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Tracking geometry and dynamics of lunar satellite, estimating orbital elements and lunar gravitational field parameters through earth based range and range rate observations
The Initial Orbit Determination (IOD) problem has been tacked since Laplace, Euler and Gauss in the service of determining the orbits of planets, asteroids, and comets. The measurements that established the orbit characteristics were angles over long arcs.1 The Space Age brought two new measurement types to bear: range and range-rate.2, 3 Initially these measurements were provided by radars through skin-tracking. Soon, however, transponders allowed better measurement accuracy and availability. To date, there are three types of IOD problems: angles only, range and angles, and range and range-rate. The Orion program exposed the need for an additional capability in the case of an extended loss of communication: when the measurements included antenna angles (azimuth and elevation or right-ascension and declination), range and range-rate. This paper contains the details of this new methodology. We will begin with state determination with range, range-rate and angle measurements. First the state estimate, given a sequence of these four time-synchronized measurements, will be analytically developed. Next the covariance matrix associated with this state estimate will be analytically developed. Finally, these will be verified by Monte Carlo simulations.
Satellite antenna rotation causing range-rate error in two-way Doppler tracking systems
The design, fabrication, and performance characteristics are described of two digital data signal enhancement filters which are capable of being inserted between the Space Shuttle Navigation Sensor outputs and the guidance computer. Commonality of interfaces has been stressed so that the filters may be evaluated through operation with simulated sensors or with actual prototype sensor hardware. The filters will provide both a smoothed range and range rate output. Different conceptual approaches are utilized for each filter. The first filter is based on a combination low pass nonrecursive filter and a cascaded simple average smoother for range and range rate, respectively. Filter number two is a tracking filter which is capable of following transient data of the type encountered during burn periods. A test simulator was also designed which generates typical shuttle navigation sensor data.
A method for finding solutions to complex trajectory optimization problems with detailed hardware and launch vehicle constraints is presented. The trajectory optimization problem is formulated as a constrained function minimization problem by modeling the control by a function of a finite number of parameters. Although any parametric control model may be selected, the natural choice of parameters is the actual parameters of the parametric guidance equations flown on the flight digital computer. A variation of the method of multipliers is presented for performing the constrained function minimization. A functional is proposed that allows incorporation of state variable inequality constraints. Finally, optimization of the HEAO-A direct-ascent trajectory is discussed. The HEAO-A mission demonstrates profile optimization to meet range safety, tracking, heating, structural integrity, and attitude rate constraints.
The availability of a coherent C-Band transponder on an orbiting vehicle has permitted the development of calibration techniques for C-Band radars. Prior coherent tracking was limited to test vehicles in powered flight or skin tracking of orbiting spacecraft. The pulse Doppler range rate data available concurrently and independently with normal range and angle data provides an extremely useful data set for assessing the internal consistency of the radars measurements, particularly when coupled with a trajectory well constrained by orbit dynamics. In order to further assess the precision of the range rate data, a technique was developed to numerically integrate the rate measurements into a pseudo-range data set showing extremely low noise and high sensitivity to systematic radar errors. Evaluation of integrated range data led to improvements in calibration of both the rate and conventional range data. In particular, proper evaluation of the very sensitive integrated ranges required the development of a processing correction for beacon delay variation with signal strength, a significant error in the conventional ranging data.
The results of the numerical tests performed in evaluating the interplanetary monitoring platform-16 orbit determination system are presented. The system is capable of performing orbit determination from satellite to satellite tracking data in applications technology satellite range and range rate format. The estimation scheme used is a Kalman filter, sequential (recursive) estimator. Descriptions of the tests performed and tabulations of the numerical results are included.
A new technique is proposed for an internal calibration of a two-layer detector assembly. Spatially coincident pairs of conical tracks on one surface and overetched tracks on the adjacent surface are selected for measurement. Both the etch rate ratio and the particle range can be obtained from the minor and major diameters of the elliptical track and the radii of the circular tracks for two etching steps. This technique was applied to CR-39 detectors exposed to fast neutrons and those flown on a high altitude balloon in order to evaluate the proton response. An improvement by using multi-step etching was also carried out. It was found that not only a single set of the etch rate ratio and the range but also the response curve could be estimated in an extended region by analyzing combined growth curves.
A tracking system error analysis computer program is reported to study the feasibility of using range sum and range-rate sum measurements through a synchronous satellite to a user satellite, and range sum and range-rate sum measurements through a synchronous satellite to a ground based transponder for tracking of synchronous satellites. Error analysis transformed noise, bias, ground station location and orbit uncertainties into expected uncertainties in each of the orbits after tracking. Results show that both of the proposed measurement methods are feasible for determining and refining the orbits of future synchronous satellites.
The highly successful 24 hour trilateration tracking and orbit determination test conducted on 3 November 1974 is described. In this test a new method of accurately computing geostationary spacecraft orbits was applied to the Applications Technology Satellite (ats-6). A single tracking station interrogates several strategically deployed ground based transponders via the synchronous satellite whose orbit is to be determined. The ATS-6 tracking data measurement noise over the 24 hour period was observed to be 0.3 mm/sec in range rate and 1.5 meters in range. By means of overlap orbit computation using 2 separate tracking data bases, the ATS-6 total position and velocity uncertainties were determined to reach a minimum of 30 meters and 0.2 cm/sec respectively. The maximum position and velocity uncertainty over this same time period was determined to be approximately 250 meters and 2 cm/sec respectively. A position determination using simultaneous tracking of the NASA-GSFC site by ATS-6 and ATS-3 was also performed. Station location recovery was to an accuracy on the order of 100 meters over the first 10 hours of tracking.
A three-dimensional (3D) Ultra-Wideband (UWB) Time-of-Arrival (TOA) tracking system has been studied at NASA Johnson Space Center (JSC) to provide the tracking capability inside the International Space Station (ISS) modules for various applications. One of applications is to locate and report the location where crew experienced possible high level of carbon-dioxide (CO2) and felt upset. Recent findings indicate that frequent, short-term crew exposure to elevated CO2 levels combined with other physiological impacts of microgravity may lead to a number of detrimental effects, including loss of vision. To evaluate the risks associated with transient elevated CO2 levels and design effective countermeasures, doctors must have access to frequent CO2 measurements in the immediate vicinity of individual crew members along with simultaneous measurements of their location in the space environment. To achieve this goal, a small, low-power, wearable system that integrates an accurate CO2 sensor with an ultra-wideband (UWB) radio capable of real-time location estimation and data communication is proposed. This system would be worn by crew members or mounted on a free-flyer and would automatically gather and transmit sampled sensor data tagged with real-time, high-resolution location information. Under the current proposed effort, a breadboard prototype of such a system has been developed. Although the initial effort is targeted to CO2 monitoring, the concept is applicable to other types of sensors. For the initial effort, a micro-controller is leveraged to integrate a low-power CO2 sensor with a commercially available UWB radio system with ranging capability. In order to accurately locate those places in a multipath intensive environment like ISS modules, it requires a robust real-time location system (RTLS) which can provide the required accuracy and update rate. A 3D UWB TOA tracking system with two-way ranging has been proposed and studied. The designed system will be tested in the Wireless Habitat Testbed which simulates the ISS module environment. This report describes the research and development effort for this prototype integrated UWB tracking and CO2 sensing system. The remainder of the report is organized as follows. In Section II, the TOA tracking methodology is introduced and the 3D tracking algorithm is derived. The simulation results are discussed in Section III. In Section VI, prototype system design and field tests are discussed. Some concluding remarks and future works are presented in Section V.
Geodetic satellite observation systems comparisons
A navigation technology known as LiAISON (Linked Autonomous Interplanetary Satellite Orbit Navigation) has been known to produce very impressive navigation results for scenarios involving two or more cooperative satellites near the Moon, such that at least one satellite must be in an orbit significantly perturbed by the Earth, such as a lunar halo orbit. The two (or more) satellites track each other using satellite-to-satellite range and/or range-rate measurements. These relative measurements yield absolute orbit navigation when one of the satellites is in a lunar halo orbit, or the like. The geometry between a lunar halo orbiter and a GEO satellite continuously changes, which dramatically improves the information content of a satellite-to-satellite tracking signal. The geometrical variations include significant out-of-plane shifts, as well as inplane shifts. Further, the GEO satellite is almost continuously in view of a lunar halo orbiter. High-fidelity simulations demonstrate that LiAISON technology improves the navigation of GEO orbiters by an order of magnitude, relative to standard ground tracking. If a GEO satellite is navigated using LiAISON- only tracking measurements, its position is typically known to better than 10 meters. If LiAISON measurements are combined with simple radiometric ground observations, then the satellite s position is typically known to better than 3 meters, which is substantially better than the current state of GEO navigation. There are two features of LiAISON that are novel and advantageous compared with conventional satellite navigation. First, ordinary satellite-to-satellite tracking data only provides relative navigation of each satellite. The novelty is the placement of one navigation satellite in an orbit that is significantly perturbed by both the Earth and the Moon. A navigation satellite can track other satellites elsewhere in the Earth-Moon system and acquire knowledge about both satellites absolute positions and velocities, as well as relative positions and velocities in space. The second novelty is that ordinarily one requires many satellites in order to achieve full navigation of any given customer s position and velocity over time. With LiAISON navigation, only a single navigation satellite is needed, provided that the satellite is significantly affected by the gravity of the Earth and the Moon. That single satellite can track another satellite elsewhere in the Earth- Moon system and obtain absolute knowledge of both satellites states.
The results of a study on the effect of mutual interference among S-band multiple access (SMA) system users of advanced tracking and data relay satellite system (ATDRSS) are presented. In the ATDRSS era, the SMA system is required to support data rates ranging from 10 kb/s to 3 Mb/s. The system will consist of four advanced tracking and data relay satellites (ATDRS) each supporting up to five telemetry links. All users have 10 MHz bandwidth with their carrier frequency equal to 2.2875 GHz. A hybrid SDMA/CDMA scheme is used to mitigate the effect of the interference among system users. SMA system interference probability is evaluated with CLASS software. User link margin degradation due to mutual interference between two users is evaluated. System interference probability is evaluated for the projected 1996 mission model, a reference mission model, and a modified reference mission model.
It is shown that for satellites in circular Earth orbits with altitudes of 500 kilometers to 1500 kilometers, and for satellites in elliptical orbits with an approximate 4000 kilometer height of perigee, a high degree least squares polynomial (e.g., a 9th or 10th degree in some cases) is required to smooth both range and range rate data for purposes of input to orbit determination programs. In order to circumvent this problem, functions of range and range rate are smoothed with lower degree least squares polynomials (e.g., 3rd and 4th degree) and it is shown that under the above geometric constraints the standard deviation of fit can be reduced to levels commensurate with typical S-band tracking system resolution which is 1 to 2 meters in range and 0.005 meters/second in range rate for a 1 per second data rate. Also shown are the effects of Gaussian random noise, biases, and periodic noise. This analysis includes numerous examples applied to the 44 point data smoothing interval currently used in much of the operational preprocessing at the Goddard Space Flight Center.
In this paper, an analysis and hardware emulation of the tracking loops for a very flexible programmable digital modem (PDM) will be presented. The modem is capable of being programmed for 2, 4, 8, 16-PSK, 16-QAM, MSK, and Offset-QPSK modulation schemes over a range of data rates from 2.34 to 300 Mbps with programmable spectral occupancy from 1.2 to 1.8 times the symbol rate; these operational parameters are executable in burst or continuous mode. All of the critical processing in both the modulator and demodulator is done at baseband with very high-speed digital hardware and memory. Quadrature analog front-ends are used for translation between baseband and the IF center frequency. The modulator is based on a table lookup approach, where precomputed samples are stored in memory and clocked out according to the incoming data pattern. The sample values are predistorted to counteract the effects of the other filtering functions in the link as well as any transmission impairments. The demodulator architecture was adapted from a joint estimator-detector (JED) mathematical analysis. Its structure is applicable to most signalling formats that can be represented in a two-dimensional space. The JED realization uses interdependent, mutually aiding tracking loops with post-detection data feedback. To expedite and provide for more reliable synchronization, initial estimates for these loops are computed in a parallel acquisition processor. The cornerstone of the demodulator realization is the pre-averager received data filter which allows operation over a broad range of data rates without any hardware changes and greatly simplifies the implementation complexity. The emulation results confirmed tracking loop operation over the entire range of operational parameters listed above, as well as the capability of achieving and maintaining synchronization at BER's in excess of 10(exp -1). The emulation results also showed very close agreement with the tracking loop analysis, and validated the resolution apportionment of the various hardware elements in the tracking loops.
The contribution of the Goddard Space Flight Center to the National Geodetic Satellite Program is reported. All of the major types of tracking systems, including those employing optical, electronic, range-and-range-rate, and laser technologies, which were developed and operated by Goddard, are described. The MINITRACK data were used to derive geodetic results. The methods used for the analysis of these data are presented.
Much of the work that the Space Shuttle will perform requires a capability to rendezvous with other orbiting objects. The formulation and design philosophy behind the Space Shuttle Orbiter rendezvous navigation system are the subjects of this paper. The current rendezvous navigation design incorporates a Kalman filter to estimate the relative position and velocity. The filter is augmented with state elements for the estimation of colored measurement noise and acceleration modeling errors. Several measurement types are available to the filter: a manual optical sighting device, an automatic optical tracking instrument, and a rendezvous radar which provides range and range rate measurements as well as the line of sight direction. The filter also includes a technique for detecting highly improbable measurements and excluding them from Kalman processing.