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Adaptive Control of a Utility-Scale Wind Turbine Operating in Region 3

Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. The turbulent and unpredictable conditions in which wind turbines operate create many challenges for their operation. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility scale, variable-speed horizontal axis wind turbine. The objective of the adaptive pitch controller in Region 3 is to regulate generator speed and reject step disturbances. The control objective is accomplished by collectively pitching the turbine blades. We use an extension of the Direct Model Reference Adaptive Control (DMRAC) approach to track a reference point and to reject persistent disturbances. The turbine simulation models the Controls Advanced Research Turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility-scale wind turbine which has a well-developed and extensively verified simulator. The adaptive collective pitch controller for Region 3 was compared in simulations with a bas celliansesical Proportional Integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the baseline PI pitch controller and it demonstrated robustness to modeling errors.

Frost, Susan A.↗

On-Orbit Solar Dynamics Observatory (SDO) Star Tracker Warm Pixel Analysis

This paper describes the process of identification and analysis of warm pixels in two autonomous star trackers on the Solar Dynamics Observatory (SDO) mission. A brief description of the mission orbit and attitude regimes is discussed and pertinent star tracker hardware specifications are given. Warm pixels are defined and the Quality Index parameter is introduced, which can be explained qualitatively as a manifestation of a possible warm pixel event. A description of the algorithm used to identify warm pixel candidates is given. Finally, analysis of dumps of on-orbit star tracker charge coupled devices (CCD) images is presented and an operational plan going forward is discussed. SDO, launched on February 11, 2010, is operated from the NASA Goddard Space Flight Center (GSFC). SDO is in a geosynchronous orbit with a 28.5 inclination. The nominal mission attitude points the spacecraft X-axis at the Sun, with the spacecraft Z-axis roughly aligned with the Solar North Pole. The spacecraft Y-axis completes the triad. In attitude, SDO moves approximately 0.04 per hour, mostly about the spacecraft Z-axis. The SDO star trackers, manufactured by Galileo Avionica, project the images of stars in their 16.4deg x 16.4deg fields-of-view onto CCD detectors consisting of 512 x 512 pixels. The trackers autonomously identify the star patterns and provide an attitude estimate. Each unit is able to track up to 9 stars. Additionally, each tracker calculates a parameter called the Quality Index, which is a measure of the quality of the attitude solution. Each pixel in the CCD measures the intensity of light and a warns pixel is defined as having a measurement consistently and significantly higher than the mean background intensity level. A warns pixel should also have lower intensity than a pixel containing a star image and will not move across the field of view as the attitude changes (as would a dim star image). It should be noted that the maximum error introduced in the star tracker attitude solution during suspected warm pixel corruptions is within the specified 36 attitude error budget requirement of [35, 70, 70] arcseconds. Thus, the star trackers provided attitude accuracy within the specification for SDO. The star tracker images are intentionally defocused so each star image is detected in more than one CCD pixel. The position of each star is calculated as an intensity-weighted average of the illuminated pixels. The exact method of finding the positions is proprietary to the tracker manufacturer. When a warm pixel happens to be in the vicinity of a star, it can corrupt the calculation of the position of that particular star, thereby corrupting the estimate of the attitude.

Felikson, Denis↗

Usability Evaluation of Indicators of Energy-Related Problems in Commercial Airline Flight Decks

A series of pilot-in-the-loop flight simulation studies were conducted at NASA Langley Research Center to evaluate indicators aimed at supporting the flight crew’s awareness of problems related to energy states. Indicators were evaluated utilizing state-of-the-art flight deck systems such as on commercial air transport aircraft. This paper presents results for four technologies: (1) conventional primary flight display speed cues, (2) an enhanced airspeed control indicator, (3) a synthetic vision baseline that provides a flight path vector, speed error, and an acceleration cue, and (4) an aural airspeed alert that triggers when current airspeed deviates beyond a specified threshold from the selected airspeed. Full-mission high-fidelity flight simulation studies were conducted using commercial airline crews. Crews were paired by airline for common crew resource management procedures and protocols. Scenarios spanned a range of complex conditions while emulating several causal factors reported in recent accidents involving loss of energy state awareness by pilots. Data collection included questionnaires administered at the completion of flight scenarios, aircraft state data, audio/video recordings of flight crew, eye tracking, pilot control inputs, and researcher observations. Questionnaire response data included subjective measures of workload, situation awareness, complexity, usability, and acceptability. This paper reports relevant findings derived from subjective measures as well as quantitative measures.

Evans, Emory T.↗

Lightning tracking system

A system is described for locating lightning strikes by developing the coordinates of a pair of lines, each of which is produced at a reference sensing station. At each station there are a pair of directional antennas which produce analog signals responsive to a lightning stroke. These analog signals are fed to a pair of integrators which integrate the signals for a predetermined period of time so as to produce the X and Y coordinate of a particular line. The analog signals are also fed through a square rooter, a Schmitt trigger circuit, and flip-flops to produce pulses for starting and stopping the integrators. The system at the remote station is similar to that at the central station and is tied to the circuitry at the central station through logic circuits to minimize the chance of error from spurious signals. Computers, printers, and plotters are utilized to plot the exact location of the lightning stroke.

Wojtasinski, R. J.↗

The impact of ozone field horizontal inhomogeneities on nadir-viewing orbital backscatter UV measurements

Radiative transfer calculations for nadir-viewing satellites normally assume the atmosphere to be horizontally homogeneous. Yet it has been shown recently that horizontal gradients can lead to significant errors in satellite infrared and microwave soundings. We extend the methodology to backscatter ultra-violet observations of ozone, and present a first estimate of the effect s magnitude. The Solar Backscatter Ultra-Violet/2 (SBUV/2) instrument, a pure nadir sounder, serves as our test bed. Our results indicate that in a vast majority of cases the abovementioned errors can be neglected. However, occurrence of higher errors, particularly at wavelengths longer than 300 nm, coincides with some of the most interesting atmospheric phenomena like tropopause folds and the South polar ozone hole. This leads to a seasonal variation of the magnitude of the effect. Due to the mostly zonal geometry of the ozone distribution, there is also the possibility that biases may be introduced, which is particularly critical if the data are to be assimilated or used to determine trends. The results presented are tested for robustness using different model atmospheres. The influence of horizontal inhomogeneities will be even more pronounced for cross-track sounders and limb viewers, and easier to detect once higher resolution atmospheric models are available. This will be investigated in future studies.

Mueller, Martin D.↗

Radiometric Spacecraft Tracking for Deep Space Navigation

Interplanetary spacecraft navigation relies on three types of terrestrial tracking observables.1) Ranging measures the distance between the observing site and the probe. 2) The line-of-sight velocity of the probe is inferred from Doppler-shift by measuring the frequency shift of the received signal with respect to the unshifted frequency. 3) Differential angular coordinates of the probe with respect to natural radio sources are nominally obtained via a differential delay technique of (Delta) DOR (Delta Differential One-way Ranging). The accuracy of spacecraft coordinate determination depends on the measurement uncertainties associated with each of these three techniques. We evaluate the corresponding sources of error and present a detailed error budget.

ranging↗

Precision Oxygen Isotope Measurements of Two C-Rich Hydrated Interplanetary Dust Particles

Introduction: Chondritic-smooth IDPs (Interplanetary Dust Particles) are low porosity objects whose mineralogy is dominated by aqueous alteration products such as Mg-rich phyllosilicates (smectite and serpentine group) and Mg-Fe carbonate minerals. Their hydrated mineralogy combined with low atmospheric entry velocities have been used to infer an origin largely from asteroidal sources. Spectroscopic studies show that the types and abundance of organic matter in CS IDPs is similar to that in CP IDPs. Although CS IDPs show broad similarities to primitive carbonaceous chondrites, only a few particles have been directly linked to specific meteorite groups such as CM and CI chondrites based on the presence of diagnostic minerals. Many CS IDPs however, have carbon contents that greatly exceed that of known meteorite groups suggesting that they either may derive from comets or represent samples of more primitive parent bodies than do meteorites. It is now recognized that many large, dark primitive asteroids in the outer main belt, as well as some trans-Neptunian objects, show spectroscopic evidence for aqueous alteration products on their surfaces. Some CS IDPs exhibit large bulk D enrichments similar to those observed in the cometary CP IDPs. While hydrated minerals in comets have not been unambiguously identified to date, the presence of the smectite group mineral nontronite has been inferred from infrared spectra obtained from the ejecta from comet 9P/Tempel 1 during the Deep Impact mission. Recent observations of low temperature sulfide minerals in Stardust mission samples suggest that limited aqueous activity occurred on comet Wild-2. All of these observations, taken together, suggest that the high-carbon hydrated IDPs are abundant and important samples of primitive solar system objects not represented in meteorite collections. Oxygen isotopic compositions of chondrites reflect mixing between a 16O-rich reservoir and a 17O,18O-rich reservoir produced via mass-independent fractionation. The composition of the 16O-rich reservoir is well constrained but material representing the 17O,18O-rich end-member is rare. Self-shielding models predict that cometary water, presumed to represent this reservoir, should be enriched in 17O and 18O by greater than 200 per mille. The high-carbon hydrated IDPs may be among the best materials available to search for preserved "cometary" H2O signatures. In order to better understand the origin and evolution of these particles, we have obtained 10 hydrated interplanetary dust particles for coordinated mineralogical, isotopic and organic analyses. We have previously reported the results of mineralogical and O isotopic measurements of two hydrated IDPs; here we present results of O isotopic measurements of three additional IDPs. Samples and Methods: Three interplanetary dust particles (L2079C35, L2083D46 and L2083E46) were embedded in S and partially ultramicrotomed into approximately 70 nanometer sections for analysis via transmission electron microscopy (TEM). The remainders of the unsliced particles were removed from S and pressed into high purity Au foil that was cleaned with HF acid and annealed at 800 degrees Centigrade. The pressed IDPs were analyzed via electron microprobe analysis (EPMA) for quantitative bulk chemical analysis. After EPMA analysis, the IDPs were subjected to precision O isotope analysis with the UCLA Cameca IMS-1270 ion probe. A 20 kiloelectronvolt, 0.5 nanoangstrom Cs+ primary beam of approximately 15 micrometers diameter was used for each measurement. Small particles of San Carlos olivine and Burma spinel were pressed into the Au foil for use as standards to correct for instrumental mass fractionation. The detection system was configured for multicollection, with 16O measured on a Faraday cup, and 17O and 18O measured on electron multipliers (EMs). Individual analyses consisted of 15 cycles of 10 seconds per cycle. Additionally, two microtome thin sections were measured for H isotopic compositions with the JSC NanoSIMS 50L ion probe. An 8 picoangstrom, 16 kiloelectronvolt Cs plus primary beam was used. Measurements consisted of H, C, 12C, 16O, and 18O collected with EMs in multicollection. Terrestrial biotite and kerogen were used for isotopic standards. A significant challenge in O isotope measurement of hydrated minerals is the interference from 16OH at mass 17O. We ensured that the 17O and 16OH peaks were fully resolved by using a mass resolution of greater than 7000 and by careful analyses of San Carlos olivine, Burma spinel and chlorite hydrated mineral standards. The hydride was further suppressed with a cold finger attached to an LN2 dewar to trap volatiles in the sample chamber. All sputtered ions were counted (i.e. presputtering was not used); after applying background, yield and deadtime corrections, we performed a change-point analysis on our data via R in order to determine when the sample reached sputtering equilibrium; data points collected prior to the change point were excluded. Change-point analysis was also used to determine whether the IDP had completely sputtered. Results: Mineralogy. IDPs C35 and E46 exhibited hydrated mineralogies, Fe-Ni sulfide grains, nanoglobules and occasional enstatite grains distributed throughout a fine-grained Mg-Fe saponite matrix. C35 also contained breunnerite (Mg,Fe)CO3; solar flare tracks were observed in enstatite, indicating minimal atmospheric entry heating. The mineralogy of D46 is dominated by a large FeS grain with a minor component of adhering silicate material. D46 was strongly heated during atmorpheric entry as evidenced by a well-developed magnetite rim. EPMA analyses show that both C35 and E46 have high carbon contents of 20 weight percentage (approximately 6X CI). D46 contains approximately 6 wt.weight percentage C. A significant amount of the carbon is present as carbon nanoglobules. Results: Hydrogen isotopes: Although the bulk delta D values of both sections of L2079C35 were within error of SMOW (minus 33 plus or minus 19 per mille, 1 plus or minus 14 per mille 1 sigma), several delta D-rich hotspots were also identified, reaching 2000 per mille. As shown in Fig. 1, these hotspots are clearly associated with discrete carbonaceous inclusions that are akin to nanoglobules found in many meteorites and other IDPs. Oxygen Isotopes. Results of the oxygen isotope measurements are shown in Figure 1. The oxygen isotope composition for L2079C35 was delta 18O equals plus11.6 plus or minus 1.9per mille, delta 17O equals plus 7.9 plus or minus 1.9per mille (2 standard errors). The oxygen isotope composition for L2083D46 was delta 18O equals minus 8.1 plus or minus 1.9 per mille, delta 17O equals minus 6.4 plus or minus 3.1 per mille (2 standard errors). The oxygen isotope composition for L2083E46 was delta 18O equals plus 12.0 plus or minus 1.9 per mille, delta 17O equals plus 9.2 plus or minus 2.0 per mille (2 standard errors). Discussion: Despite mineralogical similarities to highly aqueously altered carbonaceous chondrites, the hydrated IDPs we analyzed have oxygen isotopic compositions that are distinct from matrix materials in the CI, CM, and CR chondrites. The IDPs plot along the Young-Russell line, with delta 17O values for C35 and E46 suggestive of interaction with a 16O-poor reservoir. However, we have thus far not observed evidence of extreme 16O-poor reservoirs expected from self-shielding models and observed in Acfer 094 simplectite. The high carbon contents of the IDPs also set them apart from known meteoritic samples. The lack of atmospheric entry heating effects are consistent with low encounter velocities and suggest either an asteroidal source, or a low inclination, low eccentricity cometary origin. Conclusions: The unusual oxygen isotopic compositions, high carbon contents, and the abundance of Drich nanoglobules, together, suggest that the high-carbon, hydrated IDPs are derived from a primitive source that is not yet represented in meteorite collections.

Snead, C. J.↗

Does Commercial Space Really Need MOA?

The Mission Operations Assurance (MOA) discipline actively participates as a project member to achieve their common objective of full mission success while also providing an independent risk assessment to the Project Manager. The cornerstone element of MOA is the independent assessment of the risks the project faces in executing its mission. Especially as the project approaches critical mission events, it becomes imperative to clearly identify and assess the risks the project faces. This has been the paradigm for robotic space exploration missions, but does the same apply to commercial space operations? This is the question which is the driver for this year's MOA track at the 18th Annual Improving Space Operations workshop in April at the Jet Propulsion Laboratory, and the question we examine in this paper. Corollaries to this driving question are why shouldn't MOA apply and are there factors beyond mission success with acceptable risk which apply to commercial space operations that are not present in government scientific missions? To address these questions, areas we focus on include risk (both mission and profit) management for commercial space operations and the practical extension of robotic mission MOA to commercial space operations. Another key area to look at is command file errors which are a major concern for deep space robotic missions, but can we worry about them less with manned missions or unmanned supply mission? Further, with the growing concern about space debris, we delve into the role of MOA relative to End-of-Mission activities. This paper examines these topics and in particular the perspectives presented at the workshop to begin charting the appropriate course for MOA in the emerging sector of Commercial Space Operations.

commercial space↗

Three methods of presenting flight vector information in a head-up display during simulated STOL approaches

A simulator study was conducted to determine the usefulness of adding flight path vector symbology to a head-up display designed to improve glide-slope tracking performance during steep 7.5 deg visual approaches in STOL aircraft. All displays included a fixed attitude symbol, a pitch- and roll-stabilized horizon bar, and a glide-slope reference bar parallel to and 7.5 deg below the horizon bar. The displays differed with respect to the flight-path marker (FPM) symbol: display 1 had no FPM symbol; display 2 had an air-referenced FPM, and display 3 had a ground-referenced FPM. No differences between displays 1 and 2 were found on any of the performance measures. Display 3 was found to decrease height error in the early part of the approach and to reduce descent rate variation over the entire approach. Two measures of workload did not indicate any differences between the displays.

Dwyer, J. H., III↗

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

Tang, C. C. H.↗

Analysis of error in TOMS total ozone as a function of orbit and attitude parameters

Computer simulations of orbital scenarios were performed to examine the effects of orbital altitude, equator crossing time, attitude uncertainty, and orbital eccentricity on ozone observations by future satellites. These effects were assessed by determining changes in solar and viewing geometry and earth daytime coverage loss. The importance of these changes on ozone retrieval was determined by simulating uncertainties in the TOMS ozone retrieval algorithm. The major findings are as follows: (1) Drift of equator crossing time from local noon would have the largest effect on the quality of ozone derived from TOMS. The most significant effect of this drift is the loss of earth daytime coverage in the winter hemisphere. The loss in coverage increases from 1 degree latitude for + or - 1 hour from noon, 6 degrees for + or - 3 hours from noon, to 53 degrees for + or - 6 hours from noon. An additional effect is the increase in ozone retrieval errors due to high solar zenith angles. (2) To maintain contiguous earth coverage, the maximum scan angle of the sensor must be increased with decreasing orbital altitude. The maximum scan angle required for full coverage at the equator varies from 60 degrees at 600 km altitude to 45 degrees at 1200 km. This produces an increase in spacecraft zenith angle, theta, which decreases the ozone retrieval accuracy. The range in theta was approximately 72 degrees for 600 km to approximately 57 degrees at 1200 km. (3) The effect of elliptical orbits is to create gaps in coverage along the subsatellite track. An elliptical orbit with a 200 km perigee and 1200 km apogee produced a maximum earth coverage gap of about 45 km at the perigee at nadir. (4) An attitude uncertainty of 0.1 degree in each axis (pitch, roll, yaw) produced a maximum scan angle to view the pole, and maximum solar zenith angle).

Gregg, W. W.↗

The short-term prediction of universal time and length of day using atmospheric angular momentum

The ability to predict short-term variations in the Earth's rotation has gained importance in recent years owing to more precise spacecraft tracking requirements. Universal time (UT1), that component of the Earth's orientation corresponding to the rotation angle, can be measured by number of high-precision space geodetic techniques. A Kalman filter developed at the Jet Propulsion Laboratory (JPL) optimally combines these different data sets and generates a smoothed times series and a set of predictions for UT1, as well as for additional Earth orientation components. These UT1 predictions utilize an empirically derived random walk stochastic model for the length of the day (LOD) and require frequent and up-to-date measurements of either UT1 or LOD to keep errors from quickly accumulating. Recent studies have shown that LOD variations are correlated with changes in the Earth's axial atmospheric angular momentum (AAM) over timescales of several years down to as little as 8 days. AAM estimates and forecasts out to 10 days are routinely available from meteorological analysis centers; these data can supplement geodetic measurements to improve the short-term prediction of LOD and have therefore been incorporated as independent data types in the JPL Kalman filter. We find that AAM and, to a lesser extent, AAM forecast data are extremely helpful in generating accurate near-real-time estimates of UT1 and LOD and in improving short-term predictions of these quantities out to about 10 days.

Freedman, A. P.↗

Rotational Energy Transfer Cross Sections in N2-N2 Collisions

Rotational inelastic transitions of N2 have been studied in the coupled state (CS, also called centrifugal sudden) and infinite-order-sudden (IOS) approximations, using the N2-N2 rigid-rotor potential of van der Avoird et al. For benchmarking purposes, close coupling (CC) calculations have also been carried out over a limited energy range and for even j - even j collisions only. Both the CC and CS cross sections have been obtained with and without exchange symmetry, whereas exchange is neglected in the IOS calculations. The CS results track the CC cross sections rather well. At total energies between 113 to 219 cm(exp -1) the average deviation is 14%. The deviation decrease with increasing energy, indicating that the CS approximation can be used as a substitute at higher energies when the CC calculations become impractical. Comparison between the CS and IOS cross sections at the high energy end of the CS calculation, 500 - 680 cm(exp-1), shows significant differences between the two. In addition, the IOS results exhibits sensitivity to the amount of inelasticity and the results for large DELTA J transitions are subjected to bigger errors. At total energy 113 cm(exp -1) and above, the average deviation between state-to-state cross sections calculated with even and odd exchange symmetries is 1.5%.

Huo, Winifred M.↗

Tracking Smoke from a Prescribed Fire and its Impacts on Local Air Quality using Temporally Resolved GOES-16 ABI Aerosol Optical Depth (AOD)

Aerosol optical depth (AOD) retrieved from the GOES-16 Advanced Baseline Imager (ABI) was used to track a smoke plume from a prescribed fire in northeastern Virginia on 8 March 2020. Weather and atmospheric conditions created a favorable environment to transport the plume through the Washington, D.C., and Baltimore, Maryland, metro areas in the afternoon and concentrate smoke near the surface, degrading air quality for several hours. ABI AOD with 5-min temporal resolution and 2-km spatial resolution definitively identified the timing and geographic extent of the plume during daylight hours. Comparison to AERONET AOD indicates that ABI AOD captured the relative change in AOD due to passage of the smoke, with a mean absolute error of 0.047. Ground-based measurements of fine particulate matter (PM2.5) confirm deteriorations in air quality coincident with the progression of the smoke. Ceilometer aerosol backscatter profiles verify plume transport timing and indicate that smoke aerosols were well mixed in a shallow boundary layer. This event illustrates the advantages of using multiple datasets to analyze the impacts of aerosols on ambient air quality. Given the quickly evolving nature of the event over several hours, ABI AOD provided information for the public and decision-makers that was not available from any other source, including polar-orbiting satellite sensors. This study suggests that PM2.5 concentrations estimated from ABI AOD can be used to fill in the gaps in nationwide regulatory PM2.5 monitor networks and may be a valuable addition to EPA’s PM2.5 NowCast of current air quality conditions.

satellite observations↗

Measurement of a zonal wind profile on Titan by Doppler tracking of the Cassini entry probe

A program, called the Cassini mission, intended to study the Saturn system by utilizing a Saturn orbiter and a probe descending to the surface of Titan, is discussed. Winds are expected to cause perturbations to the probe local horizontal velocity, resulting in an anomalous drift in the probe location and a shift in the frequency of the probe telemetry, due to the Doppler effect. By using an iterative algorithm, in which the time variation of the probe telemetry frequency is monitored throughout the descent, and the probe trajectory is updated to reflect the effect of wind on the probe location, a highly accurate relative wind profile can be recovered. By adding a single wind velocity, measured by independent means, an absolute wind profile can be obtained. However, the accuracy of the zonal winds recovery is limited by errors in trajectory, and frequency.

Atkinson, D. H.↗

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

An analysis of the shortening and lengthening of the phase of satellite-to-satellite (SST) data that passed within 40-700 km above the earth surface during its ATS-6 to GEOS-3 to ATS-6 path resulted in refractivity vs height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbations from the moon, sun, and a 15th-order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occulation period and a model ionosphere was estimated by a least-squares adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the two methods were caused by orbital errors, which propagated into the solution.

Liu, A. S.↗

An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise

An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.

Reddy, C. P.↗

Mars gravity field derived from Viking-1 and Viking-2 - The navigation result

Viking-1 and Viking-2 Doppler tracking data taken during orbit phases characterized by 1500 km subperiapse altitudes have provided a basis for a determination of the Martian gravity field. Navigation results show that the linear combination of short-arc gravity estimates is an acceptable technique for obtaining gravity models over multiple data arcs. An ensemble field composed of Viking data and Mariner-9 a priori retains the inherent local accuracy of its constituent fields. At the same time, the model can be made to be valid globally by careful weighting of a priori Mariner-9 data. The sixth degree and order model presented reduces the error concerning the change in period by more than an order of magnitude during the high altitude (1500 km) phases of the Viking mission. The resulting areoid deviates by no more than 150 m from the areoid produced by the a priori Mariner-9 field.

Christensen, E. J.↗