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NASA NTRS2011

A Collisional Algorithm for Modeling Circumstellar Debris Disks

Many planetary systems harbor circumstellar disks of dust and planetesimals thought to be debris left over from planet formation. These debris disks exhibit a range of morphological features which can arise from the gravitational perturbations of planets. Accurate models of these features, accounting for the interactions of the particles in a disk with each other and with whatever planets they contain, can act as signposts for planets in debris disks that otherwise could not be detected. Such models can also constrain the planet's mass and orbital parameters. Current models for many disks consider the gravitational and radiative effects of the star and planets on the disk, but neglect the morphological consequences of collisional interactions between the planetesimals. Many observed disk features are not satisfactorily explained by the current generation of models. I am developing a new kind of debris disk model that considers both the gravitational shaping of the disk by planets and the inelastic collisions between particles. I will use a hybrid N-body integrator to numerically solve the equations of motion for the particles and planets in the disk. To include the collisional effects, I begin with an algorithm that tests for collisions at each step of the orbit integration and readjusts the velocities of colliding particles. I am adapting this algorithm to the problem at hand by allowing each particle to represent a "swarm" of planetesimals with a range of masses. When the algorithm detects an encounter between swarms, two or three swarms are produced to approximate the range of possible trajectories of the daughter planetesimals. Here I present preliminary results from my collisional algorithm.

Nesvold, Erika↗
NASA NTRS2011

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗
NASA NTRS2012

The Aquarius Salinity Retrieval Algorithm: Early Results

The Aquarius L-band radiometer/scatterometer system is designed to provide monthly salinity maps at 150 km spatial scale to a 0.2 psu accuracy. The sensor was launched on June 10, 2011, aboard the Argentine CONAE SAC-D spacecraft. The L-band radiometers and the scatterometer have been taking science data observations since August 25, 2011. The first part of this presentation gives an overview over the Aquarius salinity retrieval algorithm. The instrument calibration converts Aquarius radiometer counts into antenna temperatures (TA). The salinity retrieval algorithm converts those TA into brightness temperatures (TB) at a flat ocean surface. As a first step, contributions arising from the intrusion of solar, lunar and galactic radiation are subtracted. The antenna pattern correction (APC) removes the effects of cross-polarization contamination and spillover. The Aquarius radiometer measures the 3rd Stokes parameter in addition to vertical (v) and horizontal (h) polarizations, which allows for an easy removal of ionospheric Faraday rotation. The atmospheric absorption at L-band is almost entirely due to O2, which can be calculated based on auxiliary input fields from numerical weather prediction models and then successively removed from the TB. The final step in the TA to TB conversion is the correction for the roughness of the sea surface due to wind. This is based on the radar backscatter measurements by the scatterometer. The TB of the flat ocean surface can now be matched to a salinity value using a surface emission model that is based on a model for the dielectric constant of sea water and an auxiliary field for the sea surface temperature. In the current processing (as of writing this abstract) only v-pol TB are used for this last process and NCEP winds are used for the roughness correction. Before the salinity algorithm can be operationally implemented and its accuracy assessed by comparing versus in situ measurements, an extensive calibration and validation (cal/val) activity needs to be completed. This is necessary in order to tune the inputs to the algorithm and remove biases that arise due to the instrument calibration, foremost the values of the noise diode injection temperatures and the losses that occur in the feedhorns. This is the subject of the second part of our presentation. The basic tool is to analyze the observed difference between the Aquarius measured TA and an expected TA that is computed from a reference salinity field. It is also necessary to derive a relation between the scatterometer backscatter measurements and the radiometer emissivity that is induced by surface winds. In order to do this we collocate Aquarius radiometer and scatterometer measurements with wind speed retrievals from the WindSat and SSMIS F17 microwave radiometers. Both of these satellites fly in orbits that have the same equatorial ascending crossing time (6 pm) as the Aquarius/SAC-D observatory. Rain retrievals from WindSat and SSMIS F 17 can be used to remove Aquarius observations that are rain contaminated. A byproduct of this analysis is a prediction for the wind-induced sea surface emissivity at L-band.

Meissner, Thomas↗
NASA NTRS2012

Onboard Science and Applications Algorithm for Hyperspectral Data Reduction

An onboard processing mission concept is under development for a possible Direct Broadcast capability for the HyspIRI mission, a Hyperspectral remote sensing mission under consideration for launch in the next decade. The concept would intelligently spectrally and spatially subsample the data as well as generate science products onboard to enable return of key rapid response science and applications information despite limited downlink bandwidth. This rapid data delivery concept focuses on wildfires and volcanoes as primary applications, but also has applications to vegetation, coastal flooding, dust, and snow/ice applications. Operationally, the HyspIRI team would define a set of spatial regions of interest where specific algorithms would be executed. For example, known coastal areas would have certain products or bands downlinked, ocean areas might have other bands downlinked, and during fire seasons other areas would be processed for active fire detections. Ground operations would automatically generate the mission plans specifying the highest priority tasks executable within onboard computation, setup, and data downlink constraints. The spectral bands of the TIR (thermal infrared) instrument can accurately detect the thermal signature of fires and send down alerts, as well as the thermal and VSWIR (visible to short-wave infrared) data corresponding to the active fires. Active volcanism also produces a distinctive thermal signature that can be detected onboard to enable spatial subsampling. Onboard algorithms and ground-based algorithms suitable for onboard deployment are mature. On HyspIRI, the algorithm would perform a table-driven temperature inversion from several spectral TIR bands, and then trigger downlink of the entire spectrum for each of the hot pixels identified. Ocean and coastal applications include sea surface temperature (using a small spectral subset of TIR data, but requiring considerable ancillary data), and ocean color applications to track biological activity such as harmful algal blooms. Measuring surface water extent to track flooding is another rapid response product leveraging VSWIR spectral information.

Chien, Steve A.↗
NASA NTRS2011

Aerosol Retrieval and Atmospheric Correction Algorithms for EPIC

EPIC is a multi-spectral imager onboard planned Deep Space Climate ObserVatoRy (DSCOVR) designed for observations of the full illuminated disk of the Earth with high temporal and coarse spatial resolution (10 km) from Lagrangian L1 point. During the course of the day, EPIC will view the same Earth surface area in the full range of solar and view zenith angles at equator with fixed scattering angle near the backscattering direction. This talk will describe a new aerosol retrieval/atmospheric correction algorithm developed for EPIC and tested with EPIC Simulator data. This algorithm uses the time series approach and consists of two stages: the first stage is designed to periodically re-initialize the surface spectral bidirectional reflectance (BRF) on stable low AOD days. Such days can be selected based on the same measured reflectance between the morning and afternoon reciprocal view geometries of EPIC. On the second stage, the algorithm will monitor the diurnal cycle of aerosol optical depth and fine mode fraction based on the known spectral surface BRF. Testing of the developed algorithm with simulated EPIC data over continental USA showed a good accuracy of AOD retrievals (10-20%) except over very bright surfaces.

Wang, Yujie↗
NASA NTRS2012

An Algorithm for Detection of Ground and Canopy Cover in Micropulse Photon-Counting Lidar Altimeter Data in Preparation of the ICESat-2 Mission

The Ice, Cloud and Land Elevation Satellite-II (ICESat-2) mission has been selected by NASA as a Decadal Survey mission, to be launched in 2016. Mission objectives are to measure land ice elevation, sea ice freeboard/ thickness and changes in these variables and to collect measurements over vegetation that will facilitate determination of canopy height, with an accuracy that will allow prediction of future environmental changes and estimation of sea-level rise. The importance of the ICESat-2 project in estimation of biomass and carbon levels has increased substantially, following the recent cancellation of all other planned NASA missions with vegetation-surveying lidars. Two innovative components will characterize the ICESat-2 lidar: (1) Collection of elevation data by a multi-beam system and (2) application of micropulse lidar (photon counting) technology. A micropulse photon-counting altimeter yields clouds of discrete points, which result from returns of individual photons, and hence new data analysis techniques are required for elevation determination and association of returned points to reflectors of interest including canopy and ground in forested areas. The objective of this paper is to derive and validate an algorithm that allows detection of ground under dense canopy and identification of ground and canopy levels in simulated ICESat-2-type data. Data are based on airborne observations with a Sigma Space micropulse lidar and vary with respect to signal strength, noise levels, photon sampling options and other properties. A mathematical algorithm is developed, using spatial statistical and discrete mathematical concepts, including radial basis functions, density measures, geometrical anisotropy, eigenvectors and geostatistical classification parameters and hyperparameters. Validation shows that the algorithm works very well and that ground and canopy elevation, and hence canopy height, can be expected to be observable with a high accuracy during the ICESat-2 mission. A result relevant for instrument design is that even the two weaker beam classes considered can be expected to yield useful results for vegetation measurements (93.01-99.57% correctly selected points for a beam with expected return of 0.93 mean signals per shot (msp9) and 72.85% - 98.68% for 0.48 msp (msp4)). Resampling options affect results more than noise levels. The algorithm derived here is generally applicable for analysis of micropulse lidar altimeter data collected over forested areas as well as other surfaces, including land ice, sea ice and land surfaces.

Herzfeld, Ute C.↗
NASA NTRS2011

Development of a Real-Time Pulse Processing Algorithm for TES-Based X-Ray Microcalorimeters

We report here a real-time pulse processing algorithm for superconducting transition-edge sensor (TES) based x-ray microcalorimeters. TES-based. microca1orimeters offer ultra-high energy resolutions, but the small volume of each pixel requires that large arrays of identical microcalorimeter pixe1s be built to achieve sufficient detection efficiency. That in turn requires as much pulse processing as possible must be performed at the front end of readout electronics to avoid transferring large amounts of data to a host computer for post-processing. Therefore, a real-time pulse processing algorithm that not only can be implemented in the readout electronics but also achieve satisfactory energy resolutions is desired. We have developed an algorithm that can be easily implemented. in hardware. We then tested the algorithm offline using several data sets acquired with an 8 x 8 Goddard TES x-ray calorimeter array and 2x16 NIST time-division SQUID multiplexer. We obtained an average energy resolution of close to 3.0 eV at 6 keV for the multiplexed pixels while preserving over 99% of the events in the data sets.

Tan, Hui↗
NASA NTRS2012

Retrieving Atmospheric Temperature and Moisture Profiles from NPP CRIS/ATMS Sensors Using Crimss EDR Algorithm

The Joint Polar Satellite System (JPSS) is a U.S. National Oceanic and Atmospheric Administration (NOAA) mission in collaboration with the U.S. National Aeronautical Space Administration (NASA) and international partners. The NPP Cross-track Infrared Microwave Sounding Suite (CrIMSS) consists of the infrared (IR) Crosstrack Infrared Sounder (CrIS) and the microwave (MW) Advanced Technology Microwave Sounder (ATMS). The CrIS instrument is hyperspectral interferometer, which measures high spectral and spatial resolution upwelling infrared radiances. The ATMS is a 22-channel radiometer similar to Advanced Microwave Sounding Units (AMSU) A and B. It measures top of atmosphere MW upwelling radiation and provides capability of sounding below clouds. The CrIMSS Environmental Data Record (EDR) algorithm provides three EDRs, namely the atmospheric vertical temperature, moisture and pressure profiles (AVTP, AVMP and AVPP, respectively), with the lower tropospheric AVTP and the AVMP being JPSS Key Performance Parameters (KPPs). The operational CrIMSS EDR an algorithm was originally designed to run on large IBM computers with dedicated data management subsystem (DMS). We have ported the operational code to simple Linux systems by replacing DMS with appropriate interfaces. We also changed the interface of the operational code so that we can read data from both the CrIMSS science code and the operational code and be able to compare lookup tables, parameter files, and output results. The detail of the CrIMSS EDR algorithm is described in reference [1]. We will present results of testing the CrIMSS EDR operational algorithm using proxy data generated from the Infrared Atmospheric Sounding Interferometer (IASI) satellite data and from the NPP CrIS/ATMS data.

Liu, X.↗
NASA NTRS2012

Multi-Angle Implementation of Atmospheric Correction (MAIAC) Algorithm

Multi-Angle Implementation of Atmospheric Correction (MAIAC) is a new algorithm developed for MODIS. MAIAC uses a time series analysis and processing of groups of pixels to perform simultaneous retrievals of aerosol properties and surface bidirectional reflectance without typical assumptions about the surface. It is a generic algorithm which works over both dark and bright land surfaces, including deserts. MAIAC has an internal Cloud Mask, a dynamic land-water-snow classification and a surface change mask which allows it to flexibly choose processing path over different surfaces. A distinct feature of MAIAC is a high 1 km resolution of aerosol retrievals which is required in different applications including the air quality analysis. The novel features of MAIAC include the high quality cloud mask, discrimination of aerosol type, including biomass burning smoke and dust, and detection of surface change - all required for high quality aerosol retrievals. An overview of the algorithm, results of AERONET validation, and examples of comparison with MODIS Collection 5 aerosol product and Deep Blue algorithm for different parts of the world, will be presented.

Lyapustin, A.↗
NASA NTRS2012

The Algorithm Theoretical Basis Document for the GLAS Atmospheric Data Products

The purpose of this document is to present a detailed description of the algorithm theoretical basis for each of the GLAS data products. This will be the final version of this document. The algorithms were initially designed and written based on the authors prior experience with high altitude lidar data on systems such as the Cloud and Aerosol Lidar System (CALS) and the Cloud Physics Lidar (CPL), both of which fly on the NASA ER-2 high altitude aircraft. These lidar systems have been employed in many field experiments around the world and algorithms have been developed to analyze these data for a number of atmospheric parameters. CALS data have been analyzed for cloud top height, thin cloud optical depth, cirrus cloud emittance (Spinhirne and Hart, 1990) and boundary layer depth (Palm and Spinhirne, 1987, 1998). The successor to CALS, the CPL, has also been extensively deployed in field missions since 2000 including the validation of GLAS and CALIPSO. The CALS and early CPL data sets also served as the basis for the construction of simulated GLAS data sets which were then used to develop and test the GLAS analysis algorithms.

Palm, Stephen P.↗
NASA NTRS2013

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. In order to become a viable option for operational forecasters to incorporate into their severe storm monitoring process, the total lightning jump must be placed into the framework of several severe storm conceptual models (e.g., radar evolution, storm morphology) which forecasters have built through training and experience. Thus, one of the goals of this study is to examine and relate the lightning jump concept to often used radar parameters (e.g., dBZ vertical structure, VIL, MESH, MESO/shear) in the warning environment. Tying lightning trends and lightning jump occurrences to these radar based parameters will provide forecasters with an additional tool that they can use to build an accurate realtime depiction as to what is going on in a given environment. Furthermore, relating the lightning jump concept to these parameters could also increase confidence in a warning decision they have already made, help tip the scales on whether or not to warn on a given storm, or to draw the forecaster s attention to a particular storm that is rapidly developing. Furthermore the lightning information will add vital storm scale information in regions that are not well covered by radar, or when radar failures occur. The physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation -sized ice mass, etc.; however, very few have related the concept of the lightning jump and manifestation of severe weather to storm dynamics and microphysics using multi -Doppler and polarimetric radar techniques. Therefore, the second half of this study will combine the lightning jump algorithm and these radar techniques in order to place the lightning jump concept into a physical and dynamical framework. This analysis includes examining such parameters as mixed phase precipitation volume, charging zone, updraft strength and updraft volume. Such a study should provide increased understanding of and confidence in the strengths and limitations of the lightning jump algorithm in the storm warning process.

Schultz, Christopher J.↗
NASA NTRS2013

Data Compression Algorithm Architecture for Large Depth-of-Field Particle Image Velocimeters

A large depth-of-field particle image velocimeter (PIV) is designed to characterize dynamic dust environments on planetary surfaces. This instrument detects lofted dust particles, and senses the number of particles per unit volume, measuring their sizes, velocities (both speed and direction), and shape factors when the particles are large. To measure these particle characteristics in-flight, the instrument gathers two-dimensional image data at a high frame rate, typically >4,000 Hz, generating large amounts of data for every second of operation, approximately 6 GB/s. To characterize a planetary dust environment that is dynamic, the instrument would have to operate for at least several minutes during an observation period, easily producing more than a terabyte of data per observation. Given current technology, this amount of data would be very difficult to store onboard a spacecraft, and downlink to Earth. Since 2007, innovators have been developing an autonomous image analysis algorithm architecture for the PIV instrument to greatly reduce the amount of data that it has to store and downlink. The algorithm analyzes PIV images and automatically reduces the image information down to only the particle measurement data that is of interest, reducing the amount of data that is handled by more than 10(exp 3). The state of development for this innovation is now fairly mature, with a functional algorithm architecture, along with several key pieces of algorithm logic, that has been proven through field test data acquired with a proof-of-concept PIV instrument.

Bos, Brent↗
NASA NTRS2013

Vectorized Rebinning Algorithm for Fast Data Down-Sampling

A vectorized rebinning (down-sampling) algorithm, applicable to N-dimensional data sets, has been developed that offers a significant reduction in computer run time when compared to conventional rebinning algorithms. For clarity, a two-dimensional version of the algorithm is discussed to illustrate some specific details of the algorithm content, and using the language of image processing, 2D data will be referred to as "images," and each value in an image as a "pixel." The new approach is fully vectorized, i.e., the down-sampling procedure is done as a single step over all image rows, and then as a single step over all image columns. Data rebinning (or down-sampling) is a procedure that uses a discretely sampled N-dimensional data set to create a representation of the same data, but with fewer discrete samples. Such data down-sampling is fundamental to digital signal processing, e.g., for data compression applications.

Dean, Bruce↗
NASA NTRS2013

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Sankararaman, Shankar↗
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 NTRS2013

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

EnKR↗
NASA NTRS2014

Development and Implementation of a Hardware In-the-Loop Test Bed for Unmanned Aerial Vehicle Control Algorithms

Successful prediction and management of battery life using prognostic algorithms through ground and flight tests is important for performance evaluation of electrical systems. This paper details the design of test beds suitable for replicating loading profiles that would be encountered in deployed electrical systems. The test bed data will be used to develop and validate prognostic algorithms for predicting battery discharge time and battery failure time. Online battery prognostic algorithms will enable health management strategies. The platform used for algorithm demonstration is the EDGE 540T electric unmanned aerial vehicle (UAV). The fully designed test beds developed and detailed in this paper can be used to conduct battery life tests by controlling current and recording voltage and temperature to develop a model that makes a prediction of end-of-charge and end-of-life of the system based on rapid state of health (SOH) assessment.

Battery Testbed↗
NASA NTRS2012

A Trajectory Algorithm to Support En Route and Terminal Area Self-Spacing Concepts: Third Revision

This document describes an algorithm for the generation of a four dimensional trajectory. Input data for this algorithm are similar to an augmented Standard Terminal Arrival (STAR) with the augmentation in the form of altitude or speed crossing restrictions at waypoints on the route. This version of the algorithm accommodates constant radius turns and cruise altitude waypoints with calibrated airspeed, versus Mach, constraints. The algorithm calculates the altitude, speed, along path distance, and along path time for each waypoint. Wind data at each of these waypoints are also used for the calculation of ground speed and turn radius.

Abbott, Terence S.↗