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A new learning algorithm termed cascade error projection (CEP) is presented. CEP is an adaption of a constructive architecture from cascade correlation and the dynamical stepsize of A/D conversion from the cascade back propagation algorithm.
This report describes the activities during the fourth six month period of the investigation of acoustic propagation in the atmosphere with a realistic lapse temperature profile. A significant error was detected since the previous semi-annual report and has been corrected in both the plane wave and point source solutions. This report then describes both of these problems in some detail along with presenting some numerical results from the model. Work will begin this summer on the model of propagation in an inversion.
A spacecraft-to-spacecraft optical time-transfer simulation has been developed as a tool for informing NASA’s Surface Deformation and Change (SDC) mission architecture. The SDC mission will combine radar images from multiple spacecraft to improve understanding of the Earth’s sea-level and landscape changes. Spacecraft must be precisely synchronized in order to create sharp radar images. Simulation of multiple spacecraft time-synchronizing via laser communication can inform technology choices of a mission by providing a picosecond-precision level estimate of clock error. This timing and ranging simulation has been combined with a radar system performance analysis pipeline. The simulated timing errors are used to predict performance of bistatic SAR systems in the presence of oscillator noise and time synchronization in accuracy. This analysis includes both analytic approximation equations from existing literature, and a numerical radar simulation to extract key system performance parameters like phase error and signal-to-noise ratio (SNR)degradation. Precision time-transfer techniques facilitate the accurate synchronization of clocks between any combination of terminals. Most time-transfer technology for comparing two clocks at different terminals use radio frequencies (RF) to measure the time delay between the sending and receiving of signals. Laser technology offers the capability to transmit high data rates with systems that are of smaller size and lower power than comparable RF systems. The clocks on independent spacecraft will have some phase and frequency errors between them that result in clock drift. The two clock models that are included in this bi-directional MATLAB simulation are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC). The CSAC has flown as hardware for small satellite missions such as the University of Florida’s CHOMPTT mission. A study of example orbits, including that of NASA NASA-ISRO Synthetic Aperture Radar Mission (NISAR) mission, and lasing rates demonstrate the impact of flight configuration parameters on the synchronization error between two spacecraft. The MATLAB timing simulation uses a Runge-Kutta 4th-order method to propagate spacecraft orbits and computes the light-travel time estimate between them. The simulation outputs the estimated range and estimated clock error based on a user-defined spacecraft cluster configuration. The radar simulation and analytic approximations are applied to evaluate a potential future NASA bistatic SAR constellation architecture. In the proposed architecture, satellites follow each other in the same orbit at 800 km altitude, with a 210 km baseline. We also baseline the CSAC as an ultra stable oscillator, and use NASA’s NISAR for baseline radar system parameters to compute a clock-system introduced phase error of 5.6 degrees without synchronization by frequent time transfer. We build on this base case with a sensitivity analysis of radar performance over a proposed range of constellation and radar system parameters. With this analysis pipeline, we comment on which radar parameters should or should not be changed to minimize synchronization requirements. This analysis technique could be extended or modified to evaluate the timing requirements of other geometries for other future multistatic SAR missions, or other interferometric satellite missions.
Using an NCAR community climate model, Version I, the forecast error growth and the climate drift resulting from the omission of the upper stratosphere are investigated. In the experiment, the control simulation is a seasonal integration of a medium horizontal general circulation model with 30 levels extending from the surface to the upper mesosphere, while the main experiment uses an identical model, except that only the bottom 15 levels (below 10 mb) are retained. It is shown that both random and systematic errors develop rapidly in the lower stratosphere with some local propagation into the troposphere in the 10-30-day time range. The random growth rate in the troposphere in the case of the altered upper boundary was found to be slightly faster than that for the initial-condition uncertainty alone. However, this is not likely to make a significant impact in operational forecast models, because the initial-condition uncertainty is very large.
The goal of the Flight Dynamics Facility (FDF) attitude support is twofold: to determine spacecraft attitude and to explain deviations from nominal attitude behavior. Attitude determination often requires resolving contradictions in the sensor observations. This may be accomplished by applying calibration corrections or by revising the observation models. After accounting for all known sources of error, solution accuracy should be limited only by observation and propagation noise. The second half of the goal is to explain why the attitude may not be as originally intended. Reasons for such deviations include sensor or actuator misalignments and control system performance. In these cases, the ability to explain the behavior should, in principle, be limited only by knowledge of the sensor and actuator data and external torques. Documented here are some results obtained to date in support of the Cosmic Background Explorer (COBE). Advantages and shortcomings of the integrated attitude determination/sensor calibration software are discussed. Some preliminary attitude solutions using data from the Diffuse Infrared Background Experiment (DIRBE) instrument are presented and compared to solutions using Sun and Earth sensors. A dynamical model is constructed to illustrate the relative importance of the various sensor imprefections. This model also shows the connection between the high- and low-frequency attitude oscillations.
Alias periods and wavelengths for the M(sub 2, S(sub 2), N(sub 2), K(sub 1), O(sub 1), and P(sub 1) tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelenghts calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K(sub 1) constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are likely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M(sub 2) alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M(sub 2), N(sub 2) and O(sub 1) fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S(sub 2), K(sub 1) and P(sub 1) varies smoothly with latitude. S(sub 2) is strongly aliased for latitudes within 50 degress of the equator, while K(sub 1) and P(sub 1) are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented.
In recent years, much progress has been made in observing CO2 distributions from space. However, the use of these observations to infer source/sink distributions in inversion studies continues to be complicated by difficulty in quantifying atmospheric transport model errors. We will present results from several different experiments designed to quantify different aspects of transport error using the Goddard Earth Observing System, Version 5 (GEOS-5) Atmospheric General Circulation Model (AGCM). In the first set of experiments, an ensemble of simulations is constructed using perturbations to parameters in the model s moist physics and turbulence parameterizations that control sub-grid scale transport of trace gases. Analysis of the ensemble spread and scales of temporal and spatial variability among the simulations allows insight into how parameterized, small-scale transport processes influence simulated CO2 distributions. In the second set of experiments, atmospheric tracers representing model error are constructed using observation minus analysis statistics from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA). The goal of these simulations is to understand how errors in large scale dynamics are distributed, and how they propagate in space and time, affecting trace gas distributions. These simulations will also be compared to results from NASA's Carbon Monitoring System Flux Pilot Project that quantified the impact of uncertainty in satellite constrained CO2 flux estimates on atmospheric mixing ratios to assess the major factors governing uncertainty in global and regional trace gas distributions.
In this presentation we will explore several distributed consensus algorithms developed to maintain coordination among a fleet of heterogeneous UAS subject to external disturbances. An overview of the network assumptions and autopilot performance bounds required to meet the coordination objective will be provided. In particular, we will leverage passivity-based stability conditions for bidirectional networks that require the communication graph to be connected in an integral sense, but may fail to connect pointwise in time during the entire mission. Non-ideal autopilots that can only track a desired speed profile with a prescribed precision induce an error in vehicle coordination. The autopilot performance bounds will be propagated through the coordination dynamics to understand the limits introduced by autopilots.
Planetary spacecraft are viewed through a troposphere that absorbs and delays radio signals propagating through it. Tropospheric water, in the form of vapor, cloud liquid,and precipitation , emits radio noise which limits satellite telemetry communication link performance. Even at X-band, rain storms have severely affected several satellite experiments including a planetary encounter. The problem will worsen with DSN implementation of Ka-band becausecommunication link budgets will be dominated by tropospheric conditions. Troposphere-induced propagation delays currently limit VLBI accuracy and are significant sources of error for Doppler tracking. Additionally, the success of radio science programs such as satellite gravity wave experiments and atmospheric occultation experiments depends on minimizing the effect of watervapor-induced prop agation delays. In order to overcome limitations imposed by the troposphere, the Deep Space Network has supported a program of radiometric remote sensing. Currently, water vapor radiometers (WVRs) and microwave temperature profilers (MTPs) support many aspects of the Deep Space Network operations and research and development programs. Their capability to sense atmospheric water, microwave sky brightness, and atmospheric temperature is critical to development of Ka-band telemetry systems, communication link models, VLBI, satellite gravity waveexperiments, and r adio science missions. During 1993, WVRs provided data for propagation mode development, supp orted planetary missions, and demonstrated advanced tracking capability. Collection of atmospheric statistics is necessary to model and predict performance of Ka-band telemetry links, antenna arrays, and radio science experiments. Since the spectrum of weather variations has power at very long time scales, atmospheric measurements have been requested for periods ranging from one year to a decade at each DSN site. The resulting database would provide reliable statistics on daily, monthly, and seasonal variations. Only long-term monitoring will prevent biases from being introduced by an exceptionally wet or dry year. Support for planetary missions included tropospheric calibration for the recent Mars Observer gravity wave experiments and Ka-band link experiment (KaBLE). Additionally, several proposed radio science experiments such as profiling planetary atmospheres using satellite occultations and Ka-band gravitational wave searches require advanced radiometer technology development. Finally, there has been a consistent advanced technology program to advance satellite navigational and tracking capabilities. This year that included an experiment with radiometer based tropospheric calibration for a series of VLBI catalog measurements.
The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.
One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.
An investigation is conducted in order to expose errors in the formula for the elevation angle dependence of the hydrostatic atmospheric propagation delay, called the mapping function. A series of special VLBI experiments that involve a large fraction of group delay data from very low elevation angles are performed. Twenty-two experiments, each 26 hours in duration, were performed using VLBI antennas at Goldstone, California and at Westford, Massachusetts. Elevation angle cutoff tests were used to examine the contribution of these errors to the estimates of the vertical coordinate of site position. This contribution is determined to be about 19 mm. It is also found that, for the spacing of 1-2 months between experiments, the mapping function errors do not exhibit a coherent annual signature, but appear to be random in the long term.
An onboard navigation system was developed to aid the design and evaluation of algorithms used in autonomous satellite navigation with Global Positioning System (GPS) data. The performance of the algorithms designed for a GPS Receiver/Processor Assembly (R/PA) intended for LANDSAT-D was investigated during the development phases of the GPS (four to six satellites in the constellation). This evaluation emphasized the effects on the orbit determination accuracy of the expected user clock errors, GPS satellite visibility, force model approximations, and state and covariance propagation approximations. Results are presented giving the sensitivity of orbit determination accuracy to these constraints.
This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.
Unsteady Pressure-Sensitive Paint (uPSP) technology provides simultaneously high-frequency and high-spatial resolution surface pressure fluctuation measurements. It has demonstrated value in wind tunnel test facilities to evaluate aerospace vehicle unsteady aerodynamics. The calibration of measurements from digital pixel counts into corresponding physical units relies on both lab-based and in-situ calibration steps, and its validation is both challenging and critical to adoption of the technology. We present a rigorous methodology for direct comparison of uPSP-derived surface pressure measurements to reference pressure transducer data based on a model of the camera-based measurement error, a model of the flow field pressure signal, and their propagation through the uPSP data reduction algorithm. The methodology is demonstrated on data collected in a small-scale, subsonic wind tunnel test as well as data collected from a Space Launch System unsteady aerodynamics characterization test at the NASA Ames Research Center Unitary Plan Wind Tunnel Complex.
Unsteady Pressure-Sensitive Paint (uPSP) technology provides simultaneously high-frequency and high-spatial resolution surface pressure fluctuation measurements. It has demonstrated value in wind tunnel test facilities to evaluate aerospace vehicle unsteady aerodynamics. The calibration of measurements from digital pixel counts into corresponding physical units relies on both lab-based and in-situ calibration steps, and its validation is both challenging and critical to adoption of the technology. We present a rigorous methodology for direct comparison of uPSP-derived surface pressure measurements to reference pressure transducer data based on a model of the camera-based measurement error, a model of the flow field pressure signal, and their propagation through the uPSP data reduction algorithm. The methodology is demonstrated on data collected in a small-scale, subsonic wind tunnel test as well as data collected from a Space Launch System unsteady aerodynamics characterization test at the NASA Ames Research Center Unitary Plan Wind Tunnel Complex.
Satellite communications links are subject to distortions which result in an amplitude versus frequency response which deviates from the ideal flat response. Such distortions result from propagation effects such as multipath fading and scintillation and from transponder and ground terminal hardware imperfections. Laboratory experiments performed at NASA Lewis measured the bit-error-rate (BER) degradation resulting from several types of amplitude response distortions. Additional tests measured the amount of BER improvement obtained by flattening the amplitude response of a distorted laboratory-simulated satellite channel. This paper presents the results of these experiments.
Spectral remote sensing reflectance, Rrs(λ) (sr−1), is the fundamental quantity used to derive a host of bio-optical and biogeochemical properties of the water column from satellite ocean color measurements. Estimation of uncertainty in those derived geophysical products is therefore dependent on knowledge of the uncertainty in satellite-retrieved R rs . Furthermore, since the associated algorithms require R rs at multiple spectral bands, the spectral (i.e., band-to-band)error covariance in R rs is needed to accurately estimate the uncertainty in those derived properties. This study establishes a derivative-based approach for propagating instrument random noise, instrument systematic uncertainty, and forward model uncertainty into R rs as retrieved using NASA’s multiple-scattering epsilon (MSEPS) atmospheric correction algorithm, to generate pixel-level error covariance in R rs . The approach is applied to measurements from Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite and verified using Monte Carlo (MC) analysis. We also make use of this full spectral error covariance in R rs to calculate uncertainty in phytoplankton pigment chlorophyll-a concentration (chl a , mg/m 3 ) and diffuse attenuation coefficient of downwelling irradiance at 490 nm (K d (490), m -1 ). Accounting for the error covariance in R rs generally reduces the estimated relative uncertainty in chl a by ∼1-2% (absolute value) in waters with chl a < 0.25 mg/m 3 where the color index (CI) algorithm is used. The reduction is ∼5-10% in waters with chl a > 0.35 mg/m 3 where the blue-green ratio (OCX) algorithm is used. Such reduction can be higher than 30% in some regions. For K d (490), the reduction by error covariance is generally ∼2%, but can be higher than 20% in some regions. The error covariance in R rs is further verified through forward-calculating chl a from MODIS-retrieved and in situ R rs and comparing estimated uncertainty with observed differences. An 8-day global composite of propagated uncertainty shows that the goal of 35% uncertainty in chl a can be achieved over deep ocean waters (chl a ≤ 0.1 mg/m3). While the derivative-based approach generates reasonable error covariance in R rs some assumptions should be updated as our knowledge improves. These include the inter-band error correlation in top-of-atmosphere reflectance, and uncertainties in the calibration of MODIS 869 nm band, in ancillary data, and in the in situ data used for system vicarious calibration.