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NASA NTRSDate not supplied

Lunar Relay Onboard Navigation Performance and Effects on Lander Descent to Surface

A system of Lunar relay satellites has been proposed to address communication and navigation needs and ensure robustness for the variety of upcoming robotic and human exploration missions to the Moon. The relays are envisioned to estimate self position and time knowledge onboard, allowing the system to provide in-situ navigation services to missions in the Lunar and cis-Lunar environment. The quality and accuracy of those services are highly dependent on the navigation performance of the relay itself. To assess the Lunar relay navigation performance, a series of orbit determination (OD) Monte Carlo (MC) simulations are run using Lunar gravity modeling up to a degree and order of 250 and a variety of onboard clocks and measurement types including weak-signal GNSS, Ground Network (GN) pseudorange (PR) and Doppler, and optical navigation (OpNav) center-finding (CF). The estimated trajectories produced by these Lunar relay MC simulations, along with the associated errors, and transmitted navigation reference signal parameters, are used to evaluate the expected navigation performance of a user on a descent trajectory to the Lunar surface. The scenario features a lander system performing onboard navigation relying on one-way range and Doppler measurements from reference signals emitted by the Lunar relay. This paper can be used as a reference in determining the onboard clock and measurement types necessary to obtain acceptable navigation performance for the Lunar relay, and as a baseline for Lunar lander navigation performance using accurate measurements from a relay reference signal.

Jeffrey L. Small↗
NASA NTRSDate not supplied

Lunar Relay Onboard Navigation Performance and Effects on Lander Descent to Surface

A system of Lunar relay satellites has been proposed to address communication and navigation needs and ensure robustness for the variety of upcoming robotic and human exploration missions to the Moon. The relays are envisioned to estimate self-position and time knowledge onboard, allowing the system to provide in-situ navigation services to missions in the Lunar and cis-Lunar environment. The quality and accuracy of those services are highly dependent on the navigation performance of the relay itself. To assess the Lunar relay navigation performance, a series of orbit determination (OD) Monte Carlo (MC) simulations are run using Lunar gravity modeling up to a degree and order of 250 and a variety of onboard clocks and measurement types including weak-signal GNSS, Ground Network (GN) pseudorange (PR) and Doppler, and optical navigation (OpNav) center-finding (CF). The estimated trajectories produced by these Lunar relay MC simulations, along with the associated errors, and transmitted navigation reference signal parameters, are used to evaluate the expected navigation performance of a user on a descent trajectory to the Lunar surface. The scenario features a lander system performing onboard navigation relying on one-way range and Doppler measurements from reference signals emitted by the Lunar relay. This paper can be used as a reference in determining the onboard clock and measurement types necessary to obtain acceptable navigation performance for the Lunar relay, and as a baseline for Lunar lander navigation performance using accurate measurements from a relay reference signal.

Jeffrey L. Small↗
NASA NTRS1991

Characterization of frequency standard instability by estimation of their covariance matrix

The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.

PatriziaTravella↗
NASA NTRS2007

Compact Microwave Mercury Ion Clock for Space Applications

We review progress in developing a small Hg ion clock for space operation based on breadboard ion-clock physics package where Hg ions are shuttled between a quadrupole and a 16-pole rf trap. With this architecture we have demonstrated short-term stability approx.1-2x10(exp -13) at 1 second, averaging to 10-15 at 1 day. This development shows that H-maser quality stabilities can be produced in a small clock package, comparable in size to an ultra-stable quartz oscillator required or holding 1-2x10(exp -13) at 1 second. We have completed an ion clock physics package designed to withstand vibration of launch and are currently building a approx. 1 kg engineering model for test. We also discuss frequency steering software algorithms that simultaneously measure ion signal size and lamp light output, useful for long term operation and self-optimization of microwave power and return engineering data.

navigation↗
NASA NTRS2000

Timing analysis by model checking

The safety of modern avionics relies on high integrity software that can be verified to meet hard real-time requirements. The limits of verification technology therefore determine acceptable engineering practice. To simplify verification problems, safety-critical systems are commonly implemented under the severe constraints of a cyclic executive, which make design an expensive trial-and-error process highly intolerant of change. Important advances in analysis techniques, such as rate monotonic analysis (RMA), have provided a theoretical and practical basis for easing these onerous restrictions. But RMA and its kindred have two limitations: they apply only to verifying the requirement of schedulability (that tasks meet their deadlines) and they cannot be applied to many common programming paradigms. We address both these limitations by applying model checking, a technique with successful industrial applications in hardware design. Model checking algorithms analyze finite state machines, either by explicit state enumeration or by symbolic manipulation. Since quantitative timing properties involve a potentially unbounded state variable (a clock), our first problem is to construct a finite approximation that is conservative for the properties being analyzed-if the approximation satisfies the properties of interest, so does the infinite model. To reduce the potential for state space explosion we must further optimize this finite model. Experiments with some simple optimizations have yielded a hundred-fold efficiency improvement over published techniques.

Naydich, Dimitri↗
NASA NTRS1977

Time determination for spacecraft users of the Navstar Global Positioning System /GPS/

Global Positioning System (GPS) navigation is performed by time measurements. A description is presented of a two body model of spacecraft motion. Orbit determination is the process of inferring the position, velocity, and clock offset of the user from measurements made of the user motion in the Newtonian coordinate system. To illustrate the effect of clock errors and the accuracy with which the user spacecraft time and orbit may be determined, a low-earth-orbit spacecraft (Seasat) as tracked by six Phase I GPS space vehicles is considered. The obtained results indicate that in the absence of unmodeled dynamic parameter errors clock biases may be determined to the nanosecond level. There is, however, a high correlation between the clock bias and the uncertainty in the gravitational parameter GM, i.e., the product of the universal gravitational constant and the total mass of the earth. It is, therefore, not possible to determine clock bias to better than 25 nanosecond accuracy in the presence of a gravitational error of one part per million.

Grenchik, T. J.↗
NASA NTRS1998

Robust Real-Time Wide-Area Differential GPS Navigation

The present invention provides a method and a device for providing superior differential GPS positioning data. The system includes a group of GPS receiving ground stations covering a wide area of the Earth's surface. Unlike other differential GPS systems wherein the known position of each ground station is used to geometrically compute an ephemeris for each GPS satellite. the present system utilizes real-time computation of satellite orbits based on GPS data received from fixed ground stations through a Kalman-type filter/smoother whose output adjusts a real-time orbital model. ne orbital model produces and outputs orbital corrections allowing satellite ephemerides to be known with considerable greater accuracy than from die GPS system broadcasts. The modeled orbits are propagated ahead in time and differenced with actual pseudorange data to compute clock offsets at rapid intervals to compensate for SA clock dither. The orbital and dock calculations are based on dual frequency GPS data which allow computation of estimated signal delay at each ionospheric point. These delay data are used in real-time to construct and update an ionospheric shell map of total electron content which is output as part of the orbital correction data. thereby allowing single frequency users to estimate ionospheric delay with an accuracy approaching that of dual frequency users.

Yunck, Thomas P.↗
NASA NTRS1982

Fission track studies of xenolithic chondrites - Implications regarding brecciation and metamorphism

Fission tracks in phosphates from one gas-poor chondrite and three gas-rich ones are studied to determine their thermal history and brecciation time scales. Model fission track ages are calculated for given track densities due to Pu-244 and U-238; track densities and uranium measurements for whitlockite are shown, and possible sources of the tracks are mentioned. Details of track density and uranium measurements are discussed for each meteorite separately. Whitlockites from all the meteorites give model fission track ages of 4.4 Gyr assuming a Pu/U ratio at 4.55 Gyr of 0.045. The final brecciation event definitely did not reset the track clock in phosphates of one meteor and probably not in another two. It is concluded that the observed fission track ages date the end of metamorphic cooling in the meteorite parent bodies and support the planetesimal model for the formation of xenolithic chondrites.

Kothari, B. K.↗
NASA NTRS2001

Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog

The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic field. For the large length scales of the Sun, the flow cycle period tends to be very long. The period, however, can be made to be 22 years, provided the buoyancy frequency (stability) is sufficiently small, thus placing the proposed flow near the base of the convection zone where a dynamo is now believed to operate.

Mayr, Hans G.↗
NASA NTRS2002

Interference from the Robledo DSN Transmitters to Central Madrid IMT-2000/UMTS System through Terrain Diffraction at S-Band

This study evaluates the possible interference from DSN Robledo 70-m transmitter with Madrid IMT-2000/UMTS wireless users in Spain as both systems will share the same frequency band. Using the effective earth radius, the 50 km terrain profile between Robledo and Madrid is modified and reconstructed. The diffraction propagation losses due to mountain peaks are calculated for the receivers in Madrid urban area. The mountains along the path are simplified into a rounded knife-edge and a rounded obstacle. The results show that for a near surface receiver (1.5 m above the ground) in Madrid, interference signal powers received are less than -135 dBm, which is far below the -109 dBm, the IMT-2000 wireless phone threshold. When a receiver is located at about 40 m above the ground (e.g., the top of Clock Tower of Cibeles Palace), diffraction will generate interference power less than -115 dBm. We find that our calculation results are basically consistent with those from the Longley-Rice model, while the latter has smaller loss because of the low resolution terrain profile used. As a comparison, we also find that the measurements of interference powers of -121.2 dBm at the top of Clock tower is in the range of the estimation. We conclude that the interference through the diffraction mechanism will not cause any problem to IMT-2000/UMTS users at near the surface of Madrid urban area.

telecommunications↗
NASA NTRS1988

Optical communication with semiconductor laser diodes

Slot timing recovery in a direct detection optical PPM communication system can be achieved by processing the photodetector waveform with a nonlinear device whose output forms the input to a phase lock group. The choice of a simple transition detector as the nonlinearity is shown to give satisfactory synchronization performance. The rms phase error of the recovered slot clock and the effect of slot timing jitter on the bit error probability were directly measured. The experimental system consisted of an AlGaAs laser diode (lambda = 834 nm) and a silicon avalanche photodiode (APD) photodetector and used Q=4 PPM signaling operated at a source data rate of 25 megabits/second. The mathematical model developed to characterize system performance is shown to be in good agreement with actual performance measurements. The use of the recovered slot clock in the receiver resulted in no degradation in receiver sensitivity compared to a system with perfect slot timing. The system achieved a bit error probability of 10 to the minus 6 power at received signal energies corresponding to an average of less than 60 detected photons per information bit.

Davidson, F.↗
NASA NTRS1980

Geodetic positioning using a global positioning system of satellites

Geodetic positioning using range, integrated Doppler, and interferometric observations from a constellation of twenty-four Global Positioning System satellites is analyzed. A summary of the proposals for geodetic positioning and baseline determination is given which includes a description of measurement techniques and comments on rank deficiency and error sources. An analysis of variance comparison of range, Doppler, and interferometric time delay to determine their relative geometric strength for baseline determination is included. An analytic examination to the effect of a priori constraints on positioning using simultaneous observations from two stations is presented. Dynamic point positioning and baseline determination using range and Doppler is examined in detail. Models for the error sources influencing dynamic positioning are developed. Included is a discussion of atomic clock stability, and range and Doppler observation error statistics based on random correlated atomic clock error are derived.

Fell, P. J.↗
NASA NTRS1989

Vector performance analysis of three supercomputers - Cray-2, Cray Y-MP, and ETA10-Q

Results are presented of a series of experiments to study the single-processor performance of three supercomputers: Cray-2, Cray Y-MP, and ETA10-Q. The main object of this study is to determine the impact of certain architectural features on the performance of modern supercomputers. Features such as clock period, memory links, memory organization, multiple functional units, and chaining are considered. A simple performance model is used to examine the impact of these features on the performance of a set of basic operations. The results of implementing this set on these machines for three vector lengths and three memory strides are presented and compared. For unit stride operations, the Cray Y-MP outperformed the Cray-2 by as much as three times and the ETA10-Q by as much as four times for these operations. Moreover, unlike the Cray-2 and ETA10-Q, even-numbered strides do not cause a major performance degradation on the Cray Y-MP. Two numerical algorithms are also used for comparison. For three problem sizes of both algorithms, the Cray Y-MP outperformed the Cray-2 by 43 percent to 68 percent and the ETA10-Q by four to eight times.

Fatoohi, Rod A.↗
NASA NTRS1990

The Navstar GPS master control station's Kalman filter experience

The Navstar Global Positioning System (GPS) is a highly accurate space based navigation system providing all weather, 24 hour a day service to both military and civilian users. The system provides a Gaussian position solution with four satellites, each providing its ephemeris and clock offset with respect to GPS time. The GPS Master Clock Station (MCS) is charged with tracking each Navstar spacecraft and precisely defining the ephemeris and clock parameters for upload into the vehicle's navigation message. Briefly described here are the Navstar system and the Kalman filter estimation process used by MCS to determine, predict, and ensure quality control for each of the satellite's ephemeris and clock states. Routine performance is shown. Kalman filter reaction and response is discussed for anomalous clock behavior and trajectory perturbations. Particular attention is given to MCS efforts to improve orbital adjust modeling. The satellite out of service time due to orbital maneuvering has been reduced in the past year from four days to under twelve hours. The planning, reference trajectory model, and Kalman filter management improvements are explained.

Scardera, Michael P.↗
NASA NTRS2004

Position-Finding Instrument Built Around a Magnetometer

A coarse-positioning instrument is built around a three-axis magnetometer. The magnetometer is of a type that is made of inexpensive hardware and is suitable for use aboard spacecraft orbiting no more than 1,000 km above the surface of the Earth. A data processor programmed with suitable software and equipped with a central processing unit, random-access memory, programmable read-only memory, and interface circuitry for communication with external equipment are added to the basic magnetometer to convert it into a coarse-positioning instrument. Although the instrument was conceived for use aboard spacecraft, it could be useful for navigation on Earth under some circumstances. A major feature of the proposed instrument is an ability to generate a coarse estimate of its position in real time (that is, without start-up delay). Algorithms needed to solve the position equations have been developed. These include algorithms to work around gaps in measurement data that arise from a singularity near the minimum in the magnetic field of the Earth. Some work has been done to develop a prototype of this instrument incorporating a standard three-axis flux-gate magnetometer and a Pentium P-5 (or equivalent) processor with a clock frequency of 120 MHz. Alternatively, the processor could be of the 486 class. A computer model of the instrument has been completed and tested.

Ketchum, Eleanor↗
NASA NTRS1994

Improved modeling of GPS selective availability

Selective Availability (SA) represents the dominant error source for stand-alone users of the Global Positioning System (GPS). Even for DGPS, SA mandates the update rate required for a desired level of accuracy in realtime applications. As was witnessed in the recent literature, the ability to model this error source is crucial to the proper evaluation of GPS-based systems. A variety of SA models were proposed to date; however, each has its own shortcomings. Most of these models were based on limited data sets or data which were corrupted by additional error sources. A comprehensive treatment of the problem is presented. The phenomenon of SA is discussed and a technique is presented whereby both clock and orbit components of SA are identifiable. Extensive SA data sets collected from Block 2 satellites are presented. System Identification theory then is used to derive a robust model of SA from the data. This theory also allows for the statistical analysis of SA. The stationarity of SA over time and across different satellites is analyzed and its impact on the modeling problem is discussed.

Braasch, Michael S.↗
NASA NTRS1991

Jitter model and signal processing techniques for pulse width modulation optical recording

A jitter model and signal processing techniques are discussed for data recovery in Pulse Width Modulation (PWM) optical recording. In PWM, information is stored through modulating sizes of sequential marks alternating in magnetic polarization or in material structure. Jitter, defined as the deviation from the original mark size in the time domain, will result in error detection if it is excessively large. A new approach is taken in data recovery by first using a high speed counter clock to convert time marks to amplitude marks, and signal processing techniques are used to minimize jitter according to the jitter model. The signal processing techniques include motor speed and intersymbol interference equalization, differential and additive detection, and differential and additive modulation.

Liu, Max M.-K.↗
NASA NTRS2014

A Self-Stabilizing Hybrid-Fault Tolerant Synchronization Protocol

In this report we present a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. Our solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. Our solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. We also present a mechanical verification of a proposed protocol. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period. We believe that our proposed solution solves the general case of the clock synchronization problem.

Malekpour, Mahyar R.↗