HOME

TheInfoList



OR:

An inertial navigation system (INS) is a
navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...
device that uses motion sensors (
accelerometer An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is accele ...
s), rotation sensors ( gyroscopes) and a
computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...
to continuously calculate by
dead reckoning In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. ...
the position, the orientation, and the
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
(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 An altimeter or an altitude meter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth under water. The m ...
and sometimes by magnetic sensors ( magnetometers) and/or speed measuring devices. INSs are used on
mobile robot A mobile robot is an automatic machine that is capable of locomotion.Hu, J.; Bhowmick, P.; Lanzon, A.,Group Coordinated Control of Networked Mobile Robots with Applications to Object Transportation IEEE Transactions on Vehicular Technology, 2021 ...
s and on vehicles such as
ship A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying cargo or passengers, or in support of specialized missions, such as defense, research, and fishing. Ships are generally distinguished ...
s,
aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
,
submarine A submarine (or sub) is a watercraft capable of independent operation underwater. It differs from a submersible, which has more limited underwater capability. The term is also sometimes used historically or colloquially to refer to remotely op ...
s,
guided missile In military terminology, a missile is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles are thus also called guided missiles or guided rockets (when a previously unguided rocket ...
s, and
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
. 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.


Overview

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. It is also embedded in some mobile phones for purposes of mobile phone location and tracking. 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
accelerometer An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is accele ...
s, 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 In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
. 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 themself pressed back into their seat as the vehicle accelerates forward or pulled forward as it slows down; and feel themself pressed down into their 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, they know 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 they 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 Kinematics equations are the constraint equations of a mechanical system such as a robot manipulator that define how input movement at one or more joints specifies the configuration of the device, in order to achieve a task position or end-effect ...
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 they were blindfolded, and if they are able to keep track of both how the car has turned and how it has accelerated and decelerated since, then they can accurately know the current orientation, position, and velocity of the car at any time.


Drift rate

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.''Inertial navigation systems analysis'', Kenneth R. Britting, Wiley-Interscience, 1971. 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. Even the best accelerometers, with a standard error of 10 micro-g, would accumulate a 50-meter error within 17 minutes. 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 The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
and
air data computer An air data computer (ADC) or central air data computer (CADC) computes altitude, vertical speed, air speed, and Mach number from pressure and temperature inputs. It is an essential avionics component found in modern aircraft. This computer, rath ...
outputs to maintain
required navigation performance Required navigation performance (RNP) is a type of performance-based navigation (PBN) that allows an aircraft to fly a specific path between two 3D-defined points in space. Navigation precision Area navigation (RNAV) and RNP systems are fund ...
. 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 An attitude and heading reference system (AHRS) consists of sensors on three axes that provide attitude information for aircraft, including roll, pitch, and yaw. These are sometimes referred to as MARG (Magnetic, Angular Rate, and Gravity) sens ...
. Because the navigation error is mainly influenced by the
numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
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,''Applied Optimal Estimation'', Arthur Gelb (Editor), M.I.T. Press, 1974. provide a theoretical framework for combining information from various sensors. One of the most common alternative sensors is a
satellite navigation A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location (longitude, latitude, and altitude/elevation) to high pr ...
radio such as
GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
, which can be used for all kinds of vehicles with direct sky visibility. Indoor applications can use
pedometer A pedometer, or step-counter, is a device, usually portable and electronic or electromechanical, that counts each step a person takes by detecting the motion of the person's hands or hips. Because the distance of each person's step varies, a ...
s, distance measurement equipment, or other kinds of
position sensor A position sensor is a sensor that detects an object's position. A position sensor may indicate the absolute position of the object (its location) or its relative position (displacement) in terms of linear travel, rotational angle or three-dimensio ...
s. By properly combining the information from an INS and other systems (
GPS/INS GPS/INS is the use of GPS satellite signals to correct or calibrate a solution from an inertial navigation system (INS). The method is applicable for any GNSS/INS system. Overview GPS/INS method The GPS gives an absolute drift-free position v ...
), 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. Because inertial navigation sensors do not depend on radio signals unlike GPS, they cannot 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 For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
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.


History

Inertial navigation systems were originally developed for
rocket A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely fr ...
s. American rocketry pioneer
Robert Goddard Robert Hutchings Goddard (October 5, 1882 – August 10, 1945) was an American engineer, professor, physicist, and inventor who is credited with creating and building the world's first liquid-fueled rocket. Goddard successfully laun ...
experimented with rudimentary
gyroscopic A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rot ...
systems. Goddard's systems were of great interest to contemporary German pioneers including
Wernher von Braun Wernher Magnus Maximilian Freiherr von Braun ( , ; 23 March 191216 June 1977) was a German and American aerospace engineer and space architect. He was a member of the Nazi Party and Allgemeine SS, as well as the leading figure in the develop ...
. The systems entered more widespread use with the advent of
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
,
guided missile In military terminology, a missile is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles are thus also called guided missiles or guided rockets (when a previously unguided rocket ...
s, and commercial airliners. Early German
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
V2 guidance systems combined two gyroscopes and a lateral accelerometer with a simple
analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...
to adjust the
azimuth An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...
for the rocket in flight. Analog computer signals were used to drive four
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on large ...
rudders in the rocket exhaust for flight control. The GN&C (Guidance, Navigation, and Control) system for the V2 provided many innovations as an integrated platform with closed loop guidance. At the end of the war von Braun engineered the surrender of 500 of his top rocket scientists, along with plans and test vehicles, to the Americans. They arrived at
Fort Bliss, Texas Fort Bliss is a United States Army post in New Mexico and Texas, with its headquarters in El Paso, Texas. Named in honor of LTC William Bliss (1815–1853), a mathematics professor who was the son-in-law of President Zachary Taylor, Ft. Bliss h ...
in 1945 under the provisions of
Operation Paperclip Operation Paperclip was a secret United States intelligence program in which more than 1,600 German scientists, engineers, and technicians were taken from the former Nazi Germany to the U.S. for government employment after the end of World War ...
and were subsequently moved to
Huntsville, Alabama Huntsville is a city in Madison County, Limestone County, and Morgan County, Alabama, United States. It is the county seat of Madison County. Located in the Appalachian region of northern Alabama, Huntsville is the most populous city in t ...
, in 1950 where they worked for U.S. Army rocket research programs. In the early 1950s, the US government wanted to insulate itself against over dependency on the German team for military applications, including the development of a fully domestic missile guidance program. The MIT Instrumentation Laboratory (later to become the Charles Stark Draper Laboratory, Inc.) was chosen by the Air Force Western Development Division to provide a self-contained guidance system backup to Convair in
San Diego San Diego ( , ; ) is a city on the Pacific Ocean coast of Southern California located immediately adjacent to the Mexico–United States border. With a 2020 population of 1,386,932, it is the List of United States cities by population, eigh ...
for the new Atlas intercontinental ballistic missile (Construction and testing were completed by Arma Division of AmBosch Arma). The technical monitor for the MIT task was engineer Jim Fletcher, who later served as NASA Administrator. The Atlas guidance system was to be a combination of an on-board autonomous system and a ground-based tracking and command system. The self-contained system finally prevailed in ballistic missile applications for obvious reasons. In space exploration, a mixture of the two remains. In the summer of 1952, Dr. Richard Battin and Dr. J. Halcombe "Hal" Laning, Jr., researched computational based solutions to guidance and undertook the initial analytical work on the Atlas inertial guidance in 1954. Other key figures at Convair were Charlie Bossart, the Chief Engineer, and Walter Schweidetzky, head of the guidance group. Schweidetzky had worked with von Braun at
Peenemünde Peenemünde (, en, " Peene iverMouth") is a municipality on the Baltic Sea island of Usedom in the Vorpommern-Greifswald district in Mecklenburg-Vorpommern, Germany. It is part of the ''Amt'' (collective municipality) of Usedom-Nord. The commu ...
during World War II. The initial Delta guidance system assessed the difference in position from a reference trajectory. A velocity to be gained (VGO) calculation is made to correct the current trajectory with the objective of driving VGO to zero. The mathematics of this approach were fundamentally valid, but dropped because of the challenges in accurate inertial guidance and analog computing power. The challenges faced by the Delta efforts were overcome by the Q system (see
Q-guidance Q-guidance is a method of missile guidance used in some U.S. ballistic missiles and some civilian space flights. It was developed in the 1950s by J. Halcombe Laning and Richard Battin at the MIT Instrumentation Lab. Q-guidance is used for ...
) of guidance. The Q system's revolution was to bind the challenges of missile guidance (and associated equations of motion) in the matrix Q. The Q matrix represents the partial derivatives of the velocity with respect to the position vector. A key feature of this approach allowed for the components of the vector cross product (v, xdv, /dt) to be used as the basic autopilot rate signals—a technique that became known as ''cross-product steering''. The Q-system was presented at the first Technical Symposium on Ballistic Missiles held at the Ramo-Wooldridge Corporation in Los Angeles on 21 and 22 June 1956. The Q system was classified information through the 1960s. Derivations of this guidance are used for today's missiles.


Guidance in human spaceflight

In February 1961 NASA awarded MIT a contract for preliminary design study of a guidance and navigation system for the Apollo program. MIT and the Delco Electronics Div. of General Motors Corp. were awarded the joint contract for design and production of the Apollo Guidance and Navigation systems for the Command Module and the Lunar Module. Delco produced the IMUs ( Inertial Measurement Units) for these systems, Kollsman Instrument Corp. produced the Optical Systems, and the Apollo Guidance Computer was built by Raytheon under subcontract. For the Space Shuttle, open loop (no feedback) guidance was used to guide the Shuttle from lift-off until Solid Rocket Booster (SRB) separation. After SRB separation the primary Space Shuttle guidance is named PEG (Powered Explicit Guidance). PEG takes into account both the Q system and the predictor-corrector attributes of the original "Delta" System (PEG Guidance). Although many updates to the Shuttle's navigation system had taken place over the last 30 years (ex. GPS in the OI-22 build), the guidance core of the Shuttle GN&C system had evolved little. Within a manned system, there is a human interface needed for the guidance system. As astronauts are the customer for the system, many new teams were formed that touch GN&C as it is a primary interface to "fly" the vehicle.


Early use in aircraft inertial guidance

One example of a popular INS for commercial aircraft was the
Delco Carousel The Delco Carousel — proper name Carousel IV — was an inertial navigation system (INS) for aircraft developed by Delco Electronics. Before the advent of sophisticated flight management systems, Carousel IV allowed pilots to automate navigation ...
, which provided partial automation of navigation in the days before complete
flight management system A flight management system (FMS) is a fundamental component of a modern airliner's avionics. An FMS is a specialized computer system that automates a wide variety of in-flight tasks, reducing the workload on the flight crew to the point that mode ...
s became commonplace. The Carousel allowed pilots to enter 9 waypoints at a time and then guided the aircraft from one waypoint to the next using an INS to determine aircraft position and velocity. Boeing Corporation subcontracted the Delco Electronics Div. of General Motors to design and build the first production Carousel systems for the early models (-100, -200 and -300) of the 747 aircraft. The 747 utilized three Carousel systems operating in concert for reliability purposes. The Carousel system and derivatives thereof were subsequently adopted for use in many other commercial and military aircraft. The USAF C-141 was the first military aircraft to utilize the Carousel in a dual system configuration, followed by the C-5A which utilized the triple INS configuration, similar to the 747. The KC-135A fleet was fitted with a single Carousel IV-E system that could operate as a stand-alone INS or can be aided by the AN/APN-81 or AN/APN-218 Doppler radar. Some special-mission variants of the C-135 were fitted with dual Carousel IV-E INSs. ARINC Characteristic 704 defines the INS used in commercial air transport.


Inertial navigation systems in detail

INSs contain Inertial Measurement Units (IMUs) which have angular and linear accelerometers (for changes in position); some IMUs include a gyroscopic element (for maintaining an absolute angular reference). Angular accelerometers measure how the vehicle is rotating in space. Generally, there is at least one sensor for each of the three axes: pitch (nose up and down), yaw (nose left and right) and roll (clockwise or counter-clockwise from the cockpit). Linear accelerometers measure non-gravitational accelerationsEshbach's Handbook of Engineering Fundamentals By Ovid W. Eshbach, Byron pg 9 of the vehicle. Since it can move in three axes (up & down, left & right, forward & back), there is a linear accelerometer for each axis. A computer continually calculates the vehicle's current position. First, for each of the six degrees of freedom (x,y,z and θx, θy and θz), it integrates over time the sensed acceleration, together with an estimate of gravity, to calculate the current velocity. Then it integrates the velocity to calculate the current position. Inertial guidance is difficult without computers. The desire to use inertial guidance in the
Minuteman missile The LGM-30 Minuteman is an American land-based intercontinental ballistic missile (ICBM) in service with the Air Force Global Strike Command. , the LGM-30G Minuteman III version is the only land-based ICBM in service in the United States and re ...
and Project Apollo drove early attempts to miniaturize computers. Inertial guidance systems are now usually combined with
satellite navigation system A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisoto ...
s through a digital filtering system. The inertial system provides short term data, while the satellite system corrects accumulated errors of the inertial system. An inertial guidance system that will operate near the surface of the earth must incorporate
Schuler tuning Schuler tuning is a design principle for inertial navigation systems that accounts for the curvature of the Earth. An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directi ...
so that its platform will continue pointing towards the center of the earth as a vehicle moves from place to place.


Basic schemes


Gimballed gyrostabilized platforms

Some systems place the linear accelerometers on a gimballed gyrostabilized platform. The
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
s are a set of three rings, each with a pair of bearings initially at right angles. They let the platform twist about any rotational axis (or, rather, they let the platform keep the same orientation while the vehicle rotates around it). There are two gyroscopes (usually) on the platform. Two gyroscopes are used to cancel
gyroscopic precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...
, the tendency of a gyroscope to twist at right angles to an input torque. By mounting a pair of gyroscopes (of the same rotational inertia and spinning at the same speed in opposite directions) at right angles the precessions are cancelled and the platform will resist twisting. This system allows a vehicle's roll, pitch and yaw angles to be measured directly at the bearings of the gimbals. Relatively simple electronic circuits can be used to add up the linear accelerations, because the directions of the linear accelerometers do not change. The big disadvantage of this scheme is that it uses many expensive precision mechanical parts. It also has
moving parts Machines include both fixed and moving parts. The moving parts have controlled and constrained motions. Moving parts are machine components excluding any moving fluids, such as fuel, coolant or hydraulic fluid. Moving parts also do not include ...
that can wear out or jam and is vulnerable to
gimbal lock Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate t ...
. The primary guidance system of the
Apollo spacecraft The Apollo spacecraft was composed of three parts designed to accomplish the American Apollo program's goal of landing astronauts on the Moon by the end of the 1960s and returning them safely to Earth. The expendable (single-use) spacecraft ...
used a three-axis gyrostabilized platform, feeding data to the Apollo Guidance Computer. Maneuvers had to be carefully planned to avoid gimbal lock.


Fluid-suspended gyrostabilized platforms

Gimbal lock constrains maneuvering and it would be beneficial to eliminate the slip rings and bearings of the gimbals. Therefore, some systems use fluid bearings or a flotation chamber to mount a gyrostabilized platform. These systems can have very high precisions (e.g.,
Advanced Inertial Reference Sphere The Advanced Inertial Reference Sphere (AIRS) is a highly accurate inertial guidance system designed for use in the LGM-118A Peacekeeper ICBM which was intended for precision nuclear strikes against Soviet missile silos. Details AIRS is a Fluid-su ...
). Like all gyrostabilized platforms, this system runs well with relatively slow, low-power computers. The fluid bearings are pads with holes through which pressurized inert gas (such as helium) or oil presses against the spherical shell of the platform. The fluid bearings are very slippery and the spherical platform can turn freely. There are usually four bearing pads, mounted in a tetrahedral arrangement to support the platform. In premium systems, the angular sensors are usually specialized
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
coils made in a strip on a flexible printed circuit board. Several coil strips are mounted on great circles around the spherical shell of the gyrostabilized platform. Electronics outside the platform uses similar strip-shaped transformers to read the varying magnetic fields produced by the transformers wrapped around the spherical platform. Whenever a magnetic field changes shape, or moves, it will cut the wires of the coils on the external transformer strips. The cutting generates an electric current in the external strip-shaped coils and electronics can measure that current to derive angles. Cheap systems sometimes use
bar code A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths, spacings and sizes of parallel lines. These barcodes, now commonly referred to as linear or o ...
s to sense orientations and use
solar cell A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
s or a single transformer to power the platform. Some small missiles have powered the platform with light from a window or optic fibers to the motor. A research topic is to suspend the platform with pressure from exhaust gases. Data is returned to the outside world via the transformers, or sometimes
LED A light-emitting diode (LED) is a semiconductor Electronics, device that Light#Light sources, emits light when Electric current, current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy i ...
s communicating with external photodiodes.


Strapdown systems

Lightweight digital computers permit the system to eliminate the gimbals, creating ''strapdown'' systems, so called because their sensors are simply strapped to the vehicle. This reduces the cost, eliminates
gimbal lock Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate t ...
, removes the need for some calibrations and increases the reliability by eliminating some of the moving parts. Angular rate sensors called ''rate gyros'' measure the angular velocity of the vehicle. A strapdown system needs a dynamic measurement range several hundred times that required by a gimballed system. That is, it must integrate the vehicle's attitude changes in pitch, roll and yaw, as well as gross movements. Gimballed systems could usually do well with update rates of 50–60 Hz. However, strapdown systems normally update about 2000 Hz. The higher rate is needed to let the navigation system integrate the angular rate into an attitude accurately. The data updating algorithms (''direction cosines'' or quaternions) involved are too complex to be accurately performed except by digital electronics. However,
digital computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These program ...
s are now so inexpensive and fast that rate gyro systems can now be practically used and mass-produced. The Apollo lunar module used a strapdown system in its backup Abort Guidance System (AGS). Strapdown systems are nowadays commonly used in commercial and military applications (aircraft, ships, ROVs,
missile In military terminology, a missile is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles are thus also called guided missiles or guided rockets (when a previously unguided rocke ...
s, etc.). State-of-the-art strapdown systems are based upon Ring Laser Gyroscopes, Fibre Optic Gyrocopes or Hemispherical Resonator Gyroscopes. They are using digital electronics and advanced digital filtering techniques such as
Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
.


Motion-based alignment

The orientation of a gyroscope system can sometimes also be inferred simply from its position history (e.g., GPS). This is, in particular, the case with planes and cars, where the velocity vector usually implies the orientation of the vehicle body. For example,
Honeywell Honeywell International Inc. is an American publicly traded, multinational conglomerate corporation headquartered in Charlotte, North Carolina. It primarily operates in four areas of business: aerospace, building technologies, performance ma ...
's ''Align in Motion'' is an initialization process where the initialization occurs while the aircraft is moving, in the air or on the ground. This is accomplished using
GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
and an inertial reasonableness test, thereby allowing commercial data integrity requirements to be met. This process has been FAA certified to recover pure INS performance equivalent to stationary alignment procedures for civilian flight times up to 18 hours. It avoids the need for gyroscope batteries on aircraft.


Vibrating gyros

Less-expensive navigation systems, intended for use in automobiles, may use a
vibrating structure gyroscope A vibrating structure gyroscope, defined by the IEEE as a Coriolis vibratory gyroscope (CVG), is a gyroscope that uses a vibrating structure to determine the rate of rotation. A vibrating structure gyroscope functions much like the halteres of fl ...
to detect changes in heading and the odometer pickup to measure distance covered along the vehicle's track. This type of system is much less accurate than a higher-end INS, but it is adequate for the typical automobile application where GPS is the primary navigation system and
dead reckoning In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. ...
is only needed to fill gaps in GPS coverage when buildings or terrain block the satellite signals.


Hemispherical resonator gyros (wine glass or mushroom gyros)

If a standing wave is induced in a hemispheric resonant structure and then the resonant structure is rotated, the spherical harmonic standing wave rotates through an angle different from the quartz resonator structure due to the Coriolis force. The movement of the outer case with respect to the standing wave pattern is proportional to the total rotation angle and can be sensed by appropriate electronics. The system resonators are machined from
fused quartz Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form. This differs from all other commercial glasses in which other ingredients are added which change ...
due to its excellent mechanical properties. The electrodes that drive and sense the standing waves are deposited directly onto separate quartz structures that surround the resonator. These gyros can operate in either a whole angle mode (which gives them nearly unlimited rate capability) or a force rebalance mode that holds the standing wave in a fixed orientation with respect to the gyro housing (which gives them much better accuracy). This system has almost no moving parts and is very accurate. However it is still relatively expensive due to the cost of the precision ground and polished hollow quartz hemispheres. Northrop Grumman currently manufactures IMUs ( inertial measurement units) for spacecraft that use HRGs. These IMUs have demonstrated extremely high reliability since their initial use in 1996. Safran manufactures large numbers of HRG based inertial systems dedicated to a wide range of applications.


Quartz rate sensors

These products include "tuning fork gyros". Here, the gyro is designed as an electronically driven tuning fork, often fabricated out of a single piece of quartz or silicon. Such gyros operate in accordance with the dynamic theory that when an angle rate is applied to a translating body, a Coriolis force is generated. This system is usually integrated on a silicon chip. It has two mass-balanced quartz tuning forks, arranged "handle-to-handle" so forces cancel. Aluminum electrodes evaporated onto the forks and the underlying chip both drive and sense the motion. The system is both manufacturable and inexpensive. Since quartz is dimensionally stable, the system can be accurate. As the forks are twisted about the axis of the handle, the vibration of the tines tends to continue in the same plane of motion. This motion has to be resisted by electrostatic forces from the electrodes under the tines. By measuring the difference in capacitance between the two tines of a fork, the system can determine the rate of angular motion. Current state-of-the-art non-military technology () can build small solid-state sensors that can measure human body movements. These devices have no moving parts and weigh about . Solid-state devices using the same physical principles are used for image stabilization in small cameras or camcorders. These can be extremely small, around and are built with microelectromechanical systems (MEMS) technologies.


MHD sensor

Sensors based on magnetohydrodynamic principles can be used to measure angular velocities.


MEMS gyroscope

MEMS gyroscopes typically rely on the Coriolis effect to measure angular velocity. It consists of a resonating proof mass mounted in silicon. The gyroscope is, unlike an accelerometer, an active sensor. The proof mass is pushed back and forth by driving combs. A rotation of the gyroscope generates a Coriolis force that is acting on the mass which results in a motion in a different direction. The motion in this direction is measured by electrodes and represents the rate of turn.


Ring Laser Gyros (RLG)

A ring laser gyro splits a beam of
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
light into two beams in opposite directions through narrow tunnels in a closed circular optical path around the perimeter of a triangular block of temperature-stable Cervit glass with reflecting mirrors placed in each corner. When the gyro is rotating at some angular rate, the distance traveled by each beam will differ—the shorter path being opposite to the rotation. The phase shift between the two beams can be measured by an interferometer and is proportional to the rate of rotation (
Sagnac effect The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferomet ...
). In practice, at low rotation rates the output frequency can drop to zero as the result of
backscatter In physics, backscatter (or backscattering) is the reflection of waves, particles, or signals back to the direction from which they came. It is usually a diffuse reflection due to scattering, as opposed to specular reflection as from a mirror, a ...
ing causing the beams to synchronise and lock together. This is known as a ''lock-in'', or ''laser-lock''. The result is that there is no change in the interference pattern and therefore no measurement change. To unlock the counter-rotating light beams, laser gyros either have independent light paths for the two directions (usually in fiber optic gyros), or the laser gyro is mounted on a piezo-electric dither motor that rapidly vibrates the laser ring back and forth about its input axis through the lock-in region to decouple the light waves. The shaker is the most accurate, because both light beams use exactly the same path. Thus laser gyros retain moving parts, but they do not move as far.


Fiber optic gyros (FOG)

A more recent variation on the optical gyroscope, the
fiber optic gyroscope A fibre-optic gyroscope (FOG) senses changes in orientation using the Sagnac effect, thus performing the function of a mechanical gyroscope. However its principle of operation is instead based on the interference of light which has passed throu ...
, uses an external laser and two beams going opposite directions (counter-propagating) in long spools (several kilometers) of fiber optic filament, with the phase difference of the two beams compared after their travel through the spools of fiber. The basic mechanism, monochromatic laser light travelling in opposite paths and the
Sagnac effect The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferomet ...
, is the same in a FOG and a RLG, but the engineering details are substantially different in the FOG compared to earlier laser gyros. Precise winding of the fiber-optic coil is required to ensure the paths taken by the light in opposite directions are as similar as possible. The FOG requires more complex calibrations than a laser ring gyro making the development and manufacture of FOG's more technically challenging that for a RLG. However FOG's do not suffer from laser lock at low speeds and do not need to contain any moving parts, increasing the maximum potential accuracy and lifespan of a FOG over an equivalent RLG.


Pendular accelerometers

The basic, open-loop accelerometer consists of a mass attached to a spring. The mass is constrained to move only in line with the spring. Acceleration causes deflection of the mass and the offset distance is measured. The acceleration is derived from the values of deflection distance, mass and the spring constant. The system must also be damped to avoid oscillation. A closed-loop accelerometer achieves higher performance by using a feedback loop to cancel the deflection, thus keeping the mass nearly stationary. Whenever the mass deflects, the feedback loop causes an electric coil to apply an equally negative force on the mass, canceling the motion. Acceleration is derived from the amount of negative force applied. Because the mass barely moves, the effects of non-linearities of the spring and damping system are greatly reduced. In addition, this accelerometer provides for increased bandwidth beyond the natural frequency of the sensing element. Both types of accelerometers have been manufactured as integrated micro-machinery on silicon chips.


TIMU (Timing & Inertial Measurement Unit) sensors

DARPA The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adv ...
's Microsystems Technology Office (MTO) department is working on a Micro-PNT (Micro-Technology for Positioning, Navigation and Timing) program to design Timing & Inertial Measurement Unit (TIMU) chips that do absolute position tracking on a single chip without GPS-aided navigation.Extreme Miniaturization: Seven Devices, One Chip to Navigate without GPS
Micro-PNT adds a highly accurate master timing clock integrated into an IMU (Inertial Measurement Unit) chip, making it a Timing & Inertial Measurement Unit chip. A TIMU chip integrates 3-axis gyroscope, 3-axis accelerometer and 3-axis magnetometer together with a highly accurate master timing clock, so that it can simultaneously measure the motion tracked and combine that with timing from the synchronized clock.


Method

In one form, the navigational system of equations acquires linear and angular measurements from the inertial and body frame, respectively and calculates the final attitude and position in the NED frame of reference. Where: f is specific force, \omega is angular rate, a is acceleration, R is position, \dot R and V are velocity, \Omega is the angular velocity of the earth, g is the acceleration due to gravity, \Phi, \lambda and h are the NED location parameters. Also, super/subscripts of E, I and B are representing variables in the Earth centered, Inertial or Body reference frame, respectively and C is a transformation of reference frames.


See also

* Adam Air Flight 574 *
Attitude control Attitude control is the process of controlling the orientation of an aerospace vehicle with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle ...
*
Dead reckoning In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. ...
*
Fibre-optic gyroscope A fibre-optic gyroscope (FOG) senses changes in orientation using the Sagnac effect, thus performing the function of a mechanical gyroscope. However its principle of operation is instead based on the interference of light which has passed throu ...
* Globus navigation system * Guidance system *
Hemispherical resonator gyroscope The Hemispherical Resonator Gyroscope (HRG), also called wine-glass gyroscope or mushroom gyro, is a compact, low-noise, high-performance angular rate or rotation sensor. An HRG is made using a thin solid-state hemispherical shell, anchored by a ...
*
Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
*
Korean Air Lines Flight 007 Korean Air Lines Flight 007 (KE007/KAL007)The flight number KAL 007 was used by air traffic control, while the public flight booking system used KE 007 was a scheduled Korean Air Lines flight from New York City to Seoul via Anchorage, Alas ...
*
LN-3 inertial navigation system The LN-3 inertial navigation system is an inertial navigation system (INS) that was developed in the 1960s by Litton Industries. It equipped the Lockheed F-104 Starfighter versions used as strike aircraft in European forces. An inertial navigatio ...
*
PIGA accelerometer A PIGA (''Pendulous Integrating Gyroscopic Accelerometer'') is a type of accelerometer that can measure acceleration and simultaneously integrates this acceleration against time to produce a speed measure as well. The PIGA's main use is in Inertia ...
*
Quantum compass The terminology quantum compass often relates to an instrument which measures relative position using the technique of atom interferometry. It includes an ensemble of accelerometers and gyroscope based on quantum technology to form an Inertial Na ...
*
Rate integrating gyroscope A Rate integrating gyroscope is a rate gyro with a built in integrator. It is usually a component of an Inertial Measurement Unit or a stabilization system. Principle of operation In a rate integrating gyroscope, the gyroscope is turned at a st ...
* Ring laser gyroscope *
Schuler tuning Schuler tuning is a design principle for inertial navigation systems that accounts for the curvature of the Earth. An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directi ...
*
Spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...


References


Further reading

* * *


External links


Principle of operation of an accelerometer

Overview of inertial instrument types
* Oxford Technical Solution
Inertial Navigation Guide

Listing of open-source Inertial Navigation system

Impact of inertial sensor errors on Inertial Navigation System position and attitude errors

Introduction to Inertial Navigation Systems in UAV/Drone Applications
{{Aircraft components Aircraft instruments Aerospace engineering Avionics Spacecraft components Missile guidance Navigational equipment Technology systems Navigational aids Inertial navigation