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Analysis of the ''Range and Range Rate'' Tracking System

The "Range and Range Rate" (r(sub j) + r ̇(sub j)) System in its very simplest form is described. In particular, the errors in position and velocity are treated usingpessimistic values of the measured quantities r(sub j) and r ̇(sub j). Thus, a realistic evaluation of tracking qualities can be made for different orbits over certain tracking stations. The Range and Range Rate System briefly described in this report is a high precision tracking system. Knowledge of the uncertainty in position δ (sub x(sub i) is important, but knowledge of the uncertainty of the velocity vector δ (sub x(sub i) is of the utmost importance. Thus the use of coherent Doppler measurements to determine the velocity has a great advantage over any pulsed system and, in addition, permits extremely narrow frequency bands (in the order of 10 to 100 cps) to be employed, reducing the power requirements considerably. The basis for using range r(sub j) and range rate r ̇(sub j) only is the fact that r(sub j) and r ̇(sub j) can be measured to very high precision, thus furnishing r and r with low errors. The nature of these errors is discussed.

Tracking system

Analysis of the Range and Range Rate Tracking System

The "range and range rate"' (r(sub i) + r(sub i)) system in its very simplest form is described. In particular, the errors in position and velocity are treated using pessimistic values of the measured quantities r(sub i) and r(sub i). Thus, a realistic evaluation of tracking qualities can be made for different orbits over certain tracking stations. The range and range rate system briefly described in this paper is a high-precision tracking system. Knowledge of the uncertainty in position δ(sub xi) is important, but knowledge of the uncertainty of the velocity vector δ(sub xi) is of the utmost importance. Thus the use of coherent Doppler measurements to determine the velocity has a great advantage over any pulsed system and, in addition, permits extremely narrow frequency bandwidths (in the order of 10 to 100 cps) to be employed, reducing the power requirements considerably. The basis for using range r(sub i) and range rate r(sub i) only is the fact that r(sub i) and r(sub i) can be measured to very high precision, thus furnishing r and r with low errors. The nature of these errors is discussed.

Vonbun, F. O.

Frequency stability requirements for two way range rate tracking

Accuracy limitations to two way range rate Doppler tracking due to master (reference) oscillator frequency instabilities are discussed. Theory is developed to treat both the effects of random and nonrandom oscillator instabilities. The nonrandom instabilities treated are drift, environmental effects, and coherent phase modulation. The effects of random instabilities on range rate accuracy are shown to be describable in terms of sigma y (2, T, tau). For the typical noise processes encountered in precision oscillators, range rate error is related to the more familiar sigma y (tau) and script L (f). Three examples are discussed to show how to determine range rate error from given sigma y (tau) or script L (f) curves, and approximations are developed to simplify the treatment of complex systems. An error analysis of range determined from rate data is also given.

Reinhardt, V.

Tropospheric range-rate tracking data correction

A formula for correcting the tropospheric error in range-rate satellite tracking data is given. The formula is based on the method which was used to obtain corrections for elevation-angle and range data. In addition, an improved method is given for calculating some of the parameters required in the correction formulas.

Marini, J. W.

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

Marr, G.

Expected Seasat-A scientific results

The higher accuracy and extended coverage of the SEASAT-A altimeter allows for the determinations of a highly refined geoid, of open ocean currents and circulations, of ocean subsurface topography, and of earth surface topography. The radar altimeter on SEASAT-A is also considered as a tracking station in orbit for range and range rate tracking work.

Hoge, F. E.

GEOS 3 STDN S band Doppler tracking investigation

GEOS 3S Doppler band and laser ranging data, acquired from August 1975 to March 1976 in the spacecraft altimeter calibration area, are examined. An evaluation of two-way and three-way Doppler data, for the positioning of Spaceflight Tracking and Data Network S band stations is presented, as well as the Goddard Space Flight Center laser system that is used to reference the exact position of the Doppler stations. The two-way and three-way Doppler tracking devices, situated at Rosman and Bermuda, have yielded data for the recovery of GEOS 3 arc height with an uncertainty of only 1 m. Attention is given to the effects of beacon signal frequency instability, controlled by a temperature sensitive auxiliary crystal oscillator on board the spacecraft, and to the one-way range rate tracking noise that was found to be within a range of 2 to 10 cm/s. 1- and 2-way passes and their different arc meters are graphed, showing the Doppler tracking interval. It was concluded that other accurate computations and recovery of station coordinates could be performed employing tracking data from S band stations.

Rosenbaum, B.

Utilization of satellite-satellite tracking data for determination of the geocentric gravitational constant (GM)

Range rate tracking of GEOS 3 through the ATS 6 satellite was used, along with ground tracking of GEOS 3, to estimate the geocentric gravitational constant (GM). Using multiple half day arcs, a GM of 398600.52 + or - 0.12 cu km/sq sec was estimated using the GEM 10 gravity model, based on speed of light of 299792.458 km/sec. Tracking station coordinates were simultaneously adjusted, leaving geopotential model error as the dominant error source. Baselines between the adjusted NASA laser sites show better than 15 cm agreement with multiple short arc GEOS 3 solutions.

Martin, C. F.

KU-Band rendezvous radar performance computer simulation model

The preparation of a real time computer simulation model of the KU band rendezvous radar to be integrated into the shuttle mission simulator (SMS), the shuttle engineering simulator (SES), and the shuttle avionics integration laboratory (SAIL) simulator is described. To meet crew training requirements a radar tracking performance model, and a target modeling method were developed. The parent simulation/radar simulation interface requirements, and the method selected to model target scattering properties, including an application of this method to the SPAS spacecraft are described. The radar search and acquisition mode performance model and the radar track mode signal processor model are examined and analyzed. The angle, angle rate, range, and range rate tracking loops are also discussed.

Griffin, J. W.

Gravitational spectra from the tracking of planetary spacecraft in eccentric orbits

Two dimensional gravitational spectra are derived from simple harmonic analysis of range rate tracking data on planetary orbiters. The eccentricity of the orbit is arbitrary and results are shown to vary substantially with the aspect angle of the tracking line of sight with the orbit plane. The development for arbitrary start with stop times (with respect to periapsis) uses modified eccentricity functions evaluated by quadrature. Simulations with a point-masses model of Venus using tracking data on the Pioneer Venus Orbiter show excellent predictions of the average orbiter spectrum over one Venus day. The Venus gravitational signal should be above the tracking noise level for arc lengths longer than 40 deg (in true anomaly) about periapsis and for terms as high as 55th degree. analysis has been made of tracking residuals from a short arc fit to Mariner Mars 9 data over the Hellas Basin (using a complete 6th degree field). Results are most consistent with higher residual gravitational power than predicted from Kaula's rule for Mars.

Wagner, C. A.