Kayton, M. "Navigation Syste The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Kayton, M. “Navigation Systems” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
109 Navigation Systems 109.2 Coordinate frames 109.3 Categories of Navigation 109.4 Dead Reckoning 109.5 Radio Navigation 109.6 Celestial Navigation 109.7 Map Matching Navigation Myron Kayton 109.8 Navigation Software Kayton Engineering Co 109.9 Design Trade-Offs 109.1 Introduction Navigation is the determination of the position and velocity of a moving vehicle on land, at sea, in the air, or in space. The three components of position and the three components of velocity make up a six-component state vector that fully describes the translational motion of the vehicle because the differential equations of motion are of second order. Surveyors are beginning to use the same sensors as navigators but are achieving higher accuracy as a result of longer periods of observation, a fixed location, and more complex, non-real-time data reduction In the usual navigation system, the state vector is derived on-board, displayed to the crew, recorded on- board, or transmitted to the ground Navigation information is usually sent to other on-board subsystems; for example, to the waypoint steering, engine control, communication control, and weapon-control computers. Some navigation systems, called position-location systems, measure a vehicle's state vector using sensors on the ground or in another vehicle(Section 109.5). The external sensors usually track passive radar returns or a transponder. Position-location systems usually supply information to a dispatch or control center Traditionally, ship navigation included the art of pilotage--entering and leaving port, making use of wind and tides, and knowing the coasts and sea conditions. However, in modern usage, navigation is confined to the measurement of the state vector. The handling of the vehicle is called conning for ships, flight control for rcraft, and attitude control for spacecraft. The term guidance has two meanings, both of which are different than navigation 1. Steering toward a destination of known position from the vehicle's present position, as measured by a avigation system. The steering equations on a planet are derived from a plane triangle for nearby for distant de 2. Steering toward a destination without calculating the state vector explicitly a guided vehicle homes on radio, infrared, or visual emissions. Guidance toward a moving target is usually of interest to military tactical missiles in which a steering algorithm assures impact within the maneuver and fuel constraints of the interceptor. Guidance toward a fixed target involves beam riding, as in the Instrument Landing System, Section 109.5. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 109 Navigation Systems 109.1 Introduction 109.2 Coordinate Frames 109.3 Categories of Navigation 109.4 Dead Reckoning 109.5 Radio Navigation 109.6 Celestial Navigation 109.7 Map Matching Navigation 109.8 Navigation Software 109.9 Design Trade-Offs 109.1 Introduction Navigation is the determination of the position and velocity of a moving vehicle on land, at sea, in the air, or in space. The three components of position and the three components of velocity make up a six-component state vector that fully describes the translational motion of the vehicle because the differential equations of motion are of second order. Surveyors are beginning to use the same sensors as navigators but are achieving higher accuracy as a result of longer periods of observation, a fixed location, and more complex, non-real-time data reduction. In the usual navigation system, the state vector is derived on-board, displayed to the crew, recorded onboard, or transmitted to the ground. Navigation information is usually sent to other on-board subsystems; for example, to the waypoint steering, engine control, communication control, and weapon-control computers. Some navigation systems, called position-location systems, measure a vehicle’s state vector using sensors on the ground or in another vehicle (Section 109.5). The external sensors usually track passive radar returns or a transponder. Position-location systems usually supply information to a dispatch or control center. Traditionally, ship navigation included the art of pilotage—entering and leaving port, making use of wind and tides, and knowing the coasts and sea conditions. However, in modern usage, navigation is confined to the measurement of the state vector. The handling of the vehicle is called conning for ships, flight control for aircraft, and attitude control for spacecraft. The term guidance has two meanings, both of which are different than navigation: 1. Steering toward a destination of known position from the vehicle’s present position, as measured by a navigation system. The steering equations on a planet are derived from a plane triangle for nearby destinations and from a spherical triangle for distant destinations. 2. Steering toward a destination without calculating the state vector explicitly. A guided vehicle homes on radio, infrared, or visual emissions. Guidance toward a moving target is usually of interest to military tactical missiles in which a steering algorithm assures impact within the maneuver and fuel constraints of the interceptor. Guidance toward a fixed target involves beam riding, as in the Instrument Landing System, Section 109.5. Myron Kayton Kayton Engineering Co
Polar Axis urface of Reference FIGURE 109.1 Latitude-longitude-altitude coordinate frame. o= geodetic latitude; OP is normal to the ellipsoid at B: i 109.2 Coordinate frames respect to the local terrain or a building s walls. For navigation over hundreds of kilometers(e.g, automobiles and trucks), various map grids exist whose coordinates can be calculated from latitude-longitude(Fig. 109. 1). NATO land vehicles use a Universal Transverse Mercator grid. Long-range aircraft and ships navigate relative to an earth-bound coordinate frame, the most common of which are latitude-longitude-altitude and rectangular x,y, z(Fig. 109.1). The most accurate world-wide reference ellipsoid is described in [WGS-84, 1991]. Spacecraft in orbit around the earth navigate with respect to an earth-centered, inertially nonrotating coordinate frame whose z axis coincides with the polar axis of the earth and whose x axis lies along the equator. Interplanetary acecraft navigate with respect to a sun-centered, inertially nonrotating coordinate frame whose z axis is perpendicular to the ecliptic and whose x axis points to a convenient star [Battin, 1987 109.3 Categories of navigation Navigation systems can be categorized as 1. Absolute navigation systems that measure the state vector without regard to the path traveled by the Radio systems( Section 109.5). They consist of a network of transmitters(sometimes also receivers on the ground or in satellites. A vehicle detects the transmissions and computes its position relative to the known positions of the stations in the navigation coordinate frame. The vehicle's velocity is measured from the Doppler shift of the transmissions or from a sequence of position measurements. Celestial systems(Section 109.6). They measure the elevation and azimuth of celestial bodies relative to the land level and North. Electronic star sensors are used in special-purpose high-altitude aircraft and in spacecraft. Manual celestial navigation was practiced at sea for millennia(see Bowditch) 2. Dead-reckoning navigation systems that derive their state vector from a continuous series of measurements beginning at a known initial position. There are two kinds, those that measure vehicle heading and either e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 109.2 Coordinate Frames Navigation is with respect to a coordinate frame of the designer’s choice. Short-range robots navigate with respect to the local terrain or a building’s walls. For navigation over hundreds of kilometers (e.g., automobiles and trucks), various map grids exist whose coordinates can be calculated from latitude-longitude (Fig. 109.1). NATO land vehicles use a Universal Transverse Mercator grid. Long-range aircraft and ships navigate relative to an earth-bound coordinate frame, the most common of which are latitude-longitude-altitude and rectangular x, y, z (Fig. 109.1). The most accurate world-wide reference ellipsoid is described in [WGS-84, 1991]. Spacecraft in orbit around the earth navigate with respect to an earth-centered, inertially nonrotating coordinate frame whose z axis coincides with the polar axis of the earth and whose x axis lies along the equator. Interplanetary spacecraft navigate with respect to a sun-centered, inertially nonrotating coordinate frame whose z axis is perpendicular to the ecliptic and whose x axis points to a convenient star [Battin, 1987]. 109.3 Categories of Navigation Navigation systems can be categorized as: 1. Absolute navigation systems that measure the state vector without regard to the path traveled by the vehicle in the past. These are of two kinds: • Radio systems (Section 109.5). They consist of a network of transmitters (sometimes also receivers) on the ground or in satellites. A vehicle detects the transmissions and computes its position relative to the known positions of the stations in the navigation coordinate frame. The vehicle’s velocity is measured from the Doppler shift of the transmissions or from a sequence of position measurements. • Celestial systems (Section 109.6). They measure the elevation and azimuth of celestial bodies relative to the land level and North. Electronic star sensors are used in special-purpose high-altitude aircraft and in spacecraft. Manual celestial navigation was practiced at sea for millennia (see Bowditch). 2. Dead-reckoning navigation systems that derive their state vector from a continuous series of measurements beginning at a known initial position. There are two kinds, those that measure vehicle heading and either FIGURE 109.1 Latitude-longitude-altitude coordinate frame. f = geodetic latitude; OP is normal to the ellipsoid at B; l = geodetic longitude; h = BP = altitude above the reference ellipsoid = altitude above mean sea level
RE 109.2 Saturated core ("flux-gate)magnetometer, mounted on a"compass engine"board. The two orthog ng coils(visible)and the drive coil, wound on the toroidal core, measure two components of the magnetic field f the toroid. Courtesy of KVH Industries, Inc. speed or acceleration( Section 109.4)and those that measure emissions from continuous-wave radio stations whose signals create ambiguous"lanes"(Section 109.5) Dead reckoning systems must be reinitialized as errors accumulate and if power is lost. 3. Mapping navigation systems that observe and recognize images of the ground, profiles of altit sequences of turns, or external features( Section 109.7). They compare their observations to a sto database, often on compact disc 109.4 Dead Reckoning The simplest dead-reckoning systems measure vehicle heading and speed, resolve speed into the navigation coordinates, then integrate to obtain position( Fig. 109.3). The oldest heading sensor is the magnetic compass, a magnetized needle or electrically excited toroidal core(called a flux gate), as shown in Fig. 109.2. It measures the direction of the earths magnetic field to an accuracy of 2 degrees at a steady velocity below 60-degrees magnetic latitude. The horizontal component of the magnetic field points toward magnetic north. The angle om true to magnetic north is called magnetic variation and is stored in the computers of modern vehicles as a function of position over the region of anticipated travel [Quinn, 1996]. Magnetic deviations caused by iron in the vehicle can exceed 30 degrees and must be compensated in the navigation computer or, in older ships, by placing compensating magnets near the sensor more complex heading sensor is the gyrocompass, consisting of a spinning wheel whose axle is constrained to the horizontal plane (often by a pendulum). The ships' version points north, when properly compensated for vehicle motion, and exhibits errors less than a degree. The aircraft version(more properly called a directional gyroscope)holds any preset heading relative to earth and drifts at 50 deg/hr or more Inexpensive gyroscopes (some built on silicon chips as vibrating beams with on-chip signal conditioning) are often coupled to magnetic compasses to reduce maneuver-induced errors The simplest speed-sensor is a wheel odometer that generates electrical pulses. Ships use a dynamic-pressure probe or an electric-field sensor that measures the speed of the hull through the conductive water. Aircraft c2000 by CRC Press LLC
© 2000 by CRC Press LLC speed or acceleration (Section 109.4) and those that measure emissions from continuous-wave radio stations whose signals create ambiguous “lanes” (Section 109.5). Dead reckoning systems must be reinitialized as errors accumulate and if power is lost. 3. Mapping navigation systems that observe and recognize images of the ground, profiles of altitude, sequences of turns, or external features (Section 109.7). They compare their observations to a stored database, often on compact disc. 109.4 Dead Reckoning The simplest dead-reckoning systems measure vehicle heading and speed, resolve speed into the navigation coordinates, then integrate to obtain position (Fig. 109.3). The oldest heading sensor is the magnetic compass, a magnetized needle or electrically excited toroidal core (called a flux gate), as shown in Fig. 109.2. It measures the direction of the earth’s magnetic field to an accuracy of 2 degrees at a steady velocity below 60-degrees magnetic latitude. The horizontal component of the magnetic field points toward magnetic north. The angle from true to magnetic north is called magnetic variation and is stored in the computers of modern vehicles as a function of position over the region of anticipated travel [Quinn, 1996]. Magnetic deviations caused by iron in the vehicle can exceed 30 degrees and must be compensated in the navigation computer or, in older ships, by placing compensating magnets near the sensor. A more complex heading sensor is the gyrocompass, consisting of a spinning wheel whose axle is constrained to the horizontal plane (often by a pendulum). The ships’ version points north, when properly compensated for vehicle motion, and exhibits errors less than a degree. The aircraft version (more properly called a directional gyroscope) holds any preset heading relative to earth and drifts at 50 deg/hr or more. Inexpensive gyroscopes (some built on silicon chips as vibrating beams with on-chip signal conditioning) are often coupled to magnetic compasses to reduce maneuver-induced errors. The simplest speed-sensor is a wheel odometer that generates electrical pulses. Ships use a dynamic-pressure probe or an electric-field sensor that measures the speed of the hull through the conductive water. Aircraft FIGURE 109.2 Saturated core (“flux-gate”) magnetometer, mounted on a “compass engine” board. The two orthogonal sensing coils (visible) and the drive coil, wound on the toroidal core, measure two components of the magnetic field in the plane of the toroid. (Courtesy of KVH Industries, Inc.)
speed or Waterspeed Vector Distance Travelled along x-Axis FIGURE 109.3 Geometry of dead reckoning measure the dynamic pressure of the air stream from which they derive airspeed in an air-data computer. The velocity of the wind or sea current must be vectorially added to that of the vehicle, as measured by a dynami pressure sensor(Fig. 1093). Hence, unpredicted wind or current will introduce an error into the dead-reckoning computation. Most sensors are insensitive to the component of airspeed or waterspeed normal to their axis (leeway in a ship, drift in an aircraft). A Doppler radar measures the frequency shift in radar returns from the round or water below the aircraft, from which speed is inferred. A Doppler sonar measures a ship's speed relative to the water layer or ocean floor from which the beam reflects Multibeam Doppler radars or sonars can measure all the components of the vehicles velocity Doppler radars are widely used on military helicopters he most complex dead-reckoning system is an inertial navigator in which accelerometers measure the vehicle's acceleration while gyroscopes measure the orientation of the accelerometers. An on-board computer resolves the accelerations into navigation coordinates and integrates them to obtain velocity and position. The gyroscopes and accelerometers are mounted in either of two ways: servoed gimbals that angularly isolate them from rotations of the vehicle. 2. Fastened directly to the vehicle(strap-down"), whereupon the sensors are exposed to the maximum angular rates and accelerations of the vehicle( Fig. 109.4) Inertial-quality gyroscopes measure vehicle orientation within 0.1 degree for steering and pointing. Most accelerometers consist of a gram-sized proof-mass mounted on flexure pivots. The newest accelerometers, not yet of inertial grade, are etched into silicon chips. Older gyroscopes contained metal wheels rotating in ball bearings or gas bearings. The newest gyroscopes are evacuated cavities or optical fibers in which counter- tating laser beams are compared in phase to measure the sensor s angular velocity relative to inertial space about an axis normal to the plane of the beams. Vibrating hemispheres and rotating vibrating tines are the basis of some navigation-quality gyroscopes(drift rates less than 0. 1 deg/h) Fault-tolerant configurations of cleverly oriented redundant gyroscopes and accelerometers( typically four to six) detect and correct sensor failures. Inertial navigators are used aboard naval ships, in airliners, in most military fixed-wing aircraft, in space boosters and entry vehicles, in manned spacecraft, in tanks, and on large mobile artillery piece e 2000 by CRC Press LLC
© 2000 by CRC Press LLC measure the dynamic pressure of the air stream from which they derive airspeed in an air-data computer. The velocity of the wind or sea current must be vectorially added to that of the vehicle, as measured by a dynamicpressure sensor (Fig. 109.3). Hence, unpredicted wind or current will introduce an error into the dead-reckoning computation. Most sensors are insensitive to the component of airspeed or waterspeed normal to their axis (leeway in a ship, drift in an aircraft). A Doppler radar measures the frequency shift in radar returns from the ground or water below the aircraft, from which speed is inferred. A Doppler sonar measures a ship’s speed relative to the water layer or ocean floor from which the beam reflects. Multibeam Doppler radars or sonars can measure all the components of the vehicle’s velocity. Doppler radars are widely used on military helicopters. The most complex dead-reckoning system is an inertial navigator in which accelerometers measure the vehicle’s acceleration while gyroscopes measure the orientation of the accelerometers. An on-board computer resolves the accelerations into navigation coordinates and integrates them to obtain velocity and position. The gyroscopes and accelerometers are mounted in either of two ways: 1. In servoed gimbals that angularly isolate them from rotations of the vehicle. 2. Fastened directly to the vehicle (“strap-down”), whereupon the sensors are exposed to the maximum angular rates and accelerations of the vehicle (Fig. 109.4). Inertial-quality gyroscopes measure vehicle orientation within 0.1 degree for steering and pointing. Most accelerometers consist of a gram-sized proof-mass mounted on flexure pivots. The newest accelerometers, not yet of inertial grade, are etched into silicon chips. Older gyroscopes contained metal wheels rotating in ball bearings or gas bearings. The newest gyroscopes are evacuated cavities or optical fibers in which counterrotating laser beams are compared in phase to measure the sensor’s angular velocity relative to inertial space about an axis normal to the plane of the beams. Vibrating hemispheres and rotating vibrating tines are the basis of some navigation-quality gyroscopes (drift rates less than 0.1 deg/h). Fault-tolerant configurations of cleverly oriented redundant gyroscopes and accelerometers (typically four to six) detect and correct sensor failures. Inertial navigators are used aboard naval ships, in airliners, in most military fixed-wing aircraft, in space boosters and entry vehicles, in manned spacecraft, in tanks, and on large mobile artillery pieces. FIGURE 109.3 Geometry of dead reckoning