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At least 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Simulation and analysis of differential global positioning system for civil helicopter operations

A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.

Denaro, R. P.↗
NASA NTRS1996

The Angular Power Spectrum of BATSE 3B Gamma-Ray Bursts

We compute the angular power spectrum C(sub l) from the BATSE 3B catalog of 1122 gamma-ray bursts and find no evidence for clustering on any scale. These constraints bridge the entire range from small scales (which probe source clustering and burst repetition) to the largest scales (which constrain possible anisotropics from the Galactic halo or from nearby cosmological large-scale structures). We develop an analysis technique that takes the angular position errors into account. For specific clustering or repetition models, strong upper limits can be obtained down to scales l approx. equal to 30, corresponding to a couple of degrees on the sky. The minimum-variance burst weighting that we employ is visualized graphically as an all-sky map in which each burst is smeared out by an amount corresponding to its position uncertainty. We also present separate bandpass-filtered sky maps for the quadrupole term and for the multipole ranges l = 3-10 and l = 11-30, so that the fluctuations on different angular scales can be inspected separately for visual features such as localized 'hot spots' or structures aligned with the Galactic plane. These filtered maps reveal no apparent deviations from isotropy.

Tegmark, Max↗
NASA NTRS2000

Comprehensive Evaluation of Attitude and Orbit Estimation Using Actual Earth Magnetic Field Data

A single, augmented Extended Kalman Filter (EKF), which simultaneously and autonomously estimates spacecraft attitude and orbit has been developed and successfully tested with real magnetometer and gyro data only. Because the earth magnetic field is a function of time and position, and because time is known quite precisely, the differences between the computed and measured magnetic field components, as measured by the magnetometers throughout the entire spacecraft orbit, are a function of both orbit and attitude errors. Thus, conceivably these differences could be used to estimate both orbit and attitude; an observability study validated this assumption. The results of testing the EKF with actual magnetometer and gyro data, from four satellites supported by the NASA Goddard Space Flight Center (GSFC) Guidance, Navigation, and Control Center, are presented and evaluated. They confirm the assumption that a single EKF can estimate both attitude and orbit when using gyros and magnetometers only.

Deutschmann, Julie K.↗
NASA NTRS2010

Phased Array Noise Source Localization Measurements Made on a Williams International FJ44 Engine

A 48-microphone planar phased array system was used to acquire noise source localization data on a full-scale Williams International FJ44 turbofan engine. Data were acquired with the array at three different locations relative to the engine, two on the side and one in front of the engine. At the two side locations the planar microphone array was parallel to the engine centerline; at the front location the array was perpendicular to the engine centerline. At each of the three locations, data were acquired at eleven different engine operating conditions ranging from engine idle to maximum (take off) speed. Data obtained with the array off to the side of the engine were spatially filtered to separate the inlet and nozzle noise. Tones occurring in the inlet and nozzle spectra were traced to the low and high speed spools within the engine. The phased array data indicate that the Inflow Control Device (ICD) used during this test was not acoustically transparent; instead, some of the noise emanating from the inlet reflected off of the inlet lip of the ICD. This reflection is a source of error for far field noise measurements made during the test. The data also indicate that a total temperature rake in the inlet of the engine is a source of fan noise.

Podboy, Gary G.↗
DOE OSTI2020

Automated fault detection of residential air-conditioning systems using thermostat drive cycles

Residential air conditioning equipment comprises a significant portion of the total energy consumption of a home. Unfortunately, air-conditioning systems can be susceptible to faulty operation either from installation errors or faults that accrue over the equipment’s lifetime. This paper presents a novel automated fault detection algorithm for residential air-conditioning systems that can alert the homeowner of the presence of these faults. The proposed algorithm utilizes only the home’s thermostat and outside air temperature to perform automated fault detection over the course of the equipment’s lifetime, including immediately after installation. The algorithm uses an extended Kalman filter approach to identify a three-resistor, two-capacitor (3R2C) electrical equivalent thermodynamic model. The identified 3R2C model is used to predict cooling times during a testing period comprising of a series of thermostat drive-cycle experiments. We tested the algorithm on an EnergyPlus™ model of a typical residential building in Orlando, Florida. Duct faults, indoor airflow faults, and refrigerant undercharge faults were introduced into the building model one at a time. The algorithm was able to accurately determine duct-leak faults, 40% airflow faults, 40% undercharge faults, and no-fault cases with an accuracy of 70%, 77%, 82%, and 87%, respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navagation↗
NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

n/a↗
NASA NTRS1991

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.↗
NASA NTRS2002

Evaluation of the DAO Retrospective Data Assimilation System

We have developed and implemented a retrospective data assimilation system (RDAS) as an upgrade to the operational DAO/Terra data assimilation system. This formulation aims at improving analysis over filter analysis by the dynamically consistent incorporation of observation information past a given analysis time. The current implementation of the RDAS uses the adjoint of the tangent linear model of a simplified version of the Terra general circulation model and extensions to the physical-space statistical analysis system to propagate observation information back in time. The RDAS adopts the same assumptions of the regular data assimilation system, particularly, no explicit propagation of error covariances are involved therefore rendering a procedure that is computationally affordable. In this study, we show results of experiments conducted to investigate the performance of the 6-hour (lag-1) RDAS. Statistical results obtained over one month during a winter season indicate that the RDAS represents considerable improvement over the regular assimilation. Plans for implementation of the RDAS capability in our new finite-volume data assimilation system will also be presented at the time of the conference.

Zhu, Yanqiu↗
NASA NTRS1998

Clementine High Resolution Camera Mosaicking Project

This report constitutes the final report for NASA Contract NASW-5054. This project processed Clementine I high resolution images of the Moon, mosaicked these images together, and created a 22-disk set of compact disk read-only memory (CD-ROM) volumes. The mosaics were produced through semi-automated registration and calibration of the high resolution (HiRes) camera's data against the geometrically and photometrically controlled Ultraviolet/Visible (UV/Vis) Basemap Mosaic produced by the US Geological Survey (USGS). The HiRes mosaics were compiled from non-uniformity corrected, 750 nanometer ("D") filter high resolution nadir-looking observations. The images were spatially warped using the sinusoidal equal-area projection at a scale of 20 m/pixel for sub-polar mosaics (below 80 deg. latitude) and using the stereographic projection at a scale of 30 m/pixel for polar mosaics. Only images with emission angles less than approximately 50 were used. Images from non-mapping cross-track slews, which tended to have large SPICE errors, were generally omitted. The locations of the resulting image population were found to be offset from the UV/Vis basemap by up to 13 km (0.4 deg.). Geometric control was taken from the 100 m/pixel global and 150 m/pixel polar USGS Clementine Basemap Mosaics compiled from the 750 nm Ultraviolet/Visible Clementine imaging system. Radiometric calibration was achieved by removing the image nonuniformity dominated by the HiRes system's light intensifier. Also provided are offset and scale factors, achieved by a fit of the HiRes data to the corresponding photometrically calibrated UV/Vis basemap, that approximately transform the 8-bit HiRes data to photometric units. The sub-polar mosaics are divided into tiles that cover approximately 1.75 deg. of latitude and span the longitude range of the mosaicked frames. Images from a given orbit are map projected using the orbit's nominal central latitude. Polar mosaics are tiled into squares 2250 pixels on a side, which spans approximately 2.2 deg. Two mosaics are provided for each pole: one corresponding to data acquired while periapsis was in the south, the other while periapsis was in the north. The CD-ROMs also contain ancillary data files that support the HiRes mosaic. These files include browse images with UV/Vis context stored in a Joint Photographic Experts Group (JPEG) format, index files ('imgindx.tab' and 'srcindx.tab') that tabulate the contents of the CD, and documentation files.

Source record↗
NASA NTRS2013

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test ight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modi cations since its inception, and continues as a work-in-progress. This paper seeks to show the e orts made to-date in tuning the lter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. The results generally show Monte Carlo error performance bounded by the lter uncertainty for all phases of ight. Some future items of investigation are presented related to suspected anomalies in the trajectory truth reference le.

Holt, Greg N.↗
NASA NTRSDate not supplied

Towards Energy Scale Calibration and Drift Correction of TES Detectors for Athena X-IFU

The Athena X-Ray Integral Field Unit (X-IFU) comprises a 2376-pixel array of transition edge sensors (TES) read out with time-division multiplexing (TDM). X-IFU will provide spatially resolved, high-resolution spectroscopy (2.5 eV full-width-half-maximum up to 7 keV) over the energy range 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. The energy scale function maps the optimally filtered pulse height, in arbitrary engineering units, to real calibrated energy. Uncertainties in the calibration can result from imperfect fitting of the energy scale between the known calibration points. Furthermore, temporal changes in the TES operating environment, such as heat-sink temperature, magnetic field and bias voltage, can cause significant variations in the detector gain function over time. If not properly corrected, this can result in degradation of the energy resolution, and systematic errors in the absolute energy scale. The non-linear nature of TES detectors, coupled with the possibility of multiple simultaneously occurring sources of drift, can make effective corrections over the full bandpass of the instrument extremely challenging. Athena X-IFU will employ an on-board calibration source that provides known reference x-ray lines. This provides real-time monitoring of the gain stability of the detector system and information that can be used to correct for gain drifts. For X-IFU the baseline approach is to measure a series of calibration curves under different environmental conditions, which bound the expected drifts the instrument is predicted to see over the course of the mission. Using the information from the in-flight calibration source, these energy scale functions can be interpolated to generate a new corrected energy scale as a function of time. In this paper we discuss progress towards demonstrating that the X-IFU energy scale requirements can be met. We present measurements on ~ 200 pixels in a prototype X-IFU array read out with 8-column x 32-row TDM. We use a rotating target source containing 12 fluorescent targets to generate x-ray lines covering the energy range 4 keV (Sc-Kα) to 12 keV (Br-Kα). We present measurements of the non-linear energy scale function and show how variations in heat-sink temperature, TES bias voltage and magnetic field affect the shape of TES energy scale differently and introduce different residual gain errors over the bandpass. We explore different drift correction algorithms that use either a single or multiple referential lines to track and correct the gain from these various sources of drift. In addition to the pulse-height, the DC ‘baseline’ level of the TES can contain information about its bias conditions. Thus, we test a multi-parameter gain correction algorithm that attempts to incorporate both the pulse height and the additional baseline information into the algorithm.

Stephen J Smith↗
DOE OSTI2021

Laboratory and field studies of ice-nucleating particles from open-lot livestock facilities in Texas

Abstract. In this work, an abundance of ice-nucleating particles (INPs) from livestock facilities was studied through laboratory measurements from cloud-simulation chamber experiments and field investigation in the Texas Panhandle. Surface materials from two livestock facilities, one in the Texas Panhandle and another from McGregor, Texas, were selected as dust proxies for laboratory analyses. These two samples possessed different chemical and biological properties. A combination of aerosol interaction and dynamics in the atmosphere (AIDA) measurements and offline ice spectrometry was used to assess the immersion freezing mode ice nucleation ability and efficiency of these proxy samples at temperatures above −29 ∘C. A dynamic filter processing chamber was also used to complement the freezing efficiencies of submicron and supermicron particles collected from the AIDA chamber. For the field survey, periodic ambient particle sampling took place at four commercial livestock facilities from July 2017 to July 2019. INP concentrations of collected particles were measured using an offline freezing test system, and the data were acquired for temperatures between −5 and −25 ∘C. Our AIDA laboratory results showed that the freezing spectra of two livestock dust proxies exhibited higher freezing efficiency than previously studied soil dust samples at temperatures below −25 ∘C. Despite their differences in composition, the freezing efficiencies of both proxy livestock dust samples were comparable to each other. Our dynamic filter processing chamber results showed on average approximately 50 % supermicron size dominance in the INPs of both dust proxies. Thus, our laboratory findings suggest the importance of particle size in immersion freezing for these samples and that the size might be a more important factor for immersion freezing of livestock dust than the composition. From a 3-year field survey, we measured a high concentration of ambient INPs of 1171.6 ± 691.6 L−1 (average ± standard error) at −25 ∘C for aerosol particles collected at the downwind edges of livestock facilities. An obvious seasonal variation in INP concentration, peaking in summer, was observed, with the maximum at the same temperature exceeding 10 000 L−1 on 23 July 2018. The observed high INP concentrations suggest that a livestock facility is a substantial source of INPs. The INP concentration values from our field survey showed a strong correlation with measured particulate matter mass concentration, which supports the importance of size in ice nucleation of particles from livestock facilities.

58 GEOSCIENCES↗
NASA NTRS1979

Orbit/attitude estimation with LANDSAT Landmark data

The use of LANDSAT landmark data for orbit/attitude and camera bias estimation was studied. The preliminary results of these investigations are presented. The Goddard Trajectory Determination System (GTDS) error analysis capability was used to perform error analysis studies. A number of questions were addressed including parameter observability and sensitivity, effects on the solve-for parameter errors of data span, density, and distribution an a priori covariance weighting. The use of the GTDS differential correction capability with acutal landmark data was examined. The rms line and element observation residuals were studied as a function of the solve-for parameter set, a priori covariance weighting, force model, attitude model and data characteristics. Sample results are presented. Finally, verfication and preliminary system evaluation of the LANDSAT NAVPAK system for sequential (extended Kalman Filter) estimation of orbit, and camera bias parameters is given.

Hall, D. L.↗
NASA NTRS1992

Rate 8/9 coded 8-PSK system for downlink applications

An advanced Coded Trellis Modulation (CTM) System which achieves a 2 bits/s/Hz bandwidth efficiency at an information rate of 200 Mbit/s while minimizing satellite power requirements, was developed for downlink earth station applications. The CTM system employs a high-speed rate 8/9 convolutional code with Viterbi decoding and an 8-Phase Shift Keying (PSK) modem. The minimum Euclidean distance between the modulated waveforms corresponding to the information sequences are maximized in order to maximize the noise immunity of the system. Nyquist filters with a square-root of 40 percent roll-off are used at the transmit and receive sides of the modem in order to minimize intersymbol interference, adjacent channel interference, and distortion at the nonlinear satellite power amplifier. The use of a coded system here also minimizes the effects of co-channel interference. The developed performance of the hardware system was measured to achieve within 1.5 dB from theory at a bit error rate of 5 x 10(exp -7) over an additive white Gaussian noise channel.

Fang, Russell↗
NASA NTRS2017

CHOMPTT (CubeSat Handling of Multisystem Precision Timing Transfer): From Concept to Launch Pad

Here we present the evolution of a student satellite mission: CHOMPTT (CubeSat Handling of Multisystem Precision Time Transfer), from its original concept as a candidate for the University NanoSatellite Program 8 (UNP8), to a spacecraft ready for launch in Fall of 2017 on ELaNa XIX (Educational Launch of Nanosatellites). The 3U CubeSat houses a 1 kg, 1U OPTI (Optical Precision Timing Instrument) payload, designed and built at the University of Florida, and a 1.5U EDSNNODeS-derived bus from NASA Ames Research Center. The OPTI payload comprises of: 1) a supervisor board that handles payload data, power regulation, and mode settings, 2) an optics assembly of six 1 cm retroreflectors and four laser beacon diodes for ground-tracking; and 3) two fully redundant timing channels, each consisting of: a chip-scale atomic clock, a microprocessor with clock counter, a picosecond event timer, and an avalanche photodetector (APD) with band-pass filter. Several iterations of OPTI have been developed, tested, and designed to achieve its current functionality and design a laboratory breadboard design, a 1.5U high altitude balloon design, engineering unit design, and its current flight unit design. In-lab testing of the current OPTI design indicates a short-term precision of 100 ps, equivalent to a range accuracy of 3 cm necessary to achieve our primary objective of 200 ps time transfer error, and a long-term timing accuracy of 20 ns over one orbit (1.5 hours). After the spacecraft reaches its nominal 500 km orbit at a 85 degree inclination, an experimental laser ranging facility at Kennedy Space Center in Florida, will track and emit 1064 nm nanosecond optical pulses at the CHOMPTT spacecraft. The laser pulses will then reflect off the retroreflector array mounted on the nadir face of CHOMPTT, and return the pulse to the laser ranging facility where the laser ranging facility will record the round-trip duration of the laser pulses. At the same time the pulse arrives at the spacecraft and is reflected by the array, an APD will record the arrival time of the pulses at the nanosatellite. By comparing the arrival of the pulse at the CubeSat and the duration of the round-trip of the laser pulse, the clock discrepancy between the ground and CubeSat atomic clocks can be determined, in addition to the CubeSats range from the facility. The design and verification of the flight version of CHOMPTT will be reviewed and an overview of the lifetime development and progression of CHOMPTT from the inception to launch pad will be presented.

CHOMPTT↗
DOE OSTI2026

A Physics-Based Digital Twin for Wave Elevation and Seabed Moment Estimation of Offshore Monopiles: Preprint

In this work, we present a proof of concept of a physics-based digital twin for a monopile structure (with overhead inertia) subjected to wave loading. The digital twin is formulated using reduced-order models derived from first principles and combined with a Kalman filter for state estimation. The proposed framework estimates the monopile top motion, the wave elevation, and the section forces and moments along the pile using primarily acceleration measurements at the monopile top. Key innovations include the use of a hydrodynamic shape function to represent distributed wave loading in a compact and computationally efficient manner, and the introduction of a shaping filter to augment the state-space with wave kinematics. Synthetic measurement data are generated using OpenFAST and used as a reference to assess the performance of the digital twin. Results demonstrate that the wave elevation can be accurately reconstructed without direct sea-state measurements as long as the wave regime is inertia-dominated. Under the ideal tested conditions, the total hydrodynamic force and sea-bed bending moment are estimated with relative errors on the order of 1% and correlation coefficients exceeding 96%. Future work will evaluate the estimator's performance under operational uncertainties and more complex loading conditions.

17 WIND ENERGY↗
NASA NTRS2003

A New Objective Technique for Verifying Mesoscale Numerical Weather Prediction Models

This report presents a new objective technique to verify predictions of the sea-breeze phenomenon over east-central Florida by the Regional Atmospheric Modeling System (RAMS) mesoscale numerical weather prediction (NWP) model. The Contour Error Map (CEM) technique identifies sea-breeze transition times in objectively-analyzed grids of observed and forecast wind, verifies the forecast sea-breeze transition times against the observed times, and computes the mean post-sea breeze wind direction and speed to compare the observed and forecast winds behind the sea-breeze front. The CEM technique is superior to traditional objective verification techniques and previously-used subjective verification methodologies because: It is automated, requiring little manual intervention, It accounts for both spatial and temporal scales and variations, It accurately identifies and verifies the sea-breeze transition times, and It provides verification contour maps and simple statistical parameters for easy interpretation. The CEM uses a parallel lowpass boxcar filter and a high-order bandpass filter to identify the sea-breeze transition times in the observed and model grid points. Once the transition times are identified, CEM fits a Gaussian histogram function to the actual histogram of transition time differences between the model and observations. The fitted parameters of the Gaussian function subsequently explain the timing bias and variance of the timing differences across the valid comparison domain. Once the transition times are all identified at each grid point, the CEM computes the mean wind direction and speed during the remainder of the day for all times and grid points after the sea-breeze transition time. The CEM technique performed quite well when compared to independent meteorological assessments of the sea-breeze transition times and results from a previously published subjective evaluation. The algorithm correctly identified a forecast or observed sea-breeze occurrence or absence 93% of the time during the two- month evaluation period from July and August 2000. Nearly all failures in CEM were the result of complex precipitation features (observed or forecast) that contaminated the wind field, resulting in a false identification of a sea-breeze transition. A qualitative comparison between the CEM timing errors and the subjectively determined observed and forecast transition times indicate that the algorithm performed very well overall. Most discrepancies between the CEM results and the subjective analysis were again caused by observed or forecast areas of precipitation that led to complex wind patterns. The CEM also failed on a day when the observed sea- breeze transition affected only a very small portion of the verification domain. Based on the results of CEM, the RAMS tended to predict the onset and movement of the sea-breeze transition too early and/or quickly. The domain-wide timing biases provided by CEM indicated an early bias on 30 out of 37 days when both an observed and forecast sea breeze occurred over the same portions of the analysis domain. These results are consistent with previous subjective verifications of the RAMS sea breeze predictions. A comparison of the mean post-sea breeze winds indicate that RAMS has a positive wind-speed bias for .all days, which is also consistent with the early bias in the sea-breeze transition time since the higher wind speeds resulted in a faster inland penetration of the sea breeze compared to reality.

Case, Jonathan L.↗