A critical review of the use of Doppler frequency for range and range rate measurements
Critical review of Dopple frequency use for range and range rate measurements
RADAR TRACKING↗
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Earth-moon mass ratio from Mariner 9 radio tracking data.
The phase-coherent range and Doppler tracking data obtained as a basis for the navigation of the Mariner 9 spacecraft from earth to Mars determine also the earth-moon mass ratio. As the earth revolves about the center of mass of the earth-moon system, a sinusoidal curve is impressed on the range and Doppler tracking data with a frequency equal to the sidereal mean motion of the moon. The mass ratio was determined from range and Doppler data obtained over a period of 15 weeks. The results from the Mariner Mars 1971 data are presented in a table together with previous results obtained in connection with other spacecraft.
Wong, S. K.↗
Laboratory test results of the high speed optical tracking system for the Spaceborne Geodynamic Ranging System
The high speed, high resolution optical tracking system for the Spaceborne Geodynamic Ranging System employs a two-axis gimbaled pointing device that can operate from a Space Shuttle platform and can track multiple retroreflector ground targets with arcsec accuracy. Laboratory tests of the stepping characteristics of the pointing system for various step sizes and directions has shown arcsec repeatability with little wasted motion, overshoot, or ringing. The worst rms tracking jitter was 1 and 2 arcsec in the roll and pitch axes, respectively, at the maximum tracking rate of 2 deg/sec.
Zagwodzki, Thomas W.↗
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.↗
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.↗
Tracking strategies for laser ranging to multiple satellite targets
By the middle of the decade, several new Laser Geodynamic Satellites will be launched to join the current constellation comprised of the laser geodynamic satellite (LAGEOS) (US), Starlette (France), Ajisai (Japan), and Etalon I and II (USSR). The satellites to be launched, LAGEOS II and III (US & Italy), and Stella (France), will be injected into orbits that differ from the existing constellation so that geodetic and gravimetric quantities are sampled to enhance their resolution and accuracy. An examination of various possible tracking strategies adopted by the network of laser tracking stations has revealed that the recovery of precise geodetic parameters can be obtained over shorter intervals than is currently obtainable with the present constellation of satellites. This is particularly important in the planning of mobile laser tracking operations, given a network of permanently operating tracking sites. Through simulations, it is shown that laser tracking of certain satellite passes, pre-selected to provide optimal sky-coverage, provides the means to acquire a sufficient amount of data to allow the recovery of 1 cm station positions.
Robbins, J. W.↗
Examining the Accuracy of Differenced One-Way Doppler Orbit Determination Derived from Range-Only Relay Satellite Tracking
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Ashok Kumar Verma↗
A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms
In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.
Maddalon, Jeffrey M.↗
Orbit Determination of the Lunar Reconnaissance Orbiter: Status After Seven Years
The Lunar Reconnaissance Orbiter (LRO) has been orbiting the Moon since 2009, obtaining unique and foundational datasets important to understanding the evolution of the Moon and the Solar System. The high-resolution data acquired by LRO benefit from precise orbit determination (OD), limiting the need for geolocation and co-registration tasks. The initial position knowledge requirement (50 m) was met with radio tracking from ground stations, after combination with LOLA altimetric crossovers. LRO-specific gravity field solutions were determined and allowed radio-only OD to perform at the level of 20 m, although secular inclination changes required frequent updates. The high-accuracy gravity fields from GRAIL, with <10 km spatial resolution, further improved the radio-only orbit reconstruction quality (<10 m). However, orbit reconstruction is in part limited by the 0.3-0.5 mm/s measurement noise level in S-band tracking. One-way tracking through Laser Ranging can supplement the tracking available for OD with 28-Hz ranges with 20-cm single-shot precision, but is available only on the nearside (the lunar hemisphere facing the Earth due to tidal locking). Here, we report on the status of the OD effort since the beginning of the mission, a period spanning more than seven years. We describe modeling improvements and the use of new measurements. In particular, the LOLA altimetric data give accurate, uniform, and independent information about LRO's orbit, with a different sensitivity and geometry which includes coverage over the lunar farside and is not tied to ground-based assets. With SLDEM2015 (a combination of the LOLA topographic profiles and the Kaguya Terrain Camera stereo images), another use of altimetry is possible for OD. We extend the 'direct altimetry' technique developed for the ICESat mission to perform OD and adjust spacecraft position to minimize discrepancies between LOLA tracks and SLDEM2015. Comparisons with the radio-only orbits are used to evaluate this new tracking type, of interest for the OD of future lunar orbiters carrying a laser altimeter. LROC NAC images also provide independent accuracy estimation, through the repeated views taken of anthropogenic features for instance.
Erwan Mazarico↗
Three-Dimensional Planetary Surface Tracking Based on a Simple Ultra-Wideband Impulse-Radio Infrastructure
Several prototype ultra-wideband (UWB) impulse-radio (IR) tracking systems are currently under development at NASA Johnson Space Center (JSC). These systems are being studied for use in tracking of Lunar/Mars rovers and astronauts during early exploration missions when satellite navigation systems (such as GPS) are not available. To date, the systems that have been designed and tested are intended only for two-dimensional location and tracking, but these designs can all be extended to three-dimensional tracking with only minor modifications and increases in complexity. In this presentation, we will briefly review the design and performance of two of the current 2-D systems: one designed specifically for short-range, extremely high-precision tracking (approximately 1-2 cm resolution) and the other designed specifically for much longer range tracking with less stringent precision requirements (1-2 m resolution). We will then discuss a new multi-purpose system design based on a simple UWB-IR architecture that can be deployed easily on a planetary surface to support arbitrary three-dimensional localization and tracking applications. We will discuss utilization of this system as an infrastructure to provide both short-range and long-range tracking and analyze the localization performance of the system in several different configurations. We will give theoretical performance bounds for some canonical system configurations and compare these performance bounds with both numerical simulations of the system as well as actual experimental system performance evaluations.
Barton, Richard J.↗
Ionosphere total electron measurements as extracted from satellite tracking data
The Goddard Range and Range Rate System (GRARR) determines the range of a spacecraft by measuring the group delay of a modulated wave and the range rate by measuring the Doppler phase shift of the carrier. An analytical technique is presented for obtaining corrections and equivalent total electron content along the vertical, using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using GRARR range, range rate, and angle tracking data from Explorer 41, values of total electron content on the order of 10 to the 17th to 10 to the 18th power (electrons/sq m) were obtained. These values agree with estimates of the total electron content from ionospheric profiles using f sub o F sub 2 predict data.
Murray, C. W., Jr.↗
Real-time tracking of objects for space applications using a laser range scanner
Real-time tracking of multiple targets and three dimensional object features was demonstrated using a laser range scanner. The prototype was immune to ambient illumination and sun interference. Tracking error feedback was simultaneously obtained from individual targets, global predicted target position, and the human operator. A more complete study of calibration parameters and temperature variations on the scanner is needed to determine the exact performance of the sensor. Lissajous patterns used in three-dimensional real-time tracking prove helpful given their high resolution. The photogrammetry-based Advanced Space Vision System (ASVS) is discussed in combination with the laser range scanner.
Blais, F.↗
Charged particle tracks in polymers - No. 3 - Range and energy loss tables
Range and energy loss for ions tabulated from charged particle tracks in polymers
ENERGY LOSS↗
Venus Radar Mapper (VRM): Multimode radar system design
The surface of Venus has remained a relative mystery because of the very dense atmosphere that is opaque to visible radiation and, thus, normal photographic techniques used to explore the other terrestrial objects in the solar system are useless. The atmosphere is, however, almost transparent to radar waves and images of the surface have been produced via Earth-based and orbital radars. The technique of obtaining radar images of a surface is variously called side looking radar, imaging radar, or synthetic aperture radar (SAR). The radar requires a moving platform in which the antenna is side looking. High resolution is obtained in the cross-track or range direction by conventional radar pulse encoding. In the along-track or azimuth direction, the resolution would normally be the antenna beam width, but for the SAR case, a much longer antenna (or much sharper beam) is obtained by moving past a surface target as shown, and then combining the echoes from many pulses, by using the Doppler data, to obtain the images. The radar design of the Venus Radar Mapper (VRM) is discussed. It will acquire global radar imagery and altimetry data of the surface of Venus.
Johnson, William T. K.↗
Analysis of Satellite-to-Satellite Tracking (SST) and altimetry data from GEOS-C
Radar altimetry and satellite-to-satellite (SST) range and range rate tracking measurements were used to infer the exterior gravitational field of the earth and the structure of the geoid from GEOS-C metric data. Under the SST analysis, a direct point-by-point estimate of gravity disturbance by means of a recursive filter with backward smoothing was attempted but had to be forsaken because of poor convergence. The adopted representation consists of a more or less uniform grid of discrete masses at a depth of approximately 400 km from the earth's surface. The layer is superimposed on a spherical harmonics model. The procedure for smoothing the altimetry and inferring the fine-structured gravity field over the Atlantic test area is described. The local disturbances are represented by means of a density layer. The altimeter height biases were first estimated by a least squares adjustment at orbital crossover points. After taking out the bias, long wavelength contributions from GEM-6 as well as a calibration correction were subtracted. The residual heights were then represented by a mass distribution beneath the earth's surface.
Wong, L.↗
Ranging/tracking system for proximity operations
The hardware development and testing phase of a hand held radar for the ranging and tracking for Shuttle proximity operations are considered. The radar is to measure range to a 3 sigma accuracy of 1 m (3.28 ft) to a maximum range of 1850 m (6000 ft) and velocity to a 3 sigma accuracy of 0.03 m/s (0.1 ft/s). Size and weight are similar to hand held radars, frequently seen in use by motorcycle police officers. Meeting these goals for a target in free space was very difficult to obtain in the testing program; however, at a range of approximately 700 m, the 3 sigma range error was found to be 0.96 m. It is felt that much of this error is due to clutter in the test environment. As an example of the velocity accuracy, at a range of 450 m, a 3 sigma velocity error of 0.02 m/s was measured. The principles of the radar and recommended changes to its design are given. Analyses performed in support of the design process, the actual circuit diagrams, and the software listing are included.
Nilsen, P.↗
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.↗
The ATS-F/Nimbus-E Tracking and Data Relay Experiment
Tracking and data relay satellite system performance by ATS and Nimbus spacecraft for range and range rate tracking and command and data transmission
Heffernan, P. J.↗