An inertial guidance system consists of an Inertial Measurement Unit (IMU) combined with a set of guidance algorithms and control mechanisms, allowing the path of a vehicle to be controlled according to the position determined by the inertial navigation system. These systems are also referred to as an inertial platform. An crap is a closed system that is used to detect altitude, location, and motion. ...

An inertial navigation system (INS) provides the position, velocity, orientation, and angular velocity of a vehicle by measuring the linear and angular accelerations applied to the system in an inertial reference frame. It is widely used because it refers to no real-world item beyond itself. It is therefore immune to jamming and deception. (See the principle of relativity and Mach's principle for some background in the physics involved.) Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... The term Jamming can refer to several things: Jamming as an electronic warfare (EW) - a technique to limit the effectiveness of an opponents communications and/or detection equipment, like Radio Jamming and Radar Jamming E-Mail Jamming- used by electronic political activists or hackers to disable e-mail systems... Wikisource has original text related to this article: Relativity: The Special and General Theory A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations. ... In theoretical physics, particularly in discussions of gravitation theories, Machs principle is the name given by Einstein to a vague hypothesis first supported by the physicist and philosopher Ernst Mach. ...

Inertial navigation systems are used in submarines and spacecraft (where the use of external reference points may not be practicable). INS systems were also installed as backup systems on long-haul commercial aircraft before the advent of GPS.

Overview

Inertial guidance systems were originally developed for navigating rockets. American rocket pioneer Robert Goddard experimented with rudimentary gyroscopic systems. Dr. Goddard's systems were of great interest to contemporary German pioneers including Wernher von Braun. This article is about vehicles powered by rocket engines. ... Robert Goddard Robert Hutchings Goddard (October 5, 1882 – August 10, 1945) was one of the pioneers of modern rocketry. ... A gyroscope For other uses, see Gyroscope (disambiguation). ... For other uses of von Braun, see von Braun (disambiguation). ...

A typical inertial navigation system integrates the information gathered from a combination of gyroscopes and accelerometers in order to determine the current state of the system. A gyroscope For other uses, see Gyroscope (disambiguation). ... A depiction of an accelerometer designed at Sandia National Laboratories. ...

Gyroscopes measure the angular velocity of the system in 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, he knows what direction the car is facing but not how fast or slow it is moving, or whether it is sliding sideways. Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... The integral of f(x) from a to b is the area above the x-axis and below the curve y = f(x), minus the area below the x-axis and above the curve, for x in the interval [a,b]. Integration is a core concept of advanced mathematics, specifically...

Accelerometers measure the linear acceleration of the system in the inertial reference 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 his 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 moving relative to itself, that is, whether it is going 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 he 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 he is able to keep track of both how the car has turned and how it has accelerated and decelerated since, he can accurately know the current orientation, position, and velocity of the car at any time. Kinematics (Greek κινειν,kinein, to move) is a branch of mechanics which describes the motion of objects without the consideration of the masses or forces that bring about the motion. ...

All inertial navigation systems suffer from integration drift. As small errors in the measurement of acceleration and angular velocity are integrated into progressively larger errors in velocity, which is compounded into errors in position. This is a problem that is inherent in every open loop control system. The inaccuracy of a good-quality navigational system is normally less than 0.6 nautical miles per hour in position and on the order of tenths of a degree per hour orientation. This article is about an engineering theory called control theory. ... A nautical mile is a unit of distance, or, as physical scientists like to call it, length. ...

Inertial navigation may also be used to supplement other navigation systems, providing a higher degree of accuracy than is possible with the use of any single navigation 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.

Control 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. By properly combining the information from an INS and the GPS system, the errors in position and velocity are stableGPS/INS. In engineering and mathematics, control theory deals with the behavior of dynamical systems. ... The Kalman filter (named after its inventor, Rudolf Kalman) is an efficient recursive computational solution for tracking a time-dependent state vector with noisy equations of motion in real time by the least-squares method. ... Satellite navigation systems use radio time signals transmitted by satellites to enable mobile receivers on the ground to determine their exact location. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... In the mathematical subfield of numerical analysis, numerical stability is a property of numerical algorithms. ... GPS/INS refers to the use of GPS satellite signals to correct or calibrate a solution from an Inertial Navigation System. ...

Inertial navigation systems in detail

INSs have angular and linear accelerometers (for changes in position); some include a gyroscopic element (for maintaining an absolute positional reference). Image File history File links Size of this preview: 800 × 600 pixelsFull resolution (2048 × 1536 pixel, file size: 836 KB, MIME type: image/png) This image is supposed to replace the jpg-compressed version, Image:Flight dynamics. ... Image File history File links Size of this preview: 800 × 600 pixelsFull resolution (2048 × 1536 pixel, file size: 836 KB, MIME type: image/png) This image is supposed to replace the jpg-compressed version, Image:Flight dynamics. ...

Angular accelerometers measure how the vehicle is rotating in space. Generally, there's 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 how the vehicle is moving in space. 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 θ x, θ y and θ z), it integrates the sensed amount of acceleration over time to figure the current velocity. Then it integrates the velocity to figure the current position. In mechanical engineering, aeronautical engineering and robotics, degrees of freedom (DOF) describes flexibility of motion. ...

Inertial guidance is difficult without computers. The desire to use inertial guidance in the Minuteman missile and Project Apollo drove early attempts to miniaturize computers. The LGM-30 Minuteman is a United States nuclear missile, a land-based intercontinental ballistic missile (ICBM) (the other type is the LG-118A Peacekeeper, which is to be phased out by 2005). ... Project Apollo was a series of human spaceflight missions undertaken by the United States of America (NASA) using the Apollo spacecraft and Saturn launch vehicle, conducted during the years 1961 – 1975. ...

Inertial guidance systems are now usually combined with satellite navigation systems through a digital filtering system. The inertial system provides short term data, while the satellite system corrects accumulated errors of the inertial system. It has been suggested that this article or section be merged into Global Navigation Satellite System. ...

An inertial guidance system that will operate near the surface of the earth must incorporate Schuler tuning so that its platform will continue pointing towards the center of the earth as a vehicle moves from place to place. Schuler tuning describes the fundamental functional conditions for a gyrocompass. ...

Basic schemes

Gimbaled Gyrostabilized platforms

Some systems place the linear accelerometers on a gimbaled gyrostabilized platform. The gimbals 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. A gimbal is a mechanical device that allows the rotation of an object in multiple dimensions. ... A gyroscope For other uses, see Gyroscope (disambiguation). ...

Two gyroscopes are used to cancel gyroscopic precession, the tendency of a gyroscope to twist at right angles to an input force. By mounting a pair of gyroscopes (of the same rotational inertia and spinning at the same speed) at right angles the precessions are cancelled, and the platform will resist twisting. Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ...

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 that can wear out or jam, and is vulnerable to gimbal lock. The primary guidance system of the Apollo spacecraft used a three-axis gyrostabilized platform, feeding data to the Apollo Guidance Computer. Maneuvers had to be carefully planned to avoid gimbal lock. Moving parts are the components of a device that undergo continuous or frequent motion, most commonly rotation. ... In gyroscopic devices controlled by Euler mechanics or Euler angles, gimbal lock is caused by the alignment of two of the three gimbals together so that one of the rotation references (pitch/yaw/roll, often yaw) is cancelled. ... The Apollo Primary Guidance, Navigation and Control System (PGNCS) (pronounced pings) was a self-contained inertial guidance system that allowed Apollo spacecraft to carry out their missions when communications with Earth were interrupted, either as expected, when the spacecraft were behind the moon, or in case of a communications failure. ... Apollo Spacecraft: Command Module, Service Module, Lunar Module. ... The references in this article would be clearer with a different and/or consistent style of citation, footnoting or external linking. ...

Fluidically Suspended Gyrostabilized Platforms

Gimbal lock constrains maneuvring, 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. 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 press 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 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. Cutaway view of an LVDT. Current is driven through the primary coil at A, causing an induction current to be generated through the secondary coils at B. The linear variable differential transformer (LVDT) is a type of electrical transformer used for measuring linear displacement. ... Part of a 1983 Sinclair ZX Spectrum computer board. ...

Cheap systems sometimes use bar codes to sense orientations, and use solar cells 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 LEDs communicating with external photodiodes. Wikipedia encoded in Code 128_B A barcode (also bar code) is a machine-readable representation of information in a visual format on a surface. ... A solar cell, made from a monocrystalline silicon wafer A solar cell or photovoltaic cell is a device that converts light energy into electrical energy. ... External links LEd Category: TeX ... Photodiode closeup A photodiode A photodiode is a semiconductor diode that functions as a photodetector. ...

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, removes the need for some calibrations, and increases the reliability by eliminating some of the moving parts. Angular rate sensors called "rate gyros" measure how the angular velocity of the vehicle changes. The strapdown is an alternative to the gimbal used in INS. It is mechanically simpler, but has drawbacks as a result. ... In gyroscopic devices controlled by Euler mechanics or Euler angles, gimbal lock is caused by the alignment of two of the three gimbals together so that one of the rotation references (pitch/yaw/roll, often yaw) is cancelled. ...

A strapdown system has a dynamic measurement range several hundred times that required by a gimbaled 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 to 60 updates per second. However, strapdown systems normally update about 2000 times per second. The higher rate is needed to keep the maximum angular measurement within a practical range for real rate gyros: about 4 milliradians. Most rate gyros are now laser interferometers.

The data updating algorithms ("direction cosines" or "quaternions") involved are too complex to be accurately performed except by digital electronics. However, digital computers 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). In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... ... Description Role: Lunar landing Crew: 2; CDR, LM pilot Dimensions Height: 20. ...

GPS Align in Motion

Honeywell has developed a new initialization process called Align in Motion. Strapdown inertial navigation systems require an initialization process that establishes the relationship between the aircraft body frame and the local geographic reference. This process, called alignment, generally requires the device to remain stationary for some period of time in order to establish this initial state. This paper[[1]] describes an alignment process where the initialization occurs while the device is moving. This is possible because an accurate determination of the aircraft motion is available based on measurements obtained from GPS. Honeywell Heating Specialties Company Stock Certificate dated 1924 signed by Mark C. Honeywell - courtesy of Scripophily. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ...

Align In Motion allows initialization of a Strapdown Inertial Navigation System while an aircraft is moving, in the air or on the ground. This is accomplished using Civilian grade GPS and an inertial reasonableness test, thereby allowing commercial data integrity requirements to be met. Align In Motion has been FAA certified to recover pure INS performance equivalent to stationary align procedures for civilian flight times up to 18 hours. Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ...

This Align In Motion capability allows the removal of dedicated backup batteries on aircraft resulting in weight, cost, and reliability improvements. Align In Motion also has benefits for aircraft operations on the ground, on board ship, and in the air such as reduced turn backs, quicker dispatch, and world-wide alignment including polar regions.

Types of sensors

Laser gyros

Laser gyroscopes were supposed to eliminate the bearings in the gyroscopes, and thus the last bastion of precision machining and moving parts. A ring laser gyroscope uses interference of laser light within a bulk optic ring to detect changes in orientation and spin. ...

A laser gyro splits a beam of laser light into two beams in opposite directions through narrow tunnels in a closed optical circular path around the perimeter of a triangular block of temperature stable cervit glass block with reflecting mirrors placed in each corner. When the gyro is rotating at some angular rate, the distance traveled by each beam becomes different - 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). Experiment with a laser (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: Light Amplification by Stimulated Emission of Radiation. ... The Sagnac effect manifests itself in an experimental setup called ring interferometry. ...

In practice, at low rotation rates the output frequency can drop to zero after the result of "Back scattering" 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.

Alas, 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.

Vibrating gyros

Less expensive navigation systems intended for use in automobiles, may use a Vibrating structure gyroscope 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 is adequate for the typical automobile application where GPS is the primary navigation system, and dead reckoning is only needed to fill gaps in GPS coverage when buildings or terrain block the satellite signals. In science, a vibrating structure gyroscope is a type of gyroscope that functions much like the halteres of insects. ... Dead reckoning (DR) is the process of estimating ones current position based upon a previously determined position, or fix, and advancing that position based upon measured velocity, time, heading, as well as the effect of currents or wind. ...

Hemispherical Resonator Gyros ("Brandy Snifter Gyros")

If a standing wave is induced in a globular brandy snifter, and then the snifter is tilted, the waves tend to continue in the same plane of movement. They don't fully tilt with the snifter. This trick is used to measure angles. Instead of brandy snifters, the system uses hollow globes machined from piezoelectric materials such as quartz. The electrodes to start and sense the waves are evaporated directly onto the quartz. A snifter glass A snifter refers to a type of stemware, a short-stemmed glass whose main vessel has a wide bottom but that narrows at the top. ... Piezoelectricity is the ability of certain crystals to produce a voltage when subjected to mechanical stress. ... Quartz (from German Quarz[1]) is the second most common mineral in the Earths continental crust. ...

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 spheres.

Although successful systems were constructed, and an HRG's kinematics appear capable of greater accuracy, they never really caught on. Laser gyros were just more popular.

The classic system is the Delco 130Y Hemispherical Resonator Gyro, developed about 1986. See also [2] for a picture of an HRG resonator.

Quartz rate sensors

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 (2005) can build small solid state sensors that can measure human body movements. These devices have no moving parts, and weigh about 50 grams.

Solid state devices using the same physical principles are used to stabilize images taken with small cameras or camcorders. These can be extremely small (≈5 mm) and are built with MEMS (Microelectromechanical Systems) technologies. A mite next to a gear set produced using MEMS. Courtesy Sandia National Laboratories, SUMMiTTM Technologies, www. ...

MHD sensor

Sensors based on magnetohydrodynamic principles can be used to measure angular velocities and are described in "MHD sensor". Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. ... Principles of an MHD sensor MHD sensors are used for precision measurements of angular velocities in inertial navigation systems (i. ...

Pendular accelerometers

Principle of open loop accelerometer. Acceleration in the upward direction causes the mass to deflect downward.

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, cancelling the motion. Acceleration is derived from the amount of negative force applied. Because the mass barely moves, the non-linearities of the spring and damping system are greatly reduced. In addition, this accelerometer provides for increased bandwidth past the natural frequency of the sensing element. Image File history File links Pendular_accel. ... Image File history File links Pendular_accel. ...

Both types of accelerometers have been manufactured as integrated micromachinery on silicon chips.

See also

• Inertial measurement unit
• Aircraft
• Spacecraft
• Attitude control
• Kalman filter
• Schuler tuning
• SIGI

An crap is a closed system that is used to detect altitude, location, and motion. ... “Flying Machine” redirects here. ... The Space Shuttle Discovery as seen from the International Space Station. ... // In the context of spacecraft, attitude control is control of the angular position and rotation of the spacecraft, either relative to the object that it is orbiting, or relative to the celestial sphere. ... The Kalman filter is an efficient recursive filter that estimates the state of a dynamic system from a series of incomplete and noisy measurements. ... Schuler tuning describes the fundamental functional conditions for a gyrocompass. ... In Norse Mythology, Sigi is a one of the sons of Odin. ...

External links

• Inertial Instruments- Where to Now? a survey from Draper Lab; describes the precision needed for various applications, as well as common technologies. (.pdf format)
• A history of inertial navigation systems (.pdf format)
• Principle of Operation of an Accelerometer (.pdf format)
• GPS Align in Motion of Civilian Strapdown INS

Manufacturers

• Crossbow Technology Inc., USA
• Applanix - A Trimble Company, Canada
• Dewetron, Austria
• Deutsche Montan Technologie GmbH, Germany
• Honeywell Inc., USA
• IGI, Germany
• iMAR Navigation GmbH, Germany European solutions for global industrial and defence applications with all kinds of inertial sensor technology
• iXSea, France
• Kearfott Guidance & Navigation Corporation, USA
• Northrop Grumman Italia, Italy (a division of Northrop Grumman, USA)
• Litef, Germany (a division of Northrop Grumman, USA)
• Sperry Marine (a division of Northrop Grumman, USA)
• Microbotics Inc, USA GPS Aided INS
• nec-tokin, japan miniature ceramic sensors
• Northrop Grumman, USA, see especially

• Navigation Systems index

• Sagem, France
• SEG, Germany
• Systron Donner Inertial, USA (a company of Schneider Electric)
• Verhaert, Belgium
• Xsens, The Netherlands miniature solid state sensors
• Invensense silicon chip sensors