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NASA NTRSDate not supplied

Digital Elevation Map Parametric Error Analysis Using Corresponding NAC Images

Future lunar landing systems, particularly those used to land humans on the lunar surface aspart of the ARTEMIS program, will require precision navigation relative to the lunar surface. The most common way to meet these stringent navigation require-ments is through terrain relative navigation (TRN), which localizes a spacecraft by comparing descent im-agery with a predefined map of the surface. The accu-racy achievable using TRN is limited by the accuracy of the reference Digital Elevation Map (DEM). It is therefore critical for future lunar missions that potential errors in DEMs be quantified. This paper describes one of NASA’s current efforts to develop a process for evaluating lunar DEM quality.

Chris R Gnam↗
NASA NTRS1994

Measuring the Hubble constant and our Virgo-infall velocity independently

A sample of spiral galaxies with B(sub T) less than 14.5 located in two local volumes, one in the direction of, but behind, the Virgo Cluster (behind-Virgo volume (BV)) and the other in the opposite direction (anti-Virgo volume (AV)), were used via a Tully-Fisher (TF) relation to derive the following two parameters: H(sub AB), the mean Hubble ratio between AV and BV, and delta v(sub parallel), the peculiar velocity of the Local Group in the direction of the Virgo Cluster (VC) with respect to a uniformly expanding reference system defined by our AV and BV sub-samples. The two sampled volumes, separated by a velocity interval of 5600 km/s, form an antipodal pair. This particular geometry not only allows us to derive the two parameters independently but also reduces the dynamical effect of the Local Supercluster on H(sub AB) without increasing the Malmquist bias. By limiting our sample to spiral galaxies having large velocity widths W(sub R), we effectively reduce the TF scatter and Malmquist bias in our sample. The TF zero point and dispersion were then determined by further correcting for the small residual Malmquist bias. An additional sample of fainter galaxies was used to test for a non-Gaussian tail to the TF disperison. We found no evidence for such a tail and formally give an upper limit of about 18% for the fractional contribution of an unseen tail. The average intrinsic TF dispersion for the dominant Gaussian component is sigma(sub TF)(sup 0) approximately 0.33 mag for W(sub R) approximately equal to or greater than 180 km/s. Our numerical results are delta v(sub parallel) approximately equals 414 +/- 82 km/s and H(sub AB) approximately equals (84.0 +/- 2.4)(1 + epsilon) km/s Mpc, where (1 + epsilon) accounts for any systematic error between the calibrators and the sample galaxies. Various dynamical models were tested to explore the effect on H(sub AB) of the uncertainties in the local velocity field. Constrained by our observed delta v(sub parallel) as well as other observational quantities, we found that the rms deviation from unity of H(sub AB)/H(sub 0) (where H(sub 0) is the Hubble constant for each model) is 5%, making H(sub AB) a good indicator for H(sub 0). Taking this variation as an additional error, our formal estimate for the Hubble constant is H(sub 0) approximately equals (84 +/- 5)(1 + epsilon) km/s Mpc.

Lu, Nanyao Y.↗
NASA NTRS2021

LiDAR-Based Map Relative Localization Performance Analysis for Landing on Europa

This paper presents preliminary simulations andanalyses done to assess the feasibility of performing Map RelativeLocalization (MRL) with the Europa Lander LiDAR beingdeveloped for the Europa Lander Pre-Phase A concept. MapRelative Localization is the process of determining the horizontalposition of a lander with respect to an onboard, a-priori map,by comparing the map to sensor observations of the terrain duringdeorbit, descent, and landing (DDL). Although kilometerscaleposition knowledge is commonly available during DDL,landing in hazard-rich environments requires position errors of100 m or less. Prior knowledge in the case of Europa Landerwill be visual and topographic maps collected by the upcomingEuropa Clipper mission. The Mars 2020 Lander Vision System(LVS) uses images from a camera to localize with respect tovisual maps. This technology, as well as a 3D imaging LiDAR indevelopment for hazard detection, is currently baselined for theEuropa Lander Pre-Phase A concept. This paper investigatesthe potential use of the hazard detection LiDAR to performMRL with respect to a 3D digital elevation model (DEM)provided by the Europa Clipper mission, as an alternative orbackup solution to passive optical MRL. Compared to passiveoptical MRL, one advantage of LiDAR-based localization isthat it is insensitive to lighting conditions, potentially relaxingrequirements on synchronizing map acquisition and landingtime of day. To analyze LiDAR based MRL performance,six representative terrains are synthetically up-sampled fromGalileo-derived maps of Europa to a resolution of 0.5 m/pxand covering an area of 4 km by 4 km. These maps are usedas ground-truth to generate simulated noisy a-priori onboardtopographic maps expected from Europa Clipper as well assimulated LiDAR DEMs generated at an altitude of 5 km duringEuropa Lander DDL. The simulated LiDAR DEM is matchedagainst the simulated map via 2D normalized cross-correlation,exploiting the accurately known spacecraft attitude to avoidthe need for more computationally intensive algorithms such asIterative Closest Point (ICP). Two sources of measurement errorare identified for analysis: 1) additive Gaussian noise in therange measurements from the Europa Lander LiDAR and theEuropa Clipper derived maps and 2) errors in the LiDAR DEMinduced by errors in the Europa Lander state estimate which isused to de-warp the LiDAR scan data into a DEM format. Weassess the effect of each of these types of errors independently onmatching performance as well as the overall performance whenall types of error are introduced. Additionally, we present theresult of a sensitivity study to terrain frequency content.

Trawny, Nikolas↗
NASA NTRS1987

Design, calibration and error analysis of instrumentation for heat transfer measurements in internal combustion engines

The paper reports the methodology and uncertainty analyses of instrumentation for heat transfer measurements in internal combustion engines. Results are presented for determining the local wall heat flux in an internal combustion engine (using a surface thermocouple-type heat flux gage) and the apparent flame-temperature and soot volume fraction path length product in a diesel engine (using two-color pyrometry). It is shown that a surface thermocouple heat transfer gage suitably constructed and calibrated will have an accuracy of 5 to 10 percent. It is also shown that, when applying two-color pyrometry to measure the apparent flame temperature and soot volume fraction-path length, it is important to choose at least one of the two wavelengths to lie in the range of 1.3 to 2.3 micrometers. Carefully calibrated two-color pyrometer can ensure that random errors in the apparent flame temperature and in the soot volume fraction path length will remain small (within about 1 percent and 10-percent, respectively).

Ferguson, C. R.↗
NASA NTRS1977

Analyses of atmospheric extinction data obtained by astronomers. I - A time-trend analysis of data with internal accidental errors obtained at four observatories

Long-term time-trend analysis was performed on astronomical atmospheric extinction data in wideband UBV and various narrow-band systems recorded at Cerro Tololo, Kitt Peak, Lick, and McDonald observatories. All of the data had to be transformed into uniform monochromatic extinction data before trend analysis could be performed. The paper describes the various reduction techniques employed. The time-trend analysis was then carried out by the method of least squares. A special technique, called 'histogram shaping', was employed to adjust for the fact that the errors of the reduced monochromatic extinction data were not essentially Gaussian. On the assumption that there are no compensatory background and local extinction changes, the best values obtained for extinction trends due to background aerosol changes during the years 1960 to 1972 are 0.006 + or - 0.013 (rms) and 0.009 + or - 0.009 (rms) stellar magnitudes per air mass per decade in the blue and yellow wavelength regions, respectively.

Taylor, B. J.↗
NASA NTRS1983

Weighted least squares formulas for multiple Doppler radar analysis

An algorithm is developed for the analysis of multiple Doppler radar data in meteorological applications. The algorithm is based on the least squares linear solutions for the variable parameters of a local particle velocity field. The computational sequence for the algorithm is described, and some factors influencing the covariance of Doppler measurement errors are discussed.

Wilson, F. W., Jr.↗
NASA NTRS1984

Analysis of cure in composites processing

Finite element analysis is a general numerical tool for solving the field equations of engineering practice, and this paper demonstrates its use in modeling the nonisothermal cure of pultruded composite material. A very simple grid is used in this case to model a narrow strip of material, and this grid is then solved using a time-stepping transient algorithm to simulate the passage of the strip along the pultruder die. As time proceeds, heat is conducted into the strip from the heated boundaries at the die walls, and cure proceeds at a rate dependent on the local temperature. The computer model can be used to minimize the time needed for sufficient cure, and helps avoid such processing errors as undercure or thermal degradation.

Aylward, L.↗
NASA NTRS1987

Some plane curvature approximations

An analytical technique is developed to estimate (with second-order accuracy) the curvature of a sufficiently smooth plane curve defined in finite form. The derivation of the approximations from local information is explained in detail; the continuity and invariance of the estimates under translation and rotation are demonstrated; and examples, error estimates, and a broken-line extension are presented. The suitability of the present technique for computer implementation is indicated.

Mjolsness, R. C.↗
NASA NTRS1992

Optical Phase-Locked Loop For Optical Communication

Experimental apparatus includes two diode-pumped solid-state lasers of non-planar-ring-oscillator type, one represents the transmitting oscillator, other local oscillator in receiver. Output of transmitting oscillator is amplitude-modulated with pulse-position-modulated data stream. Phase-error variance of less than 0.05 mrad(Sup 2) achieved with relatively-narrow-band loop. Applications include free-space and fiber-optic communications, navigation, and scientific instrumentation in which receivers are required to track phases of transmitted signals.

Win, Moe Z.↗
NASA NTRS1992

Terrain effects on backscattering coefficients derived from multifrequency, polarimetric SAR data

A set of multidate, multilook angle polarimetric SAR data, acquired in Pennsylvania during July 1990 was recorded to determine the effect of local incidence angle. Cosine-based and polynomial models are found to be equally good for correcting SAR data for local incidence angle effects. A modified approach, considering the correction factor as additive rather than multiplicative, gave better results. The standard error in the estimation of soil moisture improves from 8.1 to 5.8 after applying corrections to incidence angle effects.

Rao, K. S.↗
NASA NTRS1993

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Carpenter, Mark H.↗
NASA NTRS1993

Techniques and applications of SAR interferometry for ERS-1

The ERS-1 Synthetic Aperture Radar (SAR) demonstrated that it is possible to measure high resolution topography over large areas using interferometry with repeat orbit data sets. Given that the ERS-1 orbit is known with high precision, an automatic system for generation of interferograms is presented. Least squares estimation using ground control points provides an accurate method for determining the precise interferometric baseline. The system parameters which affect the accuracy of the Digital Elevation Models (DEM's) are errors in the interferometric baseline, decorrelation caused by baseline separation, thermal noise, and surface change. An adaptive filter based on the local interferometric coherence was developed to improve phase unwrapping of the interferogram. Final accuracies of the DEM's generated for single scene pairs in Alaska (U.S.) and Bonn (Germany) are on the order of 5 to 10 m.

Werner, Charles L.↗
NASA NTRS2013

MODIS 3km Aerosol Product: Algorithm and Global Perspective

After more than a decade of producing a nominal 10 km aerosol product based on the dark target method, the MODIS aerosol team will be releasing a nominal 3 km product as part of their Collection 6 release. The new product differs from the original 10 km product only in the manner in which reflectance pixels are ingested, organized and selected by the aerosol algorithm. Overall, the 3 km product closely mirrors the 10 km product. However, the finer resolution product is able to retrieve over ocean closer to islands and coastlines, and is better able to resolve fine aerosol features such as smoke plumes over both ocean and land. In some situations, it provides retrievals over entire regions that the 10 km product barely samples. In situations traditionally difficult for the dark target algorithm, such as over bright or urban surfaces the 3 km product introduces isolated spikes of artificially high aerosol optical depth (AOD) that the 10 km algorithm avoids. Over land, globally, the 3 km product appears to be 0.01 to 0.02 higher than the 10 km product, while over ocean, the 3 km algorithm is retrieving a proportionally greater number of very low aerosol loading situations. Based on collocations with ground-based observations for only six months, expected errors associated with the 3 km land product are determined to be greater than for the 10 km product: 0.05 0.25 AOD. Over ocean, the suggestion is for expected errors to be the same as the 10 km product: 0.03 0.05 AOD. The advantage of the product is on the local scale, which will require continued evaluation not addressed here. Nevertheless, the new 3 km product is expected to provide important information complementary to existing satellite-derived products and become an important tool for the aerosol community.

Remer, L. A.↗
NASA NTRS2016

Design and Analysis of Map Relative Localization for Access to Hazardous Landing Sites on Mars

Human and robotic planetary lander missions require accurate surface relative position knowledge to land near science targets or next to pre-deployed assets. In the absence of GPS, accurate position estimates can be obtained by automatically matching sensor data collected during descent to an on-board map. The Lander Vision System (LVS) that is being developed for Mars landing applications generates landmark matches in descent imagery and combines these with inertial data to estimate vehicle position, velocity and attitude. This paper describes recent LVS design work focused on making the map relative localization algorithms robust to challenging environmental conditions like bland terrain, appearance differences between the map and image and initial input state errors. Improved results are shown using data from a recent LVS field test campaign. This paper also fills a gap in analysis to date by assessing the performance of the LVS with data sets containing significant vertical motion including a complete data set from the Mars Science Laboratory mission, a Mars landing simulation, and field test data taken over multiple altitudes above the same scene. Accurate and robust performance is achieved for all data sets indicating that vertical motion does not play a significant role in position estimation performance.

Lander Vision System↗
NASA NTRSDate not supplied

Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory

One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.

Uncertainty Quantification↗
NASA NTRS2023

Distributed Ground Sensor Fusion Based Object Tracking for Autonomous Advanced Air Mobility Operations

Autonomous operations are a crucial aspect in the context of Advanced Air Mobility and other emerging aviation markets. In order to enable this autonomy, an accurate and detailed understanding of the positions of the various vehicles in the air is necessary. Full localization independent of on-board sensors makes the system suitable for noncooperative vehicles. This paper focuses on the object tracking part that relies on distributed ground-based sensor fusion, considering specific properties and limitations of different sensor types. Results show satisfactory performance in nominal scenarios with full coverage. Dropouts of individual sensors affect the accuracy of the tracking results, which agrees with expectations for partial coverage, when full localization is not achievable anymore. Finally, a study is performed to identify which parameters have the largest impact on the fit error.

Autonomous↗
NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗
NASA NTRS1972

Ogo 5 magnetic-field data near the earth's bow shock - A correlation with theory.

Magnetic-field data obtained in the earth's bow-shock region with a high-resolution triaxial fluxgate magnetometer aboard the Ogo 5 satellite have been correlated with a theory of Tidman and Northrop (1968). These authors have shown that either of two hypotheses about the nature of low-frequency magnetic waves could be invoked to explain previous observations. We have observed exponentially decaying upstream waves that are consistent with only one of these hypotheses. This observation allows use of the theory to infer the local shock velocity and frequency of driving currents within the shock. This method of finding the shock velocity is less sensitive to errors in the plasma parameters than is the method based on the Rankine-Hugoniot relations.

Guha, J. K.↗