Inertial navigation system (INS)

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An inertial navigation system (INS) is a navigation device that uses a computer, motion sensors (accelerometers) and rotation sensors (gyroscopes) to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and occasionally by magnetic sensors (magnetometers) and/or speed measuring devices. INSs are used on vehicles such as ships, aircraft, submarines, guided missiles, and spacecraft. Other terms used to refer to inertial navigation systems or closely related devices include inertial guidance system, inertial instrument, inertial measurement unit (IMU) and many other variations. Older INS systems generally used an inertial platform as their mounting point to the vehicle and the terms are sometimes considered synonymous.


Inertial navigation is a self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity. Inertial measurement units (IMUs) typically contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration respectively. By processing signals from these devices it is possible to track the position and orientation of a device.

Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships. Recent advances in the construction of microelectromechanical systems (MEMS) have made it possible to manufacture small and light inertial navigation systems. These advances have widened the range of possible applications to include areas such as human and animal motion capture.

An inertial navigation system includes at least a computer and a platform or module containing accelerometers, gyroscopes, or other motion-sensing devices. The INS is initially provided with its position and velocity from another source (a human operator, a GPS satellite receiver, etc.) accompanied with the initial orientation 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 acceleration and angular velocity applied to the system. Since it requires no external reference (after initialization), it is immune to jamming and deception.

Inertial navigation systems are used in many different moving objects. However, their cost and complexity place constraints on the environments in which they are practical for use.

Gyroscopes measure the angular velocity of the sensor frame with respect to the inertial reference frame. By using the original orientation of the system in the inertial reference frame as the initial condition and integrating the angular velocity, the system’s current orientation is known at all times. This can be thought of as the ability of a blindfolded passenger in a car to feel the car turn left and right or tilt up and down as the car ascends or descends hills. Based on this information alone, the passenger knows what direction the car is facing but not how fast or slow it is moving, or whether it is sliding sideways.

Accelerometers measure the linear acceleration of the moving vehicle in the sensor or body frame, but in directions that can only be measured relative to the moving system (since the accelerometers are fixed to the system and rotate with the system, but are not aware of their own orientation). This can be thought of as the ability of a blindfolded passenger in a car to feel himself pressed back into his seat as the vehicle accelerates forward or pulled forward as it slows down; and feel himself pressed down into his seat as the vehicle accelerates up a hill or rise up out of their seat as the car passes over the crest of a hill and begins to descend. Based on this information alone, he knows how the vehicle is accelerating relative to itself, that is, whether it is accelerating forward, backward, left, right, up (toward the car’s ceiling), or down (toward the car’s floor) measured relative to the car, but not the direction relative to the Earth, since he did not know what direction the car was facing relative to the Earth when they felt the accelerations.

However, by tracking both the current angular velocity of the system and the current linear acceleration of the system measured relative to the moving system, it is possible to determine the linear acceleration of the system in the inertial reference frame. Performing integration on the inertial accelerations (using the original velocity as the initial conditions) using the correct kinematic equations yields the inertial velocities of the system and integration again (using the original position as the initial condition) yields the inertial position. In our example, if the blindfolded passenger knew how the car was pointed and what its velocity was before he was blindfolded and if he is able to keep track of both how the car has turned and how it has accelerated and decelerated since, then he can accurately know the current orientation, position, and velocity of the car at any time.


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 are compounded into still greater errors in position. Since the new position is calculated from the previous calculated position and the measured acceleration and angular velocity, these errors accumulate roughly proportionally to the time since the initial position was input. Therefore, the position must be periodically corrected by input from some other type of navigation system.

Accordingly, inertial navigation is usually used to supplement other navigation systems, providing a higher degree of accuracy than is possible with the use of any single system. For example, if, in terrestrial use, the inertially tracked velocity is intermittently updated to zero by stopping, the position will remain precise for a much longer time, a so-called zero velocity update. In aerospace particularly, other measurement systems are used to determine INS inaccuracies, e.g. the Honeywell LaseRefV inertial navigation systems uses GPS and air data computer outputs to maintain required navigation performance. The navigation error rises with the lower sensitivity of the sensors used. Currently, devices combining different sensors are being developed, e.g. attitude and heading reference system. Because the navigation error is mainly influenced by the numerical integration of angular rates and accelerations, the Pressure Reference System was developed to use one numerical integration of the angular rate measurements.

Estimation theory in general and Kalman filtering in particular, provide a theoretical framework for combining information from various sensors. One of the most common alternative sensors is a satellite navigation radio such as GPS, which can be used for all kinds of vehicles with direct sky visibility. Indoor applications can use pedometers, distance measurement equipment, or other kinds of position sensors. By properly combining the information from an INS and other systems (GPS/INS), the errors in position and velocity are stable. Furthermore, INS can be used as a short-term fallback while GPS signals are unavailable, for example when a vehicle passes through a tunnel.

In 2011, GPS jamming at the civilian level became a governmental concern. The relative ease in ability to jam these systems has motivated the military to reduce navigation dependence on GPS technology. As of 2015, inertial navigation sensors could not be jammed. In 2012, researchers at the U.S. Army Research Laboratory reported an inertial measurement unit consisting of micro-electromechanical system triaxial accelerometers and tri-axial gyroscopes with an array size of 10 that had a Kalman filter algorithm to estimate sensor nuisance parameters (errors) and munition position and velocity. Each array measures six data points and the system coordinates the data together to deliver a navigation solution. If one sensor consistently over or underestimates distance, the system can adjust, adjusting the corrupted sensor’s contributions to the final calculation.

The addition of the heuristic algorithm reduced a flight’s calculated distance error from 120m to 40m from the designated target. The researchers coupled the algorithm with GPS or radar technology to initial and aid the navigation algorithm. At various points during the munition’s flight they would cut off tracking and estimate the accuracy of the munition’s landing. In a forty second flight, 10s and 20s availability of aiding demonstrated little difference in error as both were approximately 35m off target. No noticeable difference was observed when experimentation took place with 100 sensor arrays rather than ten. The researchers indicate this limited experimental data signifies an optimization of navigation technology and a potential reduction in cost of military systems.

Photo By Sanjay AcharyaOwn work, CC BY-SA 4.0, Link