example, an aircraft may be parked at a surveyed location. The crew enters the known latitude, longitude, and altitude of that location into the inertial navigation system computer and allows it to remain stationary for a required period of time. The system then uses its accelerometers to determine the direction of the gravitational force, thus determining which way is up. Since the accelerometers cannot sense gravity, they actually determine the "acceleration" due to the upward force on the aircraft wheels, equal to and exactly countering the undetected force of gravity on the stationary aircraft. The gyros sense the only rotation they are undergoing, which is due to the rotation of Earth. In this way, they determine the direction of Earth's rotational axis, which is north. The system may take some time (usually several minutes or tens of minutes) to determine these two directions to the required accuracy. Once they have been determined, the orientation of the platform is known and the initialization is complete.

In other cases, one navigation system may be used to initialize another. An aircraft preparing to launch from an aircraft carrier is not stationary but may receive a continuous flow of data from the ship's inertial navigation system, which it compares to its own sensors. In this way, the relative alignment between the ship's inertial platform and the aircraft's inertial platform can be established and the initialization completed. If an aircraft is to launch an inertially guided missile, a similar exchange of data between the aircraft and missile is necessary, and the aircraft may need to perform turning maneuvers during the process to provide the inertial systems with rotational data to compare.

All inertial systems diverge over time, as errors from the sensors accumulate. This can be corrected, partially, by providing external information to the system. Most aircraft systems use an input from the aircraft's barometric altitude sensor to prevent the navigation system's estimate of the altitude from becoming unreasonable. In addition, many systems can be updated using manually entered data. For example, a pilot may fly over a known landmark and enter that landmark's location into the system. Since both the new data and the previous inertial navigation solution can have errors in them, a new position estimate is formed from both by combining them statistically.

Besides their general tendency to increase over time, errors in any inertial guidance system intended for use near Earth tend to oscillate with a period of about 84 minutes. This effect is called "Schuler oscillation" after its discoverer, Max Schuler. It reflects the fact that any system that can navigate accurately around a spherical planet must be on the edge of instability, with a tendency to oscillate at a frequency determined by the radius and mass of the planet. Any errors in the system will stimulate oscillation at this frequency.

Context

Inertial guidance systems grew naturally out of the use of gyro compasses and artificial horizons. The gyro compass uses a single gyroscope to detect the direction of Earth's rotation. These became common on ships early in the twentieth century and have remained in use on ships and in aircraft. They have the advantages that they display true north, rather than magnetic north, and they are not affected by the metal in the vehicles, as a magnetic compass would be.

Aircraft have long carried artificial horizons (also called "attitude indicators" and several other names, depending on their exact functions), which use gyroscopes to provide an indication of the attitude of the aircraft. They are useful at night or in fog or clouds when the pilot cannot see the horizon clearly. They work much like an inertial navigation system, but without the accelerometers; they keep track of attitude, but not of position changes.

The addition of the accelerometers was a straightforward idea, and the principles of modern inertial systems were described by Schuler in 1923. During World War II, the German V-2 rockets used inertial guidance to strike their targets in England. After the war, the first really accurate inertial systems were developed by Charles S. Draper and others at the Massachusetts Institute of Technology. These quickly found their way into military and civilian applications.

In the 1980's and 1990's, an alternative navigation technology arose that may ultimately displace inertial navigation for civilian purposes. This is a satellite-based system of beacons called the "Global Positioning System (GPS)." This system has global coverage, is extremely accurate, and requires only a simple and inexpensive receiver for use. It may replace inertial systems in civil aviation if questions regarding its control are resolved. At this writing, it belongs to the U.S. military, which constructed it, and which retains the option to interrupt it if necessary in time of war. It is also conceivable that a future adversary could gain the capability to attack the satellites. These uncertainties continue to make the use of inertial guidance necessary in military systems.

Principal terms

ACCELEROMETER: A device for measuring accelerations

FIBER-OPTIC GYRO: A gyroscope employing a laser diode and a coil of fiber-optic material to detect rotational rates optically

GIMBALED INERTIAL SYSTEMS: Inertial guidance or navigation systems in which the inertial platform is suspended on gimbals and is kept in a fixed spatial orientation, not following the attitude changes of the vehicle

GYROSCOPE (GYRO): A device for measuring rotational motions

INERTIAL PLATFORM: The rigid structure that holds the gyros and accelerometers of an inertial guidance system

POSITIONAL GYRO: A gyro that produces as its direct output the net angular displacement it has undergone about its sensing axis

RATE GYRO: A gyro that produces as its direct output the rate of angular displacement about its sensing axis

RING LASER GYRO: A gyroscope employing a closed triangular or square laser cavity to detect rotational displacement optically

SEISMIC MASS (PENDULOUS MASS): The mass used by an accelerometer to detect accelerations, usually by measuring the force required to keep the seismic mass stationary with respect to the accelerometer housing

STRAPDOWN INERTIAL SYSTEMS: Inertial guidance or navigation systems in which the inertial platform is rigidly fixed to the vehicle body and follows its attitude changes

Bibliography

Collinson, R. P. G. Introduction to Avionics. London: Chapman & Hall, 1996. The term "avionics" refers to aircraft electronic systems, and this book describes all the systems used by aircraft for control, communication, and navigation. It does a particularly good job of explaining the way in which aircraft-control systems (autopilot and stabilization systems) and air-data systems (airflow and altitude measuring devices) interact with navigation systems. Also includes a discussion of the operating principles of the ring-laser gyro and the fiber-optic gyro. It contains many excellent illustrations and a useful glossary.

Deimel, Richard Francis. Mechanics of the Gyroscope. New York: Dover, 1952. Presents a good introduction to the function and physical principles of the mechanical gyroscope, with discussion of applications such as gyrocompasses.

Farrell, James L. Integrated Aircraft Navigation. New York: Academic Press, 1976. Farrell's book describes the application of inertial guidance to aircraft, with special attention to the problem of incorporating other (noninertial) position information to improve the navigation solution. Includes a detailed discussion of several subtleties that enter the inertial guidance problem, including the exact shape of Earth and its gravitational field. Written as a short textbook, with numerous problems and extensive references.

Lawrence, Anthony. Modern Inertial Technology: Navigation, Guidance, and Control. New York: Springer-Verlag, 1993. Covers all aspects of inertial systems applications, including devices such as attitude indicators and autopilots that do not require a full position solution. Bibliography.

Maloney, Elbert S. Dutton's Navigation and Piloting. 14th ed. Annapolis: Naval Institute Press, 1985. Periodically updated, this is a general text and reference book intended for sailors. Contains an excellent discussion of navigation problems as well as a description of the practical application of inertial systems to ship navigation.

Zarchan, Paul. Tactical and Strategic Missile Guidance. Washington, D.C.: The American Institute of Aeronautics and Astronautics, 1990. This is primarily an engineering text, but it takes a practical point of view and is somewhat accessible to the nontechnical reader. Covers all aspects of missile guidance, including the application of inertial guidance to missile systems. When applied to missiles, the term "guidance" usually refers to the strategy used by the missile to intercept its target, which is the main topic of this book. Heavily illustrated and contains listings of a number of computer-simulation programs.