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At least 397 records · Page 22

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi Henderson↗

Attitude control system conceptual design for the GOES-N spacecraft series

The attitude determination sensing and processing of the system are considered, and inertial reference units, star trackers, and beacons and landmarks are discussed as well as an extended Kalman filter and expected attitude-determination performance. The baseline controller is overviewed, and a spacecraft motion compensation (SMC) algorithm, disturbance environment, and SMC performance expectations are covered. Detailed simulation results are presented, and emphasis is placed on dynamic models, attitude estimation and control, and SMC disturbance accommmodation. It is shown that the attitude control system employing gyro/star tracker sensing and active three-axis control with reaction wheels is capable of maintaining attitude errors of 1.7 microrad or less on all axes in the absence of attitude disturbances, and that the sensor line-of-sight pointing errors can be reduced to 0.1 microrad by SMC.

Markley, F. L.↗

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗

Effect of Clouds on Apertures of Space-based Air Fluorescence Detectors

Space-based ultra-high-energy cosmic ray detectors observe fluorescence light from extensive air showers produced by these particles in the troposphere. Clouds can scatter and absorb this light and produce systematic errors in energy determination and spectrum normalization. We study the possibility of using IR remote sensing data from MODIS and GOES satellites to delimit clear areas of the atmosphere. The efficiency for detecting ultra-high-energy cosmic rays whose showers do not intersect clouds is determined for real, night-time cloud scenes. We use the MODIS SST cloud mask product to define clear pixels for cloud scenes along the equator and use the OWL Monte Carlo to generate showers in the cloud scenes. We find the efficiency for cloud-free showers with closest approach of three pixels to a cloudy pixel is 6.5% exclusive of other factors. We conclude that defining a totally cloud-free aperture reduces the sensitivity of space-based fluorescence detectors to unacceptably small levels.

Sokolsky, P.↗

Remote Characterization of Biomass Measurements: Case Study of Mangrove Forests

Accurately quantifying forest biomass is of crucial importance for climate change studies. By quantifying the amount of above and below ground biomass and consequently carbon stored in forest ecosystems, we are able to derive estimates of carbon sequestration, emission and storage and help close the carbon budget. Mangrove forests, in addition to providing habitat and nursery grounds for over 1300 animal species, are also an important sink of biomass. Although they only constitute about 3% of the total forested area globally, their carbon storage capacity -- in forested biomass and soil carbon -- is greater than that of tropical forests (Lucas et al, 2007). In addition, the amount of mangrove carbon -- in the form of litter and leaves exported into offshore areas is immense, resulting in over 10% of the ocean's dissolved organic carbon originating from mangroves (Dittmar et al, 2006) The measurement of forest above ground biomass is carried out on two major scales: on the plot scale, biomass can be measured using field measurements through allometric equation derivation and measurements of forest plots. On the larger scale, the field data are used to calibrate remotely sensed data to obtain stand-wide or even regional estimates of biomass. Currently, biomass can be calculated using average stand biomass values and optical data, such as aerial photography or satellite images (Landsat, Modis, Ikonos, SPOT, etc.). More recent studies have concentrated on deriving forest biomass values using radar (JERS, SIR-C, SRTM, Airsar) and/or lidar (ICEsat/GLAS, LVIS) active remote sensing to retrieve more accurate and detailed measurements of forest biomass. The implementation of a generation of new active sensors (UAVSar, DesdynI, Alos/Palsar, TerraX) has prompted the development of new tecm'liques of biomass estimation that use the combination of multiple sensors and datasets, to quantify past, current and future biomass stocks. Focusing on mangrove forest biomass estimation, this book chapter has 3 main objectives: a) To describe in detail the field methodologies used to derive accurate estimates of biomass in mangrove forests b) To explain how mangrove forest biomass can be measured using several remote sensing techniques and datasets c) To give a detailed explanation of the measurement challenges and errors that arise in each estimate of forest biomass

Fatoyinbo, Temilola E.↗

Space-Time Data Fusion

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Greenhouse Gases Observing Satellite (GOSAT)↗

45 Km horizontal path optical link demonstrations

Observations made during a mountain-top-to-mountain-top horizontal optical link demonstration are described. The optical link spans a range of 45 Km at an average altitude of 2 Km above sea level. A multi-beam beacon comprised of eight laser beams emerging from multi-mode fiber coupled lasers (780 nm) are launched through a 0.6 m diameter telescope located at the JPL Table Mountain Facility (TMF) in Wrightwood, California. The multibeam beacon is received at Strawberry Peak located in the San Bernadino Mountains of California. The NASA, JPL developed optical communications demonstrator (OCD) receives the beacon, senses the atmosphere induced motion and using an upgraded fine steering loop compensates the re-transmission of a communications laser beam (852 nm, 400 Mbps) to TMF. The eight-beam beacon allowed a four reduction in normalized irradiance or scintillation index. This in turn was sufficient to eliminate beacon fades sensed b the OCD and allowed the fine steering loop performance evaluation. The uncompensated tracking error was determined to be 2.2 - 3 prad compared to a model prediction of 3.4 prad. The paper also discusses various auxiliary observations made during the campaign

Page, Norman A.↗

The LUVOIR Extreme Coronagraph for Living Planetary Systems (ECLIPS) II. Performance Evaluation, Aberration Sensitivity Analysis and Exoplanet Detection Simulations

Future space missions such as the Large UV-Optical-Infrared Surveyor (LUVOIR) and the Habitable Exoplanet Observatory (HabEx) require coronagraphs with active wavefront control to suppress starlight to discover and characterize habitable exoplanets. The Extreme Coronagraph for Living Planetary Systems (ECLIPS) is the coronagraph instrument on the LUVOIR Surveyor mission concept, an 8–15m segmented telescope. ECLIPS is split into three channels: UV (200 to 400 nm), optical (400 nm to 850 nm), and NIR (850 nm to 2.0 microns), with each channel equipped with two deformable mirrors for wavefront control, a suite of coronagraph masks, a low-order/out-of-band wavefront sensor, and separate science imagers and spectrographs. The Apodized Pupil Lyot Coronagraph (APLC) and the Vector Vortex Coronagraph (VVC) are the baselined mask technologies for ECLIPS to enable the required 10 -10 contrast for observations in the habitable zones of nearby stars. Their performance depends on active wavefront sensing and control, as well as metrology subsystems to compensate for aberrations induced by segment errors (piston and tip/tilt, among others), secondary mirror misalignment, and global low-order wavefront errors. Here we present the latest results of the simulation of these effects for the two technologies and discuss the achieved contrast for exoplanet detection and characterization after closed-loop wavefront estimation and control algorithms have been applied. Finally, we show simulated observations using high-fidelity spatial and spectral input models of complete planetary systems generated with the Haystacks code framework.

Roser Juanola-Parramon↗

Modeling and Performance Analysis of the LUVOIR Coronagraph Instrument

Future space missions such as the Large UV/Optical/Infrared Surveyor (LUVOIR) and the Habitable Exoplanet Observatory, when equipped with coronagraphs with active wavefront control to suppress starlight, will allow the discovery and characterization of habitable exoplanets. The Extreme Coronagraph for Living Planetary Systems (ECLIPS) is the coronagraph instrument on the LUVOIR Surveyor mission concept, an 8- to 15-m segmented telescope. ECLIPS is split into three channels, namely, UV (200 to 400 nm), optical (400 to 850 nm), and near IR (850 nm to 2 μm), with each channel equipped with two deformable mirrors for wavefront control, a suite of coronagraph masks, a low-order/out-of-band wavefront sensor, and separate science imagers and spectrographs. The apodized pupil Lyot coronagraph and the vector vortex coronagraph are the baselined mask technologies for ECLIPS to enable the required 10−10 contrast for observations in the habitable zones of nearby stars for LUVOIR-A (15-m telescope) and LUVOIR-B (8-m telescope), respectively. Their performance depends on active wavefront sensing and control, as well as metrology subsystems to compensate for aberrations induced by segment errors (e.g., piston and tip/tilt), secondary mirror misalignment, and global low-order wavefront errors. Here, we present the latest results of the simulation of these effects for the LUVOIR coronagraph instrument and discuss the achieved contrast for exoplanet detection and characterization after closed-loop wavefront estimation and control algorithms have been applied. Finally, we show simulated observations using high-fidelity spatial and spectral input models of complete planetary systems generated with the Haystacks code framework.

Roser Juanola-Parramon↗

Optimal Estimation Retrievals and Their Uncertainties: What Every Atmospheric Scientist Should Know

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

54 ENVIRONMENTAL SCIENCES↗

Inversion of data from diffraction-limited multiwavelength remote sensors. I - Linear case

The remote sensing inverse problem is considered in which the sensor does not necessarily view the same area on the earth at each wavelength, and spatial correlations of the geophysical parameters may be present. Under the conditions of linearity and stationary statistics, the minimum mean-square error solution to the problem of inverting such data is a spatial filter of the Wiener-Kolmogorov class. The resulting remote-sensing system can be characterized by an impulse response matrix in ordinary space or by a transfer matrix in frequency space. A signal-to-noise matrix for the geophysical parameters to be sensed is also defined; this matrix depends on the postulated a priori statistics and on the characteristics of the remote-sensing instrument. The system transfer matrix and the signal-to-noise matrix are simultaneously diagonalizable. The optimum transfer matrix filters out of the estimate vector those eigenparameters for which eigenvalues of the signal-to-noise matrix are less than unity.

Rosenkranz, P. W.↗

On the sensitivity of numerical weather prediction to remotely sensed marine surface wind data - A simulation study

The reported investigation has the objective to assess the potential impact on numerical weather prediction (NWP) of remotely sensed surface wind data. Other investigations conducted with similar objectives have not been satisfactory in connection with a use of procedures providing an unrealistic distribution of initial errors. In the current study, care has been taken to duplicate the actual distribution of information in the conventional observing system, thus shifting the emphasis from accuracy of the data to the data coverage. It is pointed out that this is an important consideration in assessing satellite observing systems since experience with sounder data has shown that improvements in forecasts due to satellite-derived information is due less to a general error reduction than to the ability to fill data-sparse regions. The reported study concentrates on the evaluation of the observing system simulation experimental design and on the assessment of the potential of remotely sensed marine surface wind data.

Cane, M. A.↗

A Micromechanical INS/GPS System for Small Satellites

The cost and complexity of large satellite space missions continue to escalate. To reduce costs, more attention is being directed toward small lightweight satellites where future demand is expected to grow dramatically. Specifically, micromechanical inertial systems and microstrip global positioning system (GPS) antennas incorporating flip-chip bonding, application specific integrated circuits (ASIC) and MCM technologies will be required. Traditional microsatellite pointing systems do not employ active control. Many systems allow the satellite to point coarsely using gravity gradient, then attempt to maintain the image on the focal plane with fast-steering mirrors. Draper's approach is to actively control the line of sight pointing by utilizing on-board attitude determination with micromechanical inertial sensors and reaction wheel control actuators. Draper has developed commercial and tactical-grade micromechanical inertial sensors, The small size, low weight, and low cost of these gyroscopes and accelerometers enable systems previously impractical because of size and cost. Evolving micromechanical inertial sensors can be applied to closed-loop, active control of small satellites for micro-radian precision-pointing missions. An inertial reference feedback control loop can be used to determine attitude and line of sight jitter to provide error information to the controller for correction. At low frequencies, the error signal is provided by GPS. At higher frequencies, feedback is provided by the micromechanical gyros. This blending of sensors provides wide-band sensing from dc to operational frequencies. First order simulation has shown that the performance of existing micromechanical gyros, with integrated GPS, is feasible for a pointing mission of 10 micro-radians of jitter stability and approximately 1 milli-radian absolute error, for a satellite with 1 meter antenna separation. Improved performance micromechanical sensors currently under development will be suitable for a range of micro-nano-satellite applications.

Barbour, N.↗

An error reduction algorithm to improve lidar turbulence estimates for wind energy

Abstract. Remote-sensing devices such as lidars are currently being investigated as alternatives to cup anemometers on meteorological towers for the measurement of wind speed and direction. Although lidars can measure mean wind speeds at heights spanning an entire turbine rotor disk and can be easily moved from one location to another, they measure different values of turbulence than an instrument on a tower. Current methods for improving lidar turbulence estimates include the use of analytical turbulence models and expensive scanning lidars. While these methods provide accurate results in a research setting, they cannot be easily applied to smaller, vertically profiling lidars in locations where high-resolution sonic anemometer data are not available. Thus, there is clearly a need for a turbulence error reduction model that is simpler and more easily applicable to lidars that are used in the wind energy industry. In this work, a new turbulence error reduction algorithm for lidars is described. The Lidar Turbulence Error Reduction Algorithm, L-TERRA, can be applied using only data from a stand-alone vertically profiling lidar and requires minimal training with meteorological tower data. The basis of L-TERRA is a series of physics-based corrections that are applied to the lidar data to mitigate errors from instrument noise, volume averaging, and variance contamination. These corrections are applied in conjunction with a trained machine-learning model to improve turbulence estimates from a vertically profiling WINDCUBE v2 lidar. The lessons learned from creating the L-TERRA model for a WINDCUBE v2 lidar can also be applied to other lidar devices. L-TERRA was tested on data from two sites in the Southern Plains region of the United States. The physics-based corrections in L-TERRA brought regression line slopes much closer to 1 at both sites and significantly reduced the sensitivity of lidar turbulence errors to atmospheric stability. The accuracy of machine-learning methods in L-TERRA was highly dependent on the input variables and training dataset used, suggesting that machine learning may not be the best technique for reducing lidar turbulence intensity (TI) error. Future work will include the use of a lidar simulator to better understand how different factors affect lidar turbulence error and to determine how these errors can be reduced using information from a stand-alone lidar.

17 WIND ENERGY↗

Constraining the Multiscale Structure of Geophysical Fields in Machine Learning: The Case of Precipitation

The use of deep-learning algorithms for estimating the value of geophysical variables from remotely sensed information is rapidly expanding. The typical objective function minimized in such algorithms is the mean square error (MSE), which is known to lead to smooth estimates with compressed dynamical range as compared to the true distribution of the variable of interest. Here, we introduce and evaluate alternative objective functions, focusing on the retrieval of precipitation rates from satellite passive microwave radiometric measurements using a deep convolutional neural network. For this testbed application, the results show that explicitly imposing the preservation of the statistical distribution and spatial wavelet power spectrum of the target variable allows to accurately reproduce extreme values and sharp gradients across multiple scales in this study.

58 GEOSCIENCES↗

Finite-element time evolution operator for the anharmonic oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Milton, Kimball A.↗

Dual-mass vibratory rate gyroscope with suppressed translational acceleration response and quadrature-error correction capability

A microfabricated vibratory rate gyroscope to measure rotation includes two proof-masses mounted in a suspension system anchored to a substrate. The suspension has two principal modes of compliance, one of which is driven into oscillation. The driven oscillation combined with rotation of the substrate about an axis perpendicular to the substrate results in Coriolis acceleration along the other mode of compliance, the sense-mode. The sense-mode is designed to respond to Coriolis accelerationwhile suppressing the response to translational acceleration. This is accomplished using one or more rigid levers connecting the two proof-masses. The lever allows the proof-masses to move in opposite directions in response to Coriolis acceleration. The invention includes a means for canceling errors, termed quadrature error, due to imperfections in implementation of the sensor. Quadrature-error cancellation utilizes electrostatic forces to cancel out undesired sense-axis motion in phase with drive-mode position.

Clark, William A.↗

Recovering noise-free quantum observables

We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems, but we illustrate it with applications to quantum information and quantum sensing. The approach corresponds to repeating the same quantum evolution many times with known variations on the underlying systems' error properties, e.g., the spontaneous emission and dephasing times $T_1$ and $T_2$. As opposed to standard quantum error correction methods, which have an overhead in the number of qubits (many physical qubits must be added for each logical qubit), our method has only an overhead in the number of evaluations, allowing the overhead to, in principle, be hidden via parallelization. We show that the effective spontaneous emission $T_1$ and dephasing $T_2$ times can be increased using this method in both simulation and experiments on an actual quantum computer. We also show how to correct more complicated entangled states and how Ramsey fringes relevant to quantum sensing can be significantly extended in time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗