Many pertinent developments have occurred since the last revision of this publication in February 1968. This chapter provides a place for subjects of interest that are not discussed in the other chapters. Some of the areas of new geodetic developments are: satellite laser ranging (Chapter VI), lunar laser ranging, very long baseline interferometry, satellite radar altimetry, the NAVSTAR Global Positioning System, satellite-to-satellite tracking, and inertial surveying.
In July 1969, the first men to set foot on the moon performed a number of tasks of scientific importance. Among these tasks was the deployment of a rack structure carrying an array of 100 fused silica retroreflectors designed to return some of the light of a pulsed laser beam to the telescope to which the laser equipment is coupled. These retroreflectors are a part of an Apollo experiment called LURE (Lunar Laser Ranging Experiment). LURE was designed to obtain extremely accurate measurements of the range from known locations on the surface of the earth to the lunar based retroreflectors and enable the improvement of our knowledge of the rotation of the earth and the moon about their center of mass and the moon's libration and motion about the earth.
Observations of extragalactic radio sources such as quasars, can provide the geodetic informa- tion to determine the vector separations between the antennas of two widely separated radio telescopes. The components of the vector are its length and direction. To accomplish this, it is necessary to measure very accurately the difference in the time of arrival, recorded at the two antennas, of a particular wavefront from a given (point) source of radio radiation. The phenomena called interference, in Very Long Baseline lnterferometry (VLBI), is produced by electronically superimposing the recorded signals to produce a resultant disturbance or "interference" pattern. The theoretical expression for the relative phase delay shows it to be a function of the source direction, the antenna locations, the relative clock error between the two sites, the time of day, the model atmosphere employed, the earth's tidal parameters, the radio frequency at which the observation is made, etc. Proper account must also be taken of the earth's rotation. Two of the main limiting factors in the VLBI technique are clock stability and atmospheric variations. A major goal of VLBI is to reduce the uncertainty in intercontinental baselines to the centimeter level.
VLBI derived baselines have already contributed scale information to the development of the DoD World Geodetic System in 1972. Baselines accurate to the centimeter level would function as standards of comparison for future world systems. Other applications of VLBI include the determination of polar motion, variations in the earth's rotation, and the monitoring of motions of the major plates that compose the earth's crust.
The development of orbiting space satellites from which microwave remote sensing of the earth can be achieved has provided a new instrument to the geodesist which measures directly the shape of the geoid in the ocean areas. The satellite altimeter consists of a downward ranging radar which measures the time delay from the transmission to the reception of a pulse of energy. Figure 32. The observed one-way distance from the transmitting antenna to the surface is equal to one-half the product of the time delay and the speed of light. From this distance or height, the local surface effects such as tides, winds and currents are removed to obtain the satellite height (h) above the geoid. Figure 33. With a precise Doppler ephemeris available for the satellite, the radius (Rsat) to the satellite, determined for the time of each observation, along with the radius (RØ) to the ellipsoid are readily at hand. It is then possible to compute the geoid height (N) by subtracting the radius RØ and the satellite height h from Rsat.
FIGURE 32 THE MEASUREMENT OF THE GEOID BY THE SATELLITE ALTIMETER
FIGURE 33 SATELLITE HEIGHT ABOVE THE GEOID
The Skylab spacecraft, launched in 1973, provided the first opportunity for satellite based radar altimetry. It was basically a research mission for which data was obtained for the designing of future altimeters. The GEOS-3 altimeter which incorporates many of the design features that were tested in the Skylab altimeter was launched in 1975 and provided geoid measurements over the water areas of the earth from 65°N to 65°S. The SEASAT altimeter which was a more sophisticated instrument with greater measurement capabilities was launched in June 1978 and added data from 72°N to 72°S.
Scientists, engineers, and planners have been tasked with making comprehensive studies of currently available navigation systems as part of an effort to devise a system capable of meeting the requirements of the United States after 1980. Since the late-1950's both military and civilian agencies have actively and independently pursued the idea of position determination and navigation using satellites. This resulted in the development of several systems with a multitude of specialized equipment responsive to particular mission requirements with varying degrees of accuracy and capabilities. In order to integrate the independent efforts of the military services, the Department of Defense issued a memorandum in 1973 naming the Air Force as the Executive Service for the initial development of a future Defense Navigation Satellite System (DNSS), designated the NAVSTAR Global Positioning System (GPS).
The GPS concept calls for a precise navigation system divided into three segments: space segment, control segment and user equipment segment. The space segment will consist of six orbital planes of satellites at inclinations of 55° in circular orbits at an altitude of 20,200 km. Figure 34. Each plane is to eventually contain three satellites. Each satellite will broadcast signals containing information as to its position. This broadcast will include an orbital ephemeris referenced to the DoD World Geodetic System. The control segment will be the ground stations necessary to track the satellites, monitor the system operation and periodically provide corrections to the navigation and time signals. The user segment will consist of the equipment necessary to convert the satellite signals into useful navigation information. By receiving signals from four satellites, the user, whether stationary or moving, can calculate his precise time, three-dimensional position and, if moving, his three-dimensional velocity. Position determination alone requires analysis of range information from three of the satellites in view. However, since the user's receiver clock will not be synchronized to the satellite clock, time of arrival measurements from four satellites are needed to update the user's clock.
FIGURE 34 GPS SATELLITE CONSTELLATION
When operational, GPS should satisfy the navigational accuracy requirements of many military- type missions on land, sea or in the air. Agencies also have many requirements for accurate geodetic positioning for which GPS will satisfy for years to come. These include establishing and densifying geodetic control, offshore positioning and the geodetic needs of national defense which brings in global requirements. GPS will also provide an excellent facility for determination of the position of other satellites and space vehicles while they are in lower earth orbits. This satellite- to-satellite tracking is discussed next.
A new technique for using artificial satellites for geodetic purposes is being studied and tested. This technique uses satellites to track other satellites. There are a number of variations which may be used for specific purposes such as gravity field investigations and orbit improvement. A high altitude satellite may act as a relay from ground tracking stations to a low altitude satellite. In this way, low altitude satellites may be observed when they are not accessible to ground stations. Figure 35. In this type of tracking, a signal generated by a tracking station is received by the relay satellite and then retransmitted to a lower altitude satellite. This signal is then returned to the ground station by the same path. Two low altitude satellites can track one another obsering mutual orbital variations caused by gravity field irregularities. Several high altitude satellites with accurately known orbits may be used to fix the position of a low altitude satellite. Figure 36. These examples present a few of the possibilities for the application of satellite-to-satellite tracking.
FIGURE 35 SATELLITE-TO-SATELLITE TRACKING (VIA RELAY SATELLITE)
FIGURE 36 SATELLITE-TO-SATELLITE TRACKING (VIA SATELLITE CONSTELLATION)
Satellite-to-satellite tracking data was first collected and analyzed in a high-low configuration between ATS-6 and GEOS-3. The data was studied to evaluate its potential for both orbit and gravitational model refinement. This experiment and others that followed proved this new technique to be an important tool for space geodesy.
Inertial Navigation is the art and science of determining the position and velocity of a vehicle solely by means of sensing that vehicle's accelerations and performing the necessary integrations to determine the position and velocity on a real-time basis. The inertial system is composed of precise accelerometers to sense specific force acting on the vehicle and precise gyros to maintain orientation of the accelerometers in a chosen coordinate frame or to determine the orientation of the accelerometers with respect to that frame. Computation is performed by a small on-board computer and the position and velocity of the vehicle are displayed on a real-time basis. In the two decades that inertial navigation has been used, continued hardware developments have brought a state-of-the-art in which the inertially determined position of the vehicle is sufficiently accurate that inertial techniques can be applied to surveying.
At the heart of the inertial surveyor is the inertial measuring unit which contains three sensitive accelerometers and three precise gyros. The accelerometers are mounted as a mutually orthogonal triad on a platform which is torqued by the gyros to maintain orientation with the local vertical and local north, that is, the three axes are oriented north-east-down. The accelerometers measure the specific force on the vehicle which is the sum of the vehicle's own accelerations and the local gravity vector. The digitized output of the accelerometers are processed in real-time by a digital computer. They are integrated once to give velocity, and integrated again to give distance travelled along each sensitive axis. The system does not yield the latitude, longitude and elevation directly. To the computed distances, which are referenced to inertial space, there must be added the initial position and a conversion to latitude, longitude, and elevation accomplished. Although high quality accelerometers and gyros are used in the system, they are still subject to drift and bias. This will cause a misalignment of the platform and errors in the sensed accelerations, which results in small errors in computed velocities and positions. The currently available inertial surveying systems must stop or hover at frequent intervals. At these times, a Kalman filter process corrects for the difference between the indicated velocity and zero, and calculates normal gravity, elevation, and anomalous gravity, but only at these points where remaining errors in platform alignment are also corrected by the Kalman filter.
It was stated above that the accelerometers sense the sum of the vehicle's acceleration and the local gravity vector and that the vehicle's accelerations are needed for integration into velocity and distance travelled. However, a model of the earth's gravity field is required to remove the accelerations due to gravity. In current systems, a very simplistic model is used in which only the downward gravity component resulting from an ellipsoidal earth is computed. Thus the system cannot correct for deflection of the vertical. Further, these deflections of the vertical result in erroneous platform alignments which may introduce errors as large as 40 cm in the computed positions.
Gravity gradiometers have been suggested as a means of independently determining the components of the gravity vector on a real-time basis. A gravity gradient is simply the spatial derivative of the gravity vector. The gradient can be thought of as the rate of change of a component of the gravity vector as measured over a small distance. Hence, the gradient can be measured by determining the difference in gravity at two close but distinct points. This principle is embodied in several recent moving-base instruments. The gravity gradient at a point is a tensor, since it is the derivative of each component of the gravity vector taken in each sensitive axis. Thus, the value of any component of the gravity vector can be known all along the path of the vehicle if gravity gradiometers are included in the system and their outputs are integrated by the system computer. In theory, an accurate gravity model will be computed in real-time and a continuous map of normal gravity, elevation, and anomalous gravity will be available.