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70-446: AIRS is a fluid-suspended gyrostabilized platform system, as opposed to one using a gimballed gyrostabilized platform . It consists of a beryllium sphere floating in fluid. Jet nozzles are used to stabilize the inertial platform as commanded from the sensors. This design not only eliminates the problem of gimbal lock , but also makes it extremely accurate (drift less than 1.5×10 °/h), to the point that any further improvement would give

140-575: A computer 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 sometimes by magnetic sensors ( magnetometers ) and/or speed measuring devices. INSs are used on mobile robots and on vehicles such as ships , aircraft , submarines , guided missiles , and spacecraft . Older INS systems generally used an inertial platform as their mounting point to

210-453: 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 it 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

280-440: A flotation chamber to mount a gyrostabilized platform. These systems can have very high precisions (e.g., Advanced Inertial Reference Sphere ). 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

350-694: 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 computers are now so inexpensive and fast that rate gyro systems can now be practically used and mass-produced. The Apollo lunar module used

420-455: 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 '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

490-488: 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 accelerations of the vehicle. Since it can move in three axes (up and down, left and right, forward and back), there

560-610: 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 during World War II. The initial Delta guidance system assessed

630-508: A negligible benefit to the missile's CEP . The sensors used in AIRS are floated gas bearing gyroscopes and SFIR accelerometers, which are derivatives of PIGA accelerometers . Although this type of accelerometer is most accurate, it contains many precise parts, making it very expensive to build (approximately $ 6,000,000 per AIRS unit in 1987, not including development costs). PIGA/SFIR accelerometers are also very susceptible to failure due to

700-408: 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 . Lightweight digital computers permit the system to eliminate

770-458: A strapdown system in its backup Abort Guidance System (AGS). Strapdown systems are nowadays commonly used in commercial and military applications (aircraft, ships, ROVs , missiles , 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 . The orientation of

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840-544: A visual phenomenon that can severely clutter up a radar display scope with useless data. Interference is not that common between ground radars, however, because they are not usually placed close enough together. It is more likely that some sort of airborne radar system is inadvertently causing the interference—especially when two or more countries are involved. The interference between airborne radars referred to above can sometimes (usually) be eliminated by frequency-shifting transmitters. The other interference often experienced

910-536: A wide range of applications. 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

980-405: 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 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

1050-421: Is accomplished using GPS 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. Less-expensive navigation systems, intended for use in automobiles, may use

1120-522: Is between the aircraft's own electronic transmitters, i.e. transponders , being picked up by its radar. This interference is eliminated by suppressing the radar's reception for the duration of the transponder's transmission. Instead of "bright-light" rabbits across the display, one would observe very small black dots. Because the external radar causing the transponder to respond is generally not synchronised with your own radar (i.e. different pulse-repetition frequencies ), these black dots appear randomly across

1190-559: Is caused by devices that reflect or re-reflect radar energy back to the radar to produce false target returns on the operator's scope. Mechanical jamming devices include chaff, corner reflectors, and decoys. Electronic jamming is a form of electronic warfare where jammers radiate interfering signals toward an enemy's radar, blocking the receiver with highly concentrated energy signals. The two main technique styles are noise techniques and repeater techniques. The three types of noise jamming are spot, sweep, and barrage. The burn-through range

1260-521: Is difficult without computers. The desire to use inertial guidance in the Minuteman missile and Project Apollo drove early attempts to miniaturize computers. 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. An inertial guidance system that will operate near

1330-399: Is fairly common because it is indiscriminate and affects any nearby radars, hostile or not. Electronic jamming can also be inadvertently caused by friendly sources, usually powerful EW platforms operating within range of the affected radar. For protective jamming, a small radar cross section of the protected aircraft will improve the jamming efficiency (higher J/S). A lower RCS also reduces

1400-510: Is held annually in October in Germany. The publications of all DGON ISA conferences over the last more than 60 years are accessible. 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

1470-500: Is possible to track the position and orientation of a device. 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

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1540-461: Is the distance from the radar at which the jamming is ineffective. When a target is within this range, the radar receives an adequate target skin return to track it. The burn through range is a function of the target RCS ( Radar cross-section ), jamming ERP ( Effective radiated power ), the radars ERP and required J/S (for the jamming to be effective). In some cases, jamming of either type may be caused by friendly sources. Inadvertent mechanical jamming

1610-452: 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.

1680-428: 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 navigation systems dedicated to

1750-534: 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. 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

1820-550: The Space Shuttle , open loop 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

1890-417: The U.S. Army Research Laboratory reported a method to merge measurements from 10 pairs of MEMS gyroscope and accelerometers (plus occasional GPS), reducing the positional error by two thirds for a projectile. The algorithm can correct for systemic biases in individual sensors, using both GPS and a heuristic based on the gun-firing acceleration force. If one sensor consistently over or underestimates distance,

1960-562: 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

2030-442: The "burn-through" range. Stealth technologies like radiation-absorbent materials can be used to reduce the return of a target. While not usually caused by the enemy, interference can greatly impede the ability of an operator to track. Interference occurs when two radars in relatively close proximity (how close they need to be depends on the power of the radars) are operating on the same frequency. This will cause "running rabbits",

2100-832: 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. INSs contain Inertial Measurement Units (IMUs) which have angular and linear accelerometers (for changes in position); some IMUs include

2170-870: 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

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2240-464: 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

2310-515: 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,

2380-554: 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 in 1945 under the provisions of Operation Paperclip and were subsequently moved to Huntsville, Alabama , in 1950 where they worked for U.S. Army rocket research programs. In

2450-429: The advent of spacecraft , guided missiles , and commercial airliners . Early German World War II V2 guidance systems combined two gyroscopes and a lateral accelerometer with a simple analog computer to adjust the azimuth for the rocket in flight. Analog computer signals were used to drive four graphite rudders in the rocket exhaust for flight control. The GN&C (Guidance, Navigation, and Control) system for

2520-435: The angular displacement, 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

2590-452: 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. 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

2660-564: The complex design. The AIRS was originally developed for the LGM-118A Peacekeeper. The first AIRS units were manufactured by Northrop . This article relating to missiles is a stub . You can help Misplaced Pages by expanding it . Fluid-suspended gyrostabilized platform An inertial navigation system ( INS ; also inertial guidance system , inertial instrument ) is a navigation device that uses motion sensors ( accelerometers ), rotation sensors ( gyroscopes ) and

2730-460: 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 . 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. To support

2800-417: The difference in capacitance between the two tines of a fork, the system can determine the rate of angular motion. Radar jamming and deception Radar jamming and deception is a form of electronic countermeasures (ECMs) that intentionally sends out radio frequency signals to interfere with the operation of radar by saturating its receiver with noise or false information. Concepts that blanket

2870-519: 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 ) of guidance. The Q system's revolution

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2940-428: The display and the operator sees through and around them. The returning image may be much larger than the "dot" or "hole", as it has become known, anyway. Keeping the transponder's pulse widths very narrow and mode of operation (single pulse rather than multi-pulse) becomes a crucial factor. The external radar could, in theory, come from an aircraft flying alongside your own, or from space. Another factor often overlooked

3010-776: 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 for

3080-488: 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

3150-419: 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

3220-449: 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 the angular velocity of the vehicle. A strapdown system needs a dynamic measurement range several hundred times that required by

3290-451: 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 they were blindfolded, and if they are able to keep track of both how

3360-563: The information from an INS and other systems ( GPS ), 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,

3430-515: 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 crewed 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. One example of a popular INS for commercial aircraft

3500-410: 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. Gyroscopes measure the angular displacement 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

3570-512: 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

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3640-413: 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

3710-537: 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,

3780-489: 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 (164-ft) error within 17 minutes. Therefore, the position must be periodically corrected by input from some other type of navigation system. Accordingly, inertial navigation

3850-401: 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 , 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

3920-502: 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 codes to sense orientations and use solar cells or

3990-492: 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 that can wear out or jam and

4060-417: The radar operator. Electronic jamming works by transmitting additional radio signals towards enemy receivers, making it difficult to detect real target signals, or take advantage of known behaviors of automated systems like radar lock-on to confuse the system. Various Electronic counter-countermeasures (ECCMs) can sometimes help radar operators maintain target detection despite jamming. Mechanical jamming

4130-446: The radar with signals so its display cannot be read are normally known as jamming , while systems that produce confusing or contradictory signals are known as deception , but it is also common for all such systems to be referred to as jamming. There are two general classes of radar jamming, mechanical and electronic. Mechanical jamming entails reflecting enemy radio signals in various ways to provide false or misleading target signals to

4200-623: The satellite signals. 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 due to its excellent mechanical properties. The electrodes that drive and sense

4270-409: 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

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4340-404: 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

4410-433: 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. Some systems place the linear accelerometers on a gimballed 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

4480-400: The system can adjust the corrupted sensor's contributions to the final calculation. Inertial navigation systems were originally developed for rockets . American rocketry pioneer Robert Goddard experimented with rudimentary gyroscopic systems. Goddard's systems were of great interest to contemporary German pioneers including Wernher von Braun . The systems entered more widespread use with

4550-504: The use of inertial technology in the best way, already in 1965 a technical working group for Inertial Sensors had been established in Germany to bring together the users, the manufacturers and the researchers of inertial sensors. This working group has been continuously developed and today it is known as DGON ISA Inertial Sensors and Application Symposium, the leading conference for inertial technologies for more than 60 years. This Symposium DGON / IEEE ISA with about 200 international attendees

4620-420: 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

4690-661: The vehicle and the terms are sometimes considered synonymous. Integrals in the time domain implicitly demand a stable and accurate clock for the quantification of elapsed time. 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

4760-553: 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. In February 1961 NASA awarded MIT a contract for preliminary design study of a guidance and navigation system for the Apollo program . MIT and

4830-486: Was the Delco Carousel , which provided partial automation of navigation in the days before complete flight management systems 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

4900-420: 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

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