When traversing unknown paths over large distances, visual or instrumental aids are required to reach one's destination. The situation is acute in space, at sea, or in a desert, since the views in all the directions are identical. In early times, the North star served as a traveler's coarse guide. During the medieval period, with the discovery of lodestone and the invention of the north-seeking compass, the traveler was relieved from the need to view the star and limit his travel to clear nights. In the early twenty-first century, with the invention of the Global Positioning System (GPS), available now in many automobiles, one's path is tracked using signals from satellites, and continuing direction provided to the motorist. GPS is not available if the signal is electronically jammed, such as in war, or shielded, such as inside a tunnel. Consequently an autonomous on-board system is required for the most demanding applications, including aircraft, spacecraft and missiles.

Newton's second law of motion, F = ma (where "F" is the force, "m" the mass, and "a" the acceleration), provides the means for mechanizing such a system, whose basic sensing device is the accelerometer. It typically involves attaching an inertial mass to a rigid structure by means of a spring. When the rigid structure is accelerated along the axis of the spring-mass assembly, the mass lags behind because of its inertia, and the spring stretches accordingly. The force on the extended spring in equilibrium is F = kx, where "k" is the spring constant (a characteristic of the chosen spring) and "x" is its extension. Thus, ma = kx, or the acceleration "a" equals (kx/m). Since "k" and "m" are known a priori, the measurement of the spring extension provides a measure of the acceleration. When the measured acceleration is integrated with respect to time, it renders velocity. A double integration renders position. Thus, one is able to know where one is and where one is going with respect to the coordinate system in which the vehicle is moving.

The measurement of acceleration for computing one's position needs to be done with respect to a coordinate system that is held rigidly in inertial space. The device that allows one to sense vehicle rotations about its various axes is a "gyroscope," or "gyro." The gyro is based on the principle of conservation of momentum, linear or angular. Linear momentum is the product of the mass and the velocity of the moving member in the gyro, while angular momentum applies to any rotating structures and is the product of their rotational analogs, the moment of inertia and angular velocity. The simplest example of a "gyro" based on conservation of angular momentum is the spinning top. When spinning, the angular momentum of the top prevents the top from falling down. It stays balanced until the speed reduces due to friction. If, during rotation, this top is pushed to one side, i.e. a rotational torque applied about a horizontal axis, the top begins to precess (rotate) about the other horizontal axis, which is a function of the degree of (push) rotation applied. This precession about the third axis then becomes a measure of the input rotation. Thus, when the coordinate system of the vehicle to which the accelerometer is mounted rotates with respect to the fixed inertial space, such as during aircraft maneuvers, the gyros sense those rotations and the necessary corrections are made, either computationally or mechanically, so that the acceleration is properly computed.

The inertial navigation system, thus, uses the accelerometer to compute position, and the gyro to help maintain the rigid coordinate system within which the calculations are made. Most of the uses of these devices, until recently, were in the most demanding high end defense and civil areas, such as strategic missiles, spacecraft, and aircraft, primarily because of their very high acquisition and life cycle costs. The high costs were associated primarily with the very high precision machining and cleaning technologies required to fabricate and assemble them. Recent low cost precision fabrication and assembly advances in the quartz watch and silicon microelectronics industries, however, have given birth to a new generation of devices, bringing about revolutionary changes in the modern lifestyle. Whereas the sizes of the traditional devices were measured in inches, the sizes of the new miniaturized quartz and silicon devices are in hundreds of micrometers, about one hundred times smaller. These devices are very reliable and cost a few tens of dollars, orders of magnitude less than the early devices, so they are now commonplace. For instance, they are widely available in guidance systems of precision munitions and tactical missiles, braking and navigating systems of automobiles, and low/no jitter platform stability systems of camcorders. The biomedical field has also begun to benefit from these devices. An example is the restoration of one's balance impaired by inner ear problems. The revolution has just begun.

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