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NASA NTRS1973

Estimates of the moon's geometry using lunar orbiter imagery and Apollo laser altimeter data

Selenographic coordinates for about 6000 lunar points identified on the Lunar Orbiter photographs are tabulated and have been combined with those lunar radii derived from the Apollo 15 laser altimeter data. These coordinates were used to derive that triaxial ellipsoid which best fits the moon's irregular surface. Fits were obtaind for different constraints on both the axial orientations and the displacement of the center of the ellipsoid. The semiaxes for the unconstrained ellipsoid were a = 1737.6 km, b = 1735.6 km, and c = 1735.0 km which correspond to a mean radius of about 1736.1 km. These axes were found to be nearly parallel to the moon's principal axes of inertia, and the origin was displaced about 2.0 km from the moon's center of gravity in a direction away from the earth and to the south of the lunar equator.

Jones, R. L.↗

NASA NTRS1973

Lunar shape via the Apollo laser altimeter.

The laser altimeter data obtained from the Apollo 15 and Apollo 16 missions provide two elevation cross sections of the moon separated by 35 degrees of latitude. The data consist of measurements of the distance from the orbiting Command and Service Module (CSM) to the lunar surface at intervals of about 20 seconds. In order to extract the lunar shape parameters from the data, the position of the CSM must be known. This was accomplished by reducing the data from earth-based radio tracking of the CSM. The most striking result obtained in the studies is the consistency of the center of gravity offset in both the X and Y directions.

Sjogren, W. L.↗

NASA NTRS1973

Detailed geoid computations for GEOS-C altimeter experiment areas

The GEOS-C spacecraft is scheduled to carry onboard a radar altimeter for the purpose of measuring the geoid undulations in oceanic areas. An independently derived geoid map will provide a valuable complement to these experiments. A detailed gravimetric geoid is presented for the Atlantic and northeast Pacific Ocean areas based upon a combination of the Goddard Space Flight Center GEM-6 earth model and surface 1 deg x 1 deg gravity data. As part of this work a number of satellite derived gravity models were evaluated to establish the model which best represented the long wave length features of the geoid in the above mentioned area. Comparisons of the detailed geoid with the astrogeodetic data provided by the National Ocean Survey and dynamically derived tracking station heights indicate that the accuracy of this combined geoid is on the order of 2 meters or better where data was dense and 5 to 7 meters where data was less dense.

Marsh, J. G.↗

NASA NTRS1973

Apollo 17 laser altimeter

The performance and operation of the Apollo 17 laser altimeter after several modifications are discussed. Functions of the instrument include precise altitude measurement of the CSM above the lunar surface, and measurement of broad scale topographic relief around the entire circumference of the moon.

Wollenhaupt, W. R.↗

NASA NTRS1972

Analysis of satellite altimeter signal characteristics and investigation of sea-truth data requirements

Results are presented of analysis of satellite signal characteristics as influenced by ocean surface roughness and an investigation of sea truth data requirements. The first subject treated is that of postflight waveform reconstruction for the Skylab S-193 radar altimeter. Sea state estimation accuracies are derived based on analytical and hybrid computer simulation techniques. An analysis of near-normal incidence, microwave backscattering from the ocean's surface is accomplished in order to obtain the minimum sea truth data necessary for good agreement between theoretical and experimental scattering results. Sea state bias is examined from the point of view of designing an experiment which will lead to a resolution of the problem. A discussion is given of some deficiencies which were found in the theory underlying the Stilwell technique for spectral measurements.

Source record↗

NASA NTRS1974

C-band station coordinate determination for the GEOS-C altimeter calibration area

Dynamical orbital techniques were employed to estimate the center-of-mass station coordinates of six C-band radars located in the designated primary GEOS-C radar altimeter calibration area. This work was performed in support of the planned GEOS-C mission (December, 1974 launch). The sites included Bermuda, Grand Turk, Antigua, Wallops Island (Virginia), and Merritt Island (Florida). Two sites were estimated independently at Wallops Island yielding better than 40 cm relative height recovery, with better than 10 cm and 1 m (relative) recovery for phi and gamma respectively. Error analysis and comparisons with other investigators indicate that better than 2 m relative recovery was achieved at all sites. The data used were exclusively that from the estimated sites and included 18 orbital arcs which were less than two orbital revolutions in length, having successive tracks over the area. The techniques employed here, given their independence of global tracking support, can be effectively employed to improve various geodetic datums by providing very long and accurate baselines. The C-band data taken on GEOS-C should be employed to improve such geodetic datums as the European-1950 using similar techniques.

Krabill, W. B.↗

NASA NTRS1974

A new approach to lightweight radar altimeters

Test results and key principles are given for a radar altimeter designed for meteorological balloons. The instrument, which weighs 160 g and consumes 0.7 W, will fill a gap in meteorological sensing using balloons - an area where pressure altitude was formerly the prevailing reference. The instrument is basically a delay-lock radar utilizing a superregenerative RF stage. Long-term absolute accuracy of plus or minus 10 m and short-term stability of better than 2 m rms were measured at altitudes of 20 km.

Levanon, N.↗

NASA NTRS1974

The S-193 radar altimeter experiment

The Skylab S-193 altimeter experiment utilizes a 10- and 100-ns pulse length, 13.9-GHz earth-pointed radar system to obtain earth-surface backscatter measurements from the Skylab spacecraft. Objectives of the experiment are to obtain precision measurements of surface profile for uses in geodesy, oceanography, and earth physics, and to measure radar-signal characteristics from an earth-orbit geometry to provide design information for future radar remote-sensors. The technical approach is that of measuring the power impulse response of the scattering surface. The hardware is designed to operate in five modes: waveform or impulse-response measurement and altitude determination; radar cross-section experiment; signal correlation experiment; 10-nsec pulse-compression evaluation; and nadir-seeker experiment.

Mcgoogan, J. T.↗

NASA NTRS1974

Station coordinates for GEOS-C altimeter calibration and experimentation

Station coordinates are given for the C-band radar GEOS-C altimeter calibration sites at Bermuda, Merritt, Grand Turk, and Wallops Islands. The coordinates were estimated in a multi-arc dynamic solution using GEOS-2 C-band radar and laser ranges with a priori information from the GSFC-1973 station coordinate solution. Comparisons with other solutions suggest a relative uncertainty of a few meters in each coordinate. Data reductions show that station coordinates of this quality can introduce a rapidly changing error into the altitude of a satellite whose orbit is determined from calibration area data alone. In contrast, global tracking constrains the orbit and results in slowly varying satellite position error.

Marsh, J. G.↗

NASA NTRS1974

C-band station coordinate determination for the Geos-C altimeter calibration area

Dynamical orbital techniques were employed to estimate the center-of-mass station coordinates of six C-band radars located in the designated primary Geos-C radar altimeter calibration area. This work was performed in support of the planned Geos-C mission (December 1974 launch). The sites included Bermuda, Grand Turk, Antigua, Wallops Island (Virginia), and Merritt Island (Florida). Two sites were estimated independently at Wallops Island yielding better than 40 cm relative height recovery, with better than 10 cm and 1m (relative) recovery for phi and lambda, respectively. The tracking data used in this analysis were taken during 1969 when the radars tracked the Geos-II transponder. In all, over 120 passes of data were used. Range biases were estimated. Error analysis and comparisons with other investigators indicate that better than 2m (1 sigma) relative recovery has been achieved at all sites.

Klosko, S. M.↗

NASA NTRS1974

Skylab radar altimeter - Short-wavelength perturbations detected in ocean surface profiles

Short-wavelength anomalies in sea surface topography, caused by the gravitational effects of major ocean bottom topographic features, have been detected by the radar altimeter aboard Skylab. Some features, such as deep ocean trenches, seamounts, and escarpments, displace the ocean surface by as much as 15 meters over 100-kilometer wavelengths. This experiment demonstrates the potential of satellite altimetry for determining the ocean geoid and for mapping major features of the ocean bottom.

Leitao, C. D.↗

NASA NTRS1974

Skylab S-193 altimeter experiment performance, results and applications

A description of the Skylab altimeter instrument system along with the appropriate system error model is presented. The data processing flow, orbit computation, and topographic recovery techniques are discussed. Some data analysis results are presented which indicate excellent correlation with underwater topographic features. In addition, results are shown which indicate that the instrument performance was as expected.

Mcgoogan, J. T.↗

NASA NTRS1974

Comment on satellite altimeter data

SKYLAB mission SEASAT-B altimeter observations in combination with surface gravity measurements provide useful data on the marine geoid and expected ocean perturbations from analyses of seamount structures.

Bowin, C.↗

NASA NTRS1976

Some problems concerned with the geodetic use of high precision altimeter data

The definition of the geoid in view of different height systems is discussed. A definition is suggested which makes it possible to take into account the influence of the unknown corrections to the various height systems on the solution of Stokes' problem. A solution to Stokes' problem with an accuracy of 10 cm is derived which allows the inclusion of the results of satellite geodesy. In addition equations are developed for the determination of spherical harmonies using altimeter measurements. The influence of the ellipticity of the reference surface is considered.

Lelgemann, D.↗

NASA NTRS1976

Advanced application flight experiment breadboard pulse compression radar altimeter program

Design, development and performance of the pulse compression radar altimeter is described. The high resolution breadboard system is designed to operate from an aircraft at 10 Kft above the ocean and to accurately measure altitude, sea wave height and sea reflectivity. The minicomputer controlled Ku band system provides six basic variables and an extensive digital recording capability for experimentation purposes. Signal bandwidths of 360 MHz are obtained using a reflective array compression line. Stretch processing is used to achieve 1000:1 pulse compression. The system range command LSB is 0.62 ns or 9.25 cm. A second order altitude tracker, aided by accelerometer inputs is implemented in the system software. During flight tests the system demonstrated an altitude resolution capability of 2.1 cm and sea wave height estimation accuracy of 10%. The altitude measurement performance exceeds that of the Skylab and GEOS-C predecessors by approximately an order of magnitude.

Source record↗

NASA NTRS1977

The spectrum of the geoid from altimeter data

A variety of sources of detailed information has been analyzed to arrive at a geoid power spectrum from global altimeter data. Using the equivalent of only two revolutions of data (mostly from GEOS-3) from all the major oceans, the high frequency geoid power (rms) is estimated (most simply) to be 80.7 n to the minus 1.47th power meters, where n is in cycles/global revolutions. This law is valid for all frequencies above 19 cycles but includes sea state. The (simple) law has more power than predicted by Kaula's rule for the geopotential. However, the data shows significantly less power for frequencies below 100 cycles. A closer approximation to the altimetry accumulates 2.18m (rss) for all frequencies higher than 19 cycles/rev. (including sea state), somewhat less power than predicted by the rule. The data permits up to 1.25 (rms) non-gravitational departures from the high frequency marine geoid.

Wagner, C. A.↗

NASA NTRS1977

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.

Fang, B. T.↗

NASA NTRS1977

SEAHT: A computer program for the use of intersecting arcs of altimeter data for sea surface height refinement

The SEAHT program is designed to process multiple passes of altimeter data with intersecting ground tracks, with the estimation of corrections for orbital errors to each pass such that the data has the best overall agreement at the crossover points. Orbit error for each pass is modeled as a polynomial in time, with optional orders of 0, 1, or 2. One or more passes may be constrained in the adjustment process, thus allowing passes with the best orbits to provide the overall level and orientation of the estimated sea surface heights. Intersections which disagree by more than an input edit level are not used in the error parameter estimation. In the program implementation, passes are grouped into South-North passes and North-South passes, with the North-South passes partitioned out for the estimation of orbit error parameters. Computer core utilization is thus dependent on the number of parameters estimated for the set of South-North arcs, but is independent on the number of North-South passes. Estimated corrections for each pass are applied to the data at its input data rate and an output tape is written which contains the corrected data.

Allen, C. P.↗