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At least 577 records · Page 32

Proof-of-Concept of a Networked Validation Environment for Distributed Air/Ground NextGen Concepts

The National Airspace System (NAS) must be improved to increase capacity, reduce flight delays, and minimize environmental impacts of air travel. NASA has been tasked with aiding the Federal Aviation Administration (FAA) in NAS modernization. Automatic Dependent Surveillance-Broadcast (ADS-B) is an enabling technology that is fundamental to realization of the Next Generation Air Transportation System (NextGen). Despite the 2020 FAA mandate requiring ADS-B Out equipage, airspace users are lacking incentives to equip with the requisite ADS-B avionics. A need exists to validate in flight tests advanced concepts of operation (ConOps) that rely on ADS-B and other data links without requiring costly equipage. A potential solution is presented in this paper. It is possible to emulate future data link capabilities using the existing in-flight Internet and reduced-cost test equipment. To establish proof-of-concept, a high-fidelity traffic operations simulation was modified to include a module that simulated Internet transmission of ADS-B messages. An advanced NASA ConOp, Flight Deck Interval Management (FIM), was used to evaluate technical feasibility. A preliminary assessment of the effects of latency and dropout rate on FIM was performed. Flight hardware that would be used by proposed test environment was connected to the simulation so that data transfer from aircraft systems to test equipment could be verified. The results indicate that the FIM ConOp, and therefore, many other advanced ConOps with equal or lesser response characteristics and data requirements, can be evaluated in flight using the proposed concept.

Grisham, James↗

Feasibility of a Networked Air Traffic Infrastructure Validation Environment for Advanced NextGen Concepts

Abstract-Next Generation Air Transportation System (NextGen) applications reliant upon aircraft data links such as Automatic Dependent Surveillance-Broadcast (ADS-B) offer a sweeping modernization of the National Airspace System (NAS), but the aviation stakeholder community has not yet established a positive business case for equipage and message content standards remain in flux. It is necessary to transition promising Air Traffic Management (ATM) Concepts of Operations (ConOps) from simulation environments to full-scale flight tests in order to validate user benefits and solidify message standards. However, flight tests are prohibitively expensive and message standards for Commercial-off-the-Shelf (COTS) systems cannot support many advanced ConOps. It is therefore proposed to simulate future aircraft surveillance and communications equipage and employ an existing commercial data link to exchange data during dedicated flight tests. This capability, referred to as the Networked Air Traffic Infrastructure Validation Environment (NATIVE), would emulate aircraft data links such as ADS-B using in-flight Internet and easily-installed test equipment. By utilizing low-cost equipment that is easy to install and certify for testing, advanced ATM ConOps can be validated, message content standards can be solidified, and new standards can be established through full-scale flight trials without necessary or expensive equipage or extensive flight test preparation. This paper presents results of a feasibility study of the NATIVE concept. To determine requirements, six NATIVE design configurations were developed for two NASA ConOps that rely on ADS-B. The performance characteristics of three existing in-flight Internet services were investigated to determine whether performance is adequate to support the concept. Next, a study of requisite hardware and software was conducted to examine whether and how the NATIVE concept might be realized. Finally, to determine a business case, economic factors were evaluated and a preliminary cost-benefit analysis was performed.

McCormack, Michael J.↗

Fabrication Method for LOBSTER-Eye Optics in <110> Silicon

Soft x-ray optics can use narrow slots to direct x-rays into a desirable pattern on a focal plane. While square-pack, square-pore, slumped optics exist for this purpose, they are costly. Silicon (Si) is being examined as a possible low-cost replacement. A fabrication method was developed for narrow slots in <110> Si demonstrating the feasibility of stacked slot optics to replace micropores. Current micropore optics exist that have 20-micron-square pores on 26-micron pitch in glass with a depth of 1 mm and an extent of several square centimeters. Among several proposals to emulate the square pore optics are stacked slot chips with etched vertical slots. When the slots in the stack are positioned orthogonally to each other, the component will approach the soft x-ray focusing observed in the micropore optics. A specific improvement Si provides is that it can have narrower sidewalls between slots to permit greater throughput of x-rays through the optics. In general, Si can have more variation in slot geometry (width, length). Further, the sidewalls can be coated with high-Z materials to enhance reflection and potentially reduce the surface roughness of the reflecting surface. Narrow, close-packed deep slots in <110> Si have been produced using potassium hydroxide (KOH) etching and a patterned silicon nitride (SiN) mask. The achieved slot geometries have sufficient wall smoothness, as observed through scanning electron microscope (SEM) imaging, to enable evaluation of these slot plates as an optical element for soft x-rays. Etches of different angles to the crystal plane of Si were evaluated to identify a specific range of etch angles that will enable low undercut slots in the Si <110> material. These slots with the narrow sidewalls are demonstrated to several hundred microns in depth, and a technical path to 500-micron deep slots in a precision geometry of narrow, closepacked slots is feasible. Although intrinsic stress in ultrathin wall Si is observed, slots with walls approaching 1.5 microns can be achieved (a significant improvement over the 6-micron walls in micro - pore optics). The major advantages of this technique are the potential for higher x-ray throughout (due to narrow slot walls) and lower cost over the existing slumped micropore glass plates. KOH etching of smooth sidewalls has been demonstrated for many applications, suggesting its feasibility for implementation in x-ray optics. Si cannot be slumped like the micropore optics, so the focusing will be achieved with millimeter-scale slot plates that populate a spherical dome. The possibility for large-scale production exists for Si parts that is more difficult to achieve in micropore parts.

Chervenak, James↗

Understanding Crew Decision-Making in the Presence of Complexity: A Flight Simulation Experiment

Crew decision making and response have long been leading causal and contributing factors associated with aircraft accidents. Further, it is anticipated that future aircraft and operational environments will increase exposure to risks related to these factors if proactive steps are not taken to account for ever-increasing complexity. A flight simulation study was designed to collect data to help in understanding how complexity can, or may, be manifest. More specifically, an experimental apparatus was constructed that allowed for manipulation of information complexity and uncertainty, while also manipulating operational complexity and uncertainty. Through these manipulations, and the aid of experienced airline pilots, several issues have been discovered, related most prominently to the influence of information content, quality, and management. Flight crews were immersed in an environment that included new operational complexities suggested for the future air transportation system as well as new technological complexities (e.g. electronic flight bags, expanded data link services, synthetic and enhanced vision systems, and interval management automation). In addition, a set of off-nominal situations were emulated. These included, for example, adverse weather conditions, traffic deviations, equipment failures, poor data quality, communication errors, and unexpected clearances, or changes to flight plans. Each situation was based on one or more reference events from past accidents or incidents, or on a similar case that had been used in previous developmental tests or studies. Over the course of the study, 10 twopilot airline crews participated, completing over 230 flights. Each flight consisted of an approach beginning at 10,000 ft. Based on the recorded data and pilot and research observations, preliminary results are presented regarding decision-making issues in the presence of the operational and technological complexities encountered during the flights.

Young, Steven D.↗

Three-Dimensional Normal Human Neutral Progenitor Tissue-Like Assemblies: A Model for Persistent Varicella-Zoster Virus Infection and Platform to Study Oxidate Stress and Damage in Multiple Hit Scenarios

The environment of space results in a multitude of challenges to the human physiology that present barriers to extended habitation and exploration. Over 40 years of investigation to define countermeasures to address space flight adaptation has left gaps in our knowledge regarding mitigation strategies partly due to the lack of investigative tools, monitoring strategies, and real time diagnostics to understand the central causative agent(s) responsible for physiologic adaptation and maintaining homeostasis. Spaceflight-adaptation syndrome is the combination of space environmental conditions and the synergistic reaction of the human physiology. Our work addresses the role of oxidative stress and damage (OSaD) as a negative and contributing Risk Factor (RF) in the following areas of combined spaceflight related dysregulation: i) radiation induced cellular damage [1], [2] ii) immune impacts and the inflammatory response [3], [4] and iii) varicella zoster virus (VZV) reactivation [5]. Varicella-zoster (VZV)/Chicken Pox virus is a neurotropic human alphaherpes virus resulting in varicella upon primary infection, suppressed by the immune system becomes latent in ganglionic neurons, and reactivates under stress events to re-express in zoster and possibly shingles. Our laboratory has developed a complex three-dimensional (3D) normal human neural tissue model that emulates several characteristics of the human trigeminal ganglia (TG) and allows the study of combinatorial experimentation which addresses, simultaneously, OSaD associated with Spaceflight adaptation and habitation [6]. By combining the RFs of microgravity, radiation, and viral infection we will demonstrate that living in the space environment leads to significant physiological consequences for the peripheral and subsequently the central nervous system (PNS, CNS) associated with OSaD generation and consequentially endangers long-duration and exploration-class missions.

Goodwin, Thomas J.↗

Calibration of International Space Station (ISS) Node 1 Vibro-Acoustic Model-Report 2

Reported here is the capability of the Energy Finite Element Method (E-FEM) to predict the vibro-acoustic sound fields within the International Space Station (ISS) Node 1 and to compare the results with simulated leak sounds. A series of electronically generated structural ultrasonic noise sources were created in the pressure wall to emulate leak signals at different locations of the Node 1 STA module during its period of storage at Stennis Space Center (SSC). The exact sound source profiles created within the pressure wall at the source were unknown, but were estimated from the closest sensor measurement. The E-FEM method represents a reverberant sound field calculation, and of importance to this application is the requirement to correctly handle the direct field effect of the sound generation. It was also important to be able to compute the sound energy fields in the ultrasonic frequency range. This report demonstrates the capability of this technology as applied to this type of application.

Zhang, Weiguo↗

Microhard MHX 2420 Orbital Performance Evaluation Using RT Logic T400CS

A major upfront cost of building low cost Nanosatellites is the communications sub-system. Most radios built for space missions cost over $4,000 per unit. This exceeds many budgets. One possible cost effective solution is the Microhard MHX2420, a commercial off-the-shelf transceiver with a unit cost under $1000. This paper aims to support the Nanosatellite community seeking an inexpensive radio by characterizing Microhard's performance envelope. Though not intended for space operations, the ability to test edge cases and increase average data transfer speeds through optimization positions this radio as a solution for Nanosatellite communications by expanding usage to include more missions. The second objective of this paper is to test and verify the optimal radio settings for the most common cases to improve downlinking. All tests were conducted with the aid of the RT Logic T400CS, a hardware-in-the-loop channel simulator designed to emulate real-world radio frequency (RF) link effects. This study provides recommended settings to optimize the downlink speed as well as the environmental parameters that cause the link to fail.

Microhard MHX 2420↗

Live Virtual Constructive Distributed Test Environment Characterization Report

This report documents message latencies observed over various Live, Virtual, Constructive, (LVC) simulation environment configurations designed to emulate possible system architectures for the Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS) Project integrated tests. For each configuration, four scenarios with progressively increasing air traffic loads were used to determine system throughput and bandwidth impacts on message latency.

UAS↗

Water Based Phase Change Material Heat Exchanger Development

In a cyclical heat load environment such as low Lunar orbit, a spacecraft’s radiators are not sized to reject the full heat load requirement. Traditionally, a supplemental heat rejection device (SHReD) such as an evaporator or sublimator is used to act as a “topper” to meet the additional heat rejection demands. Utilizing a Phase Change Material (PCM) heat exchanger (HX) as a SHReD provides an attractive alternative to evaporators and sublimators as PCM HXs do not use a consumable, thereby leading to reduced launch mass and volume requirements. Studies conducted in this paper investigate utilizing water’s high latent heat of formation as a PCM, as opposed to traditional waxes, and corresponding complications surrounding freezing water in an enclosed volume. Work highlighted in this study is primarily visual and includes understanding ice formation, freeze front propagation, and the solidification process of water/ice. Various test coupons were constructed of copper to emulate the interstitial pin configuration (to aid in conduction) of the proposed water PCM HX design. Construction of a prototypic HX was also completed in which a flexible bladder material and interstitial pin configurations were tested. Additionally, a microgravity flight was conducted where three copper test articles were frozen continuously during microgravity and 2-g periods and individual water droplets were frozen during microgravity.

Hansen, Scott W.↗

Review of Ground Systems Development and Operations (GSDO) Tools for Verifying Command and Control Software

The Exploration Systems Development (ESD) Standing Review Board (SRB) requested the NASA Engineering and Safety Center (NESC) conduct an independent review of the plan developed by Ground Systems Development and Operations (GSDO) for identifying models and emulators to create a tool(s) to verify their command and control software. The NESC was requested to identify any issues or weaknesses in the GSDO plan. This document contains the outcome of the NESC review.

Aguilar, Michael L.↗

NASA's Optical Measurement Program 2014

The Optical Measurements Group (OMG) within the NASA Orbital Debris Program Office (ODPO) addresses U.S. National Space Policy goals by monitoring and characterizing debris. Since 2001, the OMG has used the Michigan Orbital Debris Survey Telescope (MODEST) at Cerro Tololo Inter-American Observatory (CTIO) in Chile for general orbital debris survey. The 0.6-m Schmidt MODEST provides calibrated astronomical data of GEO targets, both catalogued and uncatalogued debris, with excellent image quality. The data are utilized by the ODPO modeling group and are included in the Orbital Debris Engineering Model (ORDEM) v. 3.0. MODEST and the CTIO/SMARTS (Small and Moderate Aperture Research Telescope System) 0.9 m both acquire filter photometric data, as well as synchronously observing targets in selected optical filters. This information provides data used in material composition studies as well as longer orbital arc data on the same target, without time delay or bias from a rotating, tumbling, or spinning target. NASA, in collaboration with the University of Michigan, began using the twin 6.5-m Magellan telescopes at Las Campanas Observatory in Chile for deep imaging (Baade) and spectroscopic data (Clay) in 2011. Through the data acquired on Baade, debris have been detected that are ~3 magnitudes fainter than detections with MODEST, while the data from Clay provide better resolved information used in material characterization analyses via selected bandpasses. To better characterize and model optical data, the Optical Measurements Center (OMC) at NASA/JSC has been in operation since 2005, resulting in a database of comparison laboratory data. The OMC is designed to emulate illumination conditions in space using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. Lastly, the OMG is building the Meter Class Autonomous Telescope (MCAT) at Ascension Island. The 1.3-m telescope is designed to observe GEO and LEO targets, using a modified Ritchey-Chrétien configuration on a double horseshoe equatorial mount to allow tracking objects at LEO rates through the dome's keyhole at zenith. Through the data collection techniques employed at these unique facilities, NASA's ODPO has developed a multi-faceted approach to characterize the orbital debris risk to satellites in various altitudes and provide material characterization of debris via photometric and spectroscopic measurements. Ultimately, the data are used in conjunction with in-situ and radar measurements to provide accurate data for models of our space environment and service spacecraft risk assessment.

Cowardin, H.↗

NASA's Optical Measurement Program 2014

The Optical Measurements Group (OMG) within the NASA Orbital Debris Program Office (ODPO) addresses U.S. National Space Policy goals by monitoring and characterizing debris. Since 2001, the OMG has used the Michigan Orbital Debris Survey Telescope (MODEST) at Cerro Tololo Inter-American Observatory (CTIO) in Chile for general orbital debris surveys. The 0.6-m Schmidt MODEST provides calibrated astronomical data of GEO targets, both catalogued and uncatalogued debris, with excellent image quality. The data are utilized by the ODPO modeling group and are included in the Orbital Debris Engineering Model (ORDEM) v. 3.0. MODEST and the CTIO/SMARTS (Small and Moderate Aperture Research Telescope System) 0.9 m are both employed to acquire filter photometry data as well as synchronously observe targets in selected optical filters. Obtaining data synchronously yields data for material composition studies as well as longer orbital arc data on the same target without time delay or bias from a rotating, tumbling, or spinning target. Observations of GEO orbital debris using the twin 6.5-m Magellan telescopes at Las Campanas Observatory in Chile for deep imaging (Baade) and spectroscopic data (Clay) began in 2011. Through the data acquired on Baade, debris has been detected that reaches approx. 3 magnitudes fainter than detections with MODEST, while the spectral data from Clay provide better resolved information used in material characterization analyses. To better characterize and model optical data, the Optical Measurements Center (OMC) at NASA/JSC has been in operation since 2005, resulting in a database of comparison laboratory data. The OMC is designed to emulate illumination conditions in space using equipment and techniques that parallel telescopic observations and sourcetarget- sensor orientations. Lastly, the OMG is building the Meter Class Autonomous Telescope (MCAT) at Ascension Island. The 1.3-m telescope is designed to observe GEO and LEO targets, using a modified Ritchey-Chrétien configuration on a double horseshoe equatorial mount to allow tracking objects at LEO rates through the dome's keyhole at zenith. Through the data collection techniques employed at these unique facilities, NASA's ODPO has developed a multifaceted approach to characterize the orbital debris risk to satellites in various altitudes and provide insight leading toward material characterization of debris via photometric and spectroscopic measurements. Ultimately, the data are used in conjunction with in-situ and radar measurements to provide accurate data for models of our space environment and for facilitating spacecraft risk assessment.

Cowardin, H.↗

Three-Dimensional Normal Human Neural Progenitor Tissue-Like Assemblies: A Model for Persistent Varicell-Zoster Virus Infection and Platform to Study Viral Infectivity and Oxidative Stress and Damage

The environment of space results in a multitude of challenges to the human physiology that present barriers to extended habitation and exploration. Over 40 years of investigation to define countermeasures to address space flight adaptation has left gaps in our knowledge regarding mitigation strategies partly due to the lack of investigative tools, monitoring strategies, and real time diagnostics to understand the central causative agent(s) responsible for physiologic adaptation and maintaining homeostasis. Spaceflight-adaptation syndrome is the combination of space environmental conditions and the synergistic reaction of the human physiology. Our work addresses the role of oxidative stress and damage (OSaD) as a negative and contributing Risk Factor (RF) in the following areas of combined spaceflight related dysregulation: i) radiation induced cellular damage [1], [2] ii) immune impacts and the inflammatory response [3], [4] and iii) varicella zoster virus (VZV) reactivation [5]. Varicella-zoster (VZV)/Chicken Pox virus is a neurotropic human alphaherpesvirus resulting in varicella upon primary infection, suppressed by the immune system becomes latent in ganglionic neurons, and reactivates under stress events to re-express in zoster and possibly shingles. Our laboratory has developed a complex threedimensional (3D) normal human neural tissue model that emulates several characteristics of the human trigeminal ganglia (TG) and allows the study of combinatorial experimentation which addresses, simultaneously, OSaD associated with Spaceflight adaptation and habitation [6].

Goodwin, T. J.↗

Extending the Capabilities of Closed-loop Distributed Engine Control Simulations Using LAN Communication

Distributed Engine Control (DEC) is an enabling technology that has the potential to advance the state-of-the-art in gas turbine engine control. To analyze the capabilities that DEC offers, a Hardware-In-the-Loop (HIL) test bed is being developed at NASA Glenn Research Center. This test bed will support a systems-level analysis of control capabilities in closed-loop engine simulations. The structure of the HIL emulates a virtual test cell by implementing the operator functions, control system, and engine on three separate computers. This implementation increases the flexibility and extensibility of the HIL. Here, a method is discussed for implementing these interfaces by connecting the three platforms over a dedicated Local Area Network (LAN). This approach is verified using the Commercial Modular Aero-Propulsion System Simulation 40k (C-MAPSS40k), which is typically implemented on one computer. There are marginal differences between the results from simulation of the typical and the three-computer implementation. Additional analysis of the LAN network, including characterization of network load, packet drop, and latency, is presented. The three-computer setup supports the incorporation of complex control models and proprietary engine models into the HIL framework.

propulsion simulation↗

Influence of Combined Whole-Body Vibration Plus G-Loading on Visual Performance

Recent engineering analyses of the integrated Ares-Orion stack show that vibration levels for Orion crews have the potential to be much higher than those experienced in Gemini, Apollo, and Shuttle vehicles. Of particular concern to the Constellation Program (CxP) is the 12 Hz thrust oscillation (TO) that the Ares-I rocket develops during the final ~20 seconds preceding first-stage separation, at maximum G-loading. While the structural-dynamic mitigations being considered can assure that vibration due to TO is reduced to below the CxP crew health limit, it remains to be determined how far below this limit vibration must be reduced to enable effective crew performance during launch. Moreover, this "performance" vibration limit will inform the operations concepts (and crew-system interface designs) for this critical phase of flight. While Gemini and Apollo studies provide preliminary guidance, the data supporting the historical limits were obtained using less advanced interface technologies and very different operations concepts. In this study, supported by the Exploration Systems Mission Directorate (ESMD) Human Research Program, we investigated display readability-a fundamental prerequisite for any interaction with electronic crew-vehicle interfaces-while observers were subjected to 12 Hz vibration superimposed on the 3.8 G loading expected for the TO period of ascent. Two age-matched groups of participants (16 general population and 13 Crew Office) performed a numerical display reading task while undergoing sustained 3.8 G loading and whole-body vibration at 0, 0.15, 0.3, 0.5, and 0.7 g in the eyeballs in/out (x-axis) direction. The time-constrained reading task used an Orion-like display with 10- and 14-pt non-proportional sans-serif fonts, and was designed to emulate the visual acquisition and processing essential for crew system monitoring. Compared to the no-vibration baseline, we found no significant effect of vibration at 0.15 and 0.3 g on task error rates (ER) or response times (RT). Significant degradations in both ER and RT, however, were observed at 0.5 and 0.7 g for 10-pt, and at 0.7 g for 14-pt font displays. These objective performance measures were mirrored by participants' subjective ratings. Interestingly, we found that the impact of vibration on ER increased with distance from the center of the display, but only for vertical displacements. Furthermore, no significant ER or RT aftereffects were detected immediately following vibration, regardless of amplitude. Lastly, given that our reading task required no specialized spaceflight expertise, our finding that effects were not statistically distinct between our two groups is not surprising. The results from this empirical study provide initial guidance for evaluating the display readability trade-space between text-font size and vibration amplitude. However, the outcome of this work should be considered preliminary in nature for a number of reasons: 1. The single 12 Hz x-axis vibration employed was based on earlier load-cycle models of the induced TO environment at the end of Ares-I first stage flight. Recent analyses of TO mitigation designs suggest that significant concurrent off-axis vibration may also occur. 2. The shirtsleeve environment in which we tested fails to capture the full kinematic and dynamic complexity of the physical interface between crewmember and the still-to-bematured helmet-suit-seat designs, and the impact these will have for vibration transmission and consequent performance. 3. By examining performance in this reading and number processing task, we are only assessing readability, a first and necessary step that in itself does not directly address the performance of more sophisticated operational tasks such as vehicle-health monitoring or manual control of the vehicle.

readability↗

X-ray Pulsar Navigation Algorithms and Testbed for SEXTANT

The Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) is a NASA funded technologydemonstration. SEXTANT will, for the first time, demonstrate real-time, on-board X-ray Pulsar-based Navigation (XNAV), a significant milestone in the quest to establish a GPS-like navigation capability available throughout our Solar System and beyond. This paper describes the basic design of the SEXTANT system with a focus on core models and algorithms, and the design and continued development of the GSFC X-ray Navigation Laboratory Testbed (GXLT) with its dynamic pulsar emulation capability. We also present early results from GXLT modeling of the combined NICER X-ray timing instrument hardware and SEXTANT flight software algorithms.

Pulsar Navigation↗

SEXTANT - Station Explorer for X-Ray Timing and Navigation Technology

The Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) is a NASA funded technology- demonstration. SEXTANT will, for the first time, demonstrate real-time, on-board X-ray Pulsar-based Navigation (XNAV), a significant milestone in the quest to establish a GPS-like navigation capability available throughout our Solar System and beyond. This paper describes the basic design of the SEXTANT system with a focus on core models and algorithms, and the design and continued development of the GSFC X-ray Navigation Laboratory Testbed (GXLT) with its dynamic pulsar emulation capability. We also present early results from GXLT modeling of the combined NICER X-ray timing instrument hardware and SEXTANT flight software algorithms.

X-rays↗

Station Explorer for X-Ray Timing and Navigation Technology (SEXTANT)

The Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) is a NASA funded technology- demonstration. SEXTANT will, for the first time, demonstrate real-time, on-board X-ray Pulsar-based Navigation (XNAV), a significant milestone in the quest to establish a GPS-like navigation capability available throughout our Solar System and beyond. This paper describes the basic design of the SEXTANT system with a focus on core models and algorithms, and the design and continued development of the GSFC X-ray Navigation Laboratory Testbed (GXLT) with its dynamic pulsar emulation capability. We also present early results from GXLT modeling of the combined NICER X-ray timing instrument hardware and SEXTANT flight software algorithms.

Timing↗