Kejin Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen. The Space-Stabilized Terrestrial Navigator. Notes Includes bibliographical references p. Packed with valuable, time-saving bgitting and models, the book helps engineers design optimal navigation systems by comparing the performance of the various types of system mechanizations.
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Overview[ edit ] 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 the mostly nowadays mobile phone for purpose 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 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. 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.
This can be thought of as the ability of a blindfolded passenger in a car to feel the car turn left and right or tilt up and down as the car ascends or descends hills. Based on this information alone, the passenger knows what direction the car is facing but not how fast or slow it is moving, or whether it is sliding sideways. Accelerometers measure the linear acceleration of the moving vehicle in the sensor or body frame, but in directions that can only be measured relative to the moving system since the accelerometers are fixed to the system and rotate with the system, but are not aware of their own orientation.
This can be thought of as the ability of a blindfolded passenger in a car to feel himself pressed back into his seat as the vehicle accelerates forward or pulled forward as it slows down; and feel himself pressed down into his seat as the vehicle accelerates up a hill or rise up out of their seat as the car passes over the crest of a hill and begins to descend. However, by tracking both the current angular velocity of the system and the current linear acceleration of the system measured relative to the moving system, it is possible to determine the linear acceleration of the system in the inertial reference frame.
Performing integration on the inertial accelerations using the original velocity as the initial conditions using the correct kinematic equations yields the inertial velocities of the system and integration again using the original position as the initial condition yields the inertial position.
In our example, if the blindfolded passenger knew how the car was pointed and what its velocity was before he was blindfolded and if he is able to keep track of both how the car has turned and how it has accelerated and decelerated since, then he can accurately know the current orientation, position, and velocity of the car at any time.
Error[ edit ] 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.
Even the best accelerometers, with a standard error of 10 micro-g, would accumulate a meter error within 17 minutes. 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.
The navigation error rises with the lower sensitivity of the sensors used. Currently, devices combining different sensors are being developed, e. Because the navigation error is mainly influenced by the numerical integration of angular rates and accelerations, the Pressure Reference System was developed to use one numerical integration of the angular rate measurements.
Estimation theory in general and Kalman filtering in particular,  provide a theoretical framework for combining information from various sensors. One of the most common alternative sensors is a satellite navigation radio such as GPS , which can be used for all kinds of vehicles with direct sky visibility. Indoor applications can use pedometers , distance measurement equipment, or other kinds of position sensors.
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 , GPS jamming at the civilian level became a governmental concern. Army Research Laboratory reported an inertial measurement unit consisting of micro-electromechanical system triaxial accelerometers and tri-axial gyroscopes with an array size of 10 that had a Kalman filter algorithm to estimate sensor nuisance parameters errors and munition position and velocity.
The researchers coupled the algorithm with GPS or radar technology to initial and aid the navigation algorithm. 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 sensor arrays rather than ten. You may improve this section , discuss the issue on the talk page , or create a new section, as appropriate.
January Learn how and when to remove this template message Inertial navigation systems were originally developed for rockets. American rocketry pioneer Robert Goddard experimented with rudimentary gyroscopic systems. The systems entered more widespread use with 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. At the end of the war von Braun engineered the surrender of of his top rocket scientists, along with plans and test vehicles, to the Americans.
They arrived at Fort Bliss, Texas in under the provisions of Operation Paperclip and were subsequently moved to Huntsville, Alabama , in  where they worked for U. Army rocket research programs. In the early s, 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 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 , Dr. Richard Battin and Dr. Halcombe "Hal" Laning, Jr.
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 of guidance. The Q matrix represents the partial derivatives of the velocity with respect to the position vector. The Q system was classified information through the s. Within a manned system, there is a human interface needed for the guidance system. Aircraft inertial guidance[ edit ] One example of a popular INS for commercial aircraft 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. The 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 KC fleet was fitted with a dual Carousel system that was aided by a Doppler radar. 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 accelerations  of the vehicle. 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 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 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.
Basic schemes[ edit ] Gimballed gyrostabilized platforms[ edit ] 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 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 the precessions are cancelled and the platform will resist twisting.
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. Fluid-suspended gyrostabilized platforms[ edit ] 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. 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 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.
Kenneth R. Britting-Inertial Navigation Systems Analysis-John Wiley & Sons Inc (1971)
All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Sections or of the United States Copyright Act without the permission of the copyright owner is unlawful. Library of Congress Catalog Card Number: ISBN X Printed in the United States of America To the memory of ANNE Foreword Although the technique of inertial guidance can be said to have originated more than sixty years ago with the appearance of the gyrocompass, it did not attain full navigational status until the impetus of technology after World War I1 made it practical as well as feasible.
047110485x - Inertial Navigation Systems Analysis by Britting, Kenneth R
Grozahn Mathematical Notation and Techniques. The Space-Stabilized Terrestrial Navigator. We were unable to find this edition in any bookshop we are able to search. Doc Fisher Geoscience Library.
Inertial navigation system