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High-Rate Delay Tolerant Networking (HDTN) User Guide Version 1.3.0

Delay Tolerant Networking (DTN) has been identified as a key technology to enable and facilitate the development and growth of future space networks. Classically, space communications networks are collections of disparate links that are manually managed either point-to-point or use space relays. The accelerating accessibility of space enables a new scaling of space nodes, yet both the manual management of configurations and scheduling and the lack of structure connecting links precisely prohibit scaling. This challenge gives rise to newer and larger classes of communications needs that are met by DTN, which must overcome the disconnection, disruption, latency, and mobility featured in space communications systems. DTN joins the underlying links as an overlay, and can be made to communicate over any protocol stack. The core actions of DTN are store, carry, and forward, where data are stored instead of dropped if there is no immediately available outduct. It does this by taking the DTN unit of data, bundles, and providing necessary layers to adapt these bundles to the underlying transport protocols of choice; these are called convergence layers. DTN's Bundle Protocol (BP) can then be used on top of terrestrial protocol stacks, such as TCP/IP, as well as protocols for space, such as LTP/AOS, all in the same network. For emphasis it is noted that bundles can be of essentially any size, and hence this convergence to lower layers of choice is necessary. Existing DTN implementations have operated in constrained environments with limited resources, resulting in low data speeds. However, as various technologies have advanced, data transfer rates and efficiency have advanced, which has pushed the need for a DTN implementation for ground systems and for spacecraft that is performance-oriented in order to not impose an unnecessary bottleneck. High-rate Delay Tolerant Networking (HDTN) takes advantage of modern hardware platforms to substantially reduce latency and improve throughput compared to today’s DTN operations. The HDTN implementation maintains interoperability with existing deployments of DTN that conform to IETF RFCs 4838, 5050, and 9171. At the same time, HDTN defines a new data format better suited to higher-rate operation. It defines and adopts a massively parallel pipelined and message-oriented architecture, allowing the system to scale gracefully as its resources increase. HDTN’s architecture also supports hooks to replace various processing pipeline elements with specialized hardware accelerators. This offers improved Size, Weight, and Power (SWaP) characteristics while reducing development complexity and cost.

Delay Tolerant Networking↗

Space Technology Mission Directorate Game Changing Development Program FY2015 Annual Program Review: Advanced Manufacturing Technology

The Advance Manufacturing Technology (AMT) Project supports multiple activities within the Administration's National Manufacturing Initiative. A key component of the Initiative is the Advanced Manufacturing National Program Office (AMNPO), which includes participation from all federal agencies involved in U.S. manufacturing. In support of the AMNPO the AMT Project supports building and Growing the National Network for Manufacturing Innovation through a public-private partnership designed to help the industrial community accelerate manufacturing innovation. Integration with other projects/programs and partnerships: STMD (Space Technology Mission Directorate), HEOMD, other Centers; Industry, Academia; OGA's (e.g., DOD, DOE, DOC, USDA, NASA, NSF); Office of Science and Technology Policy, NIST Advanced Manufacturing Program Office; Generate insight within NASA and cross-agency for technology development priorities and investments. Technology Infusion Plan: PC; Potential customer infusion (TDM, HEOMD, SMD, OGA, Industry); Leverage; Collaborate with other Agencies, Industry and Academia; NASA roadmap. Initiatives include: Advanced Near Net Shape Technology Integrally Stiffened Cylinder Process Development (launch vehicles, sounding rockets); Materials Genome; Low Cost Upper Stage-Class Propulsion; Additive Construction with Mobile Emplacement (ACME); National Center for Advanced Manufacturing.

Vickers, John↗

Tiny sensor-transmitter can withstand extreme acceleration, gives digital output

A self-pulsing oscillator transmits a pulsed signal. The time between pulses and the frequency are controlled by two networks. Variations in the component values in each of the two networks, due to environmental changes, appear as changes in frequency and time between pulses in the transmitted signal. Such a sensor is used to measure physical magnitudes.

Mossino, R. L.↗

Enabling a Larger Deep Space Mission Suite: A Deep Space Network Queuing Antenna for Demand Access

The advent of deep space small spacecraft, as exemplified by the Mars Cubesat One (MarCO), Lunar Trailblazer, Janus, the Escape and Plasma Acceleration and Dynamics Explorers (EscaPADE), and the thirteen Artemis 1 missions, opens the possibility that a much larger number of deep space spacecraft may be launched over the next 10 years and beyond. While scientifically exciting, the prospect of a (much) larger mission suite raises significant challenges for the current approach to ground stations and mission operations. We have been investigating an integrated approach for ground stations and missions operations to enable new modes of operation while maintaining the capabilities of the current operational techniques. This integrated approach is built around three core capabilities: (1) A queuing antenna that enables monitoring the status of a much larger number of spacecraft, and allows spacecraft to transmit requests for telemetry with NASA’s Deep Space Network (DSN); (2) a flexible scheduling system that expands the current DSN scheduling services to enable allocating time on DSN antennas in near real-time; and (3) a cloud-based ground data system that can be spun up and down according to how tracks are assigned by the flexible scheduling system. We shall show that an 18 meter DSN queuing antenna equipped with cyrogenic receivers would enable use of the DSN Demand Access Service for small spacecraft throughout the inner Solar System, thus providing service to a large mission suite. We first discuss the architecture of the queuing antenna and its supporting systems, including, for instance, the service required to generate the schedule for the queueing antenna (which dictates how it slews to monitor multiple spacecraft in a day of operations). Next, we describe the signaling scheme used to encode a request, which is inherited from the already operational DSN Beacon Tone Service, and describe two alternative ways to detect the incoming tone at the ground station, one based on maximum likelihood estimation (MLE), and another one based on Fast-Fourier Transfer (FFT) processing. We then use these results to estimate the maximum range at which a request can be reliably detected as a function of the spacecraft and ground station communication capabilities. Finally, the last part of this part of this paper briefly describes the prototyping effort undertaken at Morehead State University (MSU) and JPL to demonstrate the viability of this new DSN demand access. In particular, we describe the suite of tests conducted using MSU’s 21 meter ground station to validate its use a queuing antenna.

Mattle, Emily↗

The 1989 NASA-ASEE Summer Faculty Fellowship Program in Aeronautics and Research

The 1989 NASA-ASEE Summer Faculty Fellowship Program at the Goddard Space Flight Center was conducted during 5 Jun. 1989 to 11 Aug. 1989. The research projects were previously assigned. Work summaries are presented for the following topics: optical properties data base; particle acceleration; satellite imagery; telemetry workstation; spectroscopy; image processing; stellar spectra; optical radar; robotics; atmospheric composition; semiconductors computer networks; remote sensing; software engineering; solar flares; and glaciers.

Boroson, Harold R.↗

Observations related to the acceleration, injection, and interplanetary propagation of energetic protons during the solar cosmic ray event on February 16, 1984

This paper presents an analysis of data collected by the worldwide network of neutron monitors and from IMP-8 cosmic-ray telescopes, as well as by particle detectors on the GOES 5 and 6 and ICE satellites, on the solar cosmic ray event that took place on February 16, 1984. Using these data, the intensity-time (IT) profiles, the anisotropy-time profiles, the energy spectra, and the pitch angle distributions of the solar protons near earth were deduced. It was found that the solar protons propagated essentially scatter-free from the sun to the earth. The solar protons had easy access to the IMF lines to earth; the time from the onset to maximum intensity and the shape of the IT profiles at earth as a function of energy could be explained by the diffusion of the flare protons near the acceleration region. The energy spectrum of the solar flare protons injected into the undisturbed IMF at the sun was changing with time in both amplitude and shape. The observations suggest a shock acceleration process.

Debrunner, H.↗

Using EMG to anticipate head motion for virtual-environment applications

In virtual environment (VE) applications, where virtual objects are presented in a see-through head-mounted display, virtual images must be continuously stabilized in space in response to user's head motion. Time delays in head-motion compensation cause virtual objects to "swim" around instead of being stable in space which results in misalignment errors when overlaying virtual and real objects. Visual update delays are a critical technical obstacle for implementing head-mounted displays in applications such as battlefield simulation/training, telerobotics, and telemedicine. Head motion is currently measurable by a head-mounted 6-degrees-of-freedom inertial measurement unit. However, even given this information, overall VE-system latencies cannot be reduced under about 25 ms. We present a novel approach to eliminating latencies, which is premised on the fact that myoelectric signals from a muscle precede its exertion of force, thereby limb or head acceleration. We thus suggest utilizing neck-muscles' myoelectric signals to anticipate head motion. We trained a neural network to map such signals onto equivalent time-advanced inertial outputs. The resulting network can achieve time advances of up to 70 ms.

Clinical Trial↗

The Source of Alfven Waves That Heat the Solar Corona

We suggest a source for high-frequency Alfven waves invoked in coronal heating and acceleration of the solar wind. The source is associated with small-scale magnetic loops in the chromospheric network.

Alfven Waves Heat Solar Corona solar wind solar wi↗

Development of Machine Learning Algorithms to Segment and Study Images of Astromaterial Samples

Introduction: Micrometer-scale chemical analyses of chondritic meteorites and mission-returned asteroid samples can reveal details of the physical and chemical processes operating in the early solar system, including processes that gave rise to planets, moons, and minor bodies. These primitive astromaterials are comprised of chondrules, calcium- and aluminum-rich inclusions (CAI), and many other silicates, oxides, metals, sulfides, and fine-grained materials. The chemical and mineralogical complexity of these samples, vast populations of different components, and heterogeneity across mm to km scales, all limit our understanding of the origin and evolution of these materials. Here, we describe recent efforts to use machine learning techniques to automate the segmentation of chemical maps of chondritic meteorites, designed to aid studies of asteroid samples returned by spacecraft. By automating the task of segmentation it will become possible to rapidly analyze and interpret the sizes, shapes, mineralogy, chemistry, and other properties of every chondrule, calcium- and aluminum-rich inclusion (CAI) and other clast within and between asteroid samples. Sample return missions significantly accelerate and heighten the need to develop such new data analysis techniques, and associated data repositories. Techniques: Neural networks require abundant training data, i.e. images which have been segmented by a human user. We have manually segmented data available from previous petrologic and chemical work at NASA Johnson Space Center and the American Museum of Natural History [1-4]. These data were derived from energy- and wavelength-dispersive X-ray spectroscopy (EDS, WDS) mapping of samples from many chondrite groups. The Deeplabv3+ [5] neural network architecture was trained on human-labeled masks and used to create machine-labeled masks. Several different algorithms were investigated, with inputs ranging from common RGB image formats through to hyperspectral datasets, with raw data comprising greyscale maps of Mg, Ca, and Al, with or without Si, Fe, Ti for both EDS and WDS data, and extending to other elements in EDS only. Each greyscale image was paired with a binary mask for each labelled particle type. Results: The trained algorithms can segment (Fig 1), classify, and measure the dimensions of thousands of particles in chemical maps of a standard 1-inch round petrographic section in seconds to minutes, rather than many hours needed by a human. Accuracy of the algorithms varied from chondrite to chondrite and across particle types. Further results and details of the algorithms will be presented at the workshop. Future directions: Machine learning has the potential to revolutionize our understanding of complex particle populations contained within primitive astromaterial, with segmentation being a critical first step. Example applications include better understanding of particle transport, nebular reservoirs, parent body accretion, and a deeper understanding of the relationships between particle populations and bulk rock elemental and isotopic compositions. In addition to benefits that machine learning can bring to individual researchers, building a community data repository of thousands to millions of particles across hundreds of samples will open up many other possibilities. For example, with a large enough dataset it will be possible to search for exceptionally closely matching particles across disparate samples. Such a capability would enable a single CAI from OSIRISREx or Hayabusa/II samples to be matched to chondritic CAIs that exhibit near-identical size, texture, and mineralogy, down to the level of similar core phenocrysts, zonation, and rim sequences. Such comparative analyses will help to disentangle precursor chemistry, chronology, gas/dust reservoirs during heating, and accretion. Such an endeavor would be impossible without machine learning and a large community data repository of astromaterial chemical/mineralogic maps.

Machine Learning↗

Stiffness and Fatigue Life Estimator for Polymer Composite Laminates Using Machine Learning

Machine learning (ML) models are increasingly being used in many engineering fields due to the advancements in ML algorithms and availability of high-speed computing power. One of the most popular ML class of models is artificial neural networks (ANN). ML is increasingly being used in the design and analysis of composite materials and structures, specifically in the constitutive modeling of composite materials with the focus on greatly accelerating multiscale analyses of composite materials and structures through development of surrogate models. Towards that end, Python-based neural nets have been developed to predict initial stiffness and fatigue life of an eight-ply symmetric polymer matrix composite laminate. Two types of neural networks, a Multilayer Perceptron (MLP) and a Recurrent Neural Network (RNN), have been established. Results show that both neural net type algorithms can provide an excellent estimate of initial laminate stiffness as well as fatigue life of eight-ply symmetric polymer matrix composite laminates (PMCs). RNNs are better able to capture the shape of the fatigue curve of a laminate. The resulting tool and GUI can be very useful for system level studies to obtain an estimate of desired properties and life of PMC composite laminates. Further, the associated surrogate models can also be used in composite multiscale analyses to replace the actual physics-based calculations at lower scales and thereby significantly increase the computational efficiency of such analyses and thus make micromechanics-based multiscale analyses a viable industrial tool for large scale structural problems.

multiscale analysis↗

Stiffness and Fatigue Life Estimator for Polymer Composite Laminates Using Machine Learning

Machine learning (ML) models are increasingly being used in many engineering fields due to the advancements in ML algorithms and availability of high-speed computing power. One of the most popular ML class of models is artificial neural networks (ANN). ML is increasingly being used in the design and analysis of composite materials and structures, specifically in the constitutive modeling of composite materials with the focus on greatly accelerating multiscale analyses of composite materials and structures through development of surrogate models. Towards that end, Python-based neural nets have been developed to predict initial stiffness and fatigue life of an eight-ply symmetric polymer matrix composite laminate. Two types of neural networks, a Multilayer Perceptron (MLP) and a Recurrent Neural Network (RNN), have been established. Results show that both neural net type algorithms can provide an excellent estimate of initial laminate stiffness as well as fatigue life of eight-ply symmetric polymer matrix composite laminates (PMCs). RNNs are better able to capture the shape of the fatigue curve of a laminate. The resulting tool and GUI can be very useful for system level studies to obtain an estimate of desired properties and life of PMC composite laminates. Further, the associated surrogate models can also be used in composite multiscale analyses to replace the actual physics-based calculations at lower scales and thereby significantly increase the computational efficiency of such analyses and thus make micromechanics-based multiscale analyses a viable industrial tool for large scale structural problems.

multiscale analysis↗

On-line, adaptive state estimator for active noise control

Dynamic characteristics of airframe structures are expected to vary as aircraft flight conditions change. Accurate knowledge of the changing dynamic characteristics is crucial to enhancing the performance of the active noise control system using feedback control. This research investigates the development of an adaptive, on-line state estimator using a neural network concept to conduct active noise control. In this research, an algorithm has been developed that can be used to estimate displacement and velocity responses at any locations on the structure from a limited number of acceleration measurements and input force information. The algorithm employs band-pass filters to extract from the measurement signal the frequency contents corresponding to a desired mode. The filtered signal is then used to train a neural network which consists of a linear neuron with three weights. The structure of the neural network is designed as simple as possible to increase the sampling frequency as much as possible. The weights obtained through neural network training are then used to construct the transfer function of a mode in z-domain and to identify modal properties of each mode. By using the identified transfer function and interpolating the mode shape obtained at sensor locations, the displacement and velocity responses are estimated with reasonable accuracy at any locations on the structure. The accuracy of the response estimates depends on the number of modes incorporated in the estimates and the number of sensors employed to conduct mode shape interpolation. Computer simulation demonstrates that the algorithm is capable of adapting to the varying dynamic characteristics of structural properties. Experimental implementation of the algorithm on a DSP (digital signal processing) board for a plate structure is underway. The algorithm is expected to reach the sampling frequency range of about 10 kHz to 20 kHz which needs to be maintained for a typical active noise control application.

Lim, Tae W.↗

Neural Networks Analyze Data In Particle-Impact-Noise Tests

Electronic neural networks and computers put to use in analyzing data acquired in particle-impact-noise-detection (PIND) tests of packaged electronic components. PIND tests detect loose particles in packages that cause failures during subsequent operation of packages in presence of accelerations or other effects - for example, loose electrically conductive particles that bounce into positions in which they cause short circuits. Interpretation of test data more objective and accurate. Preliminary results suggest use of neural networks result in significant improvement in quality and reliability and decrease in cost of PIND testing.

Scaglione, Lois J.↗

Prediction of Stiffness and Fatigue Lives of Polymer Matrix Composite Laminates Using Artificial Neural Networks

Machine learning (ML) models are increasingly being used in many engineering fields due to the advancements in ML algorithms and availability of high-speed computing power. One of the most popular ML class of models is artificial neural networks (ANN). ML is increasingly being used in the design and analysis of composite materials and structures, specifically in the constitutive modeling of composite materials with the focus on greatly accelerating multiscale analyses of composite materials and structures through development of surrogate models. Towards that end, both Python and MATLAB-based neural nets have been developed to predict initial stiffness and fatigue life of an eight-ply symmetric polymer matrix composite laminate. Two types of neural networks, a Multilayer Perceptron (MLP) and a Recurrent Neural Network (RNN), have been developed for both platforms. Results show that the both neural net types can provide an excellent estimate of initial stiffness as well as fatigue life of eight-ply symmetric polymer matrix composite laminate. RNNs are better able to capture the shape of the fatigue curve of a laminate. This tool can be very useful for system level studies to obtain an estimate of desired properties and life of PMC composite laminates. The associated surrogate models could also be used in composite multiscale analyses to replace the actual physics-based calculations at lower scales and thereby significantly increase the computational efficiency of such analyses and thus make multiscale analyses a viable industrial tool for large scale structural problems.

Composite↗

Macular Bioaccelerometers on Earth and in Space

Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth.

Ross, M. D.↗

Cooperative high-performance storage in the accelerated strategic computing initiative

The use and acceptance of new high-performance, parallel computing platforms will be impeded by the absence of an infrastructure capable of supporting orders-of-magnitude improvement in hierarchical storage and high-speed I/O (Input/Output). The distribution of these high-performance platforms and supporting infrastructures across a wide-area network further compounds this problem. We describe an architectural design and phased implementation plan for a distributed, Cooperative Storage Environment (CSE) to achieve the necessary performance, user transparency, site autonomy, communication, and security features needed to support the Accelerated Strategic Computing Initiative (ASCI). ASCI is a Department of Energy (DOE) program attempting to apply terascale platforms and Problem-Solving Environments (PSEs) toward real-world computational modeling and simulation problems. The ASCI mission must be carried out through a unified, multilaboratory effort, and will require highly secure, efficient access to vast amounts of data. The CSE provides a logically simple, geographically distributed, storage infrastructure of semi-autonomous cooperating sites to meet the strategic ASCI PSE goal of highperformance data storage and access at the user desktop.

Gary, Mark↗

Detonation to Deflagration-Mode Transitions in Pulsed Plasma Accelerators

PULSED plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas. The current in such discharges will ionize the gas and produce a strong magnetic field, which interacts with the flowing current to accelerate the plasma through the Lorentz body force. For the present work, two plasma accelerator types employing this general scheme are of interest: the gas-fed pulsed plasma thruster (PPT) 1 and the quasi-steady magnetoplasmadynamic (MPD) accelerator. 2 The gas-fed pulsed plasma accelerator is generally understood as a completely transient device discharging in ∼1-10 μs. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j × B body force, entraining and accelerating propellant it encounters. This process is sometimes referred to in literature as 'snowplowing' the propellant or accelerating the gas in a detonation-mode because the current sheet representation approximates that of a strong detonation shockwave propagating through the gas. For these devices, acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new 'crowbar' discharge at the breech and depriving the initial sheet of additional acceleration. In general, PPTs typically claim thrust efficiencies (ratio of jet kinetic energy to input electrical energy) registering in the teens or lower. 3 In the quasi-steady MPD accelerator, the pulse is lengthened to ∼1 ms or longer and maintained at an approximately constant level during discharge through the use of a pulse-forming network (PFN) of capacitors. After an initial transient discharge, which is typically short relative to the overall discharge period, the plasma assumes a relatively steady-state configuration, known as 'quasi-steady' MPD operation. 2 In this state, ionized gas flows through a stationary current channel in a manner that is sometimes referred to as deflagration-mode operation owing to the similarities to deflagration waves in gases. The plasma experiences electromagnetic acceleration as the plasma flows through the current channel towards the exit of the device. Quasi-steady MPD thrusters claim efficiencies up to 50% for certain propellants.4 There has been significant and sustained research over several decades on both gas-fed PPTs and quasi-steady MPD thrusters, however there have been pulsed thrusters that do not appear to exactly fit either classification, instead possessing a mixture of operational qualities characteristic of both thruster variants. The Coaxial High ENerGy (CHENG) thruster by Cheng, et al.5 operated on the short 10 μs timescales characteristic of PPTs, but claimed the high thrust densities, high efficiencies, and low electrode erosion rates that are more consistent with the MPD/deflagration mode of plasma acceleration. Gas-fed PPT research by Ziemer, et al. 3, 6 identified two separate regimes of performance in those thrusters. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency as a function of mass bit, while the second regime at very low mass bits (termed Mode II) exhibited an increase in efficiency with decreasing mass bit. Work by Poehlmann et al.7 and by Sitaraman and Raja8 sought to understand the performance of the CHENG thruster and the Mode I/Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes of plasma acceleration representing two distinct sets of solutions to the relevant conservation laws. In these works, it was proposed that the values of the various controllable parameters determined whether the accelerator would operate in detonation or deflagration mode. Our hypothesized view of the acceleration process in the CHENG thruster and in PPTs experiencing a transition from Mode I to Mode II is inspired by observations of the transition from the PPT mode of operation to the quasi-steady MPD mode. Specifically, the quasi-steady MPD was discovered by driving a PPT to extended pulse lengths. Above a certain pulse length threshold the transient plasma current sheet transitions into a stable plasma acceleration mode that 'replicates in every observable detail steady flow self-field magnetoplasmadynamic acceleration.' 9 In the present work, instead of treating the accelerator as if it were only operating in a single mode during a pulse, we consider the initial stage of the discharge in all cases as a current sheet forming at the breach of the accelerator and moving towards the exit as a detonation wave. If the current sheet reaches the exit of the accelerator before the discharge is completed, the view of the acceleration mode transitions to the deflagration mode-type found in quasi-steady MPD thrusters. In previous work10 we presented a modeling framework that first captured the time-evolution of the current sheet (detonation) mode of the thruster and then transitioned into the quasi-steady MPD (deflagration) mode of plasma acceleration. In the present work, variations of the controllable parameters - specifically the pulsed circuit properties, the amount of mass injected into the thruster, and the relative timing between the initial gas injection and the initiation of the plasma current sheet - will be used to explore the thruster performance. A range of parameters are explored to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

Improved Carrier Tracking by Smoothing Estimators

Smoothing as a way to improve the carrier phase estimation is proposed and analyzed. The performance of first and second order Kalman optimum smoothers are investigated. This performance is evaluated in terms of steady state covariance error computation, dynamic tracking, and noise response. It is shown that with practical amounts of memory, a second order smoother can have a position error due to an acceleration or jerk step input less than any prescribed maximum. As an example of importance to the NASA Deep Space Network, a second order smoother can be used to track the Voyager spacecraft at Uranus and Neptune encounters with significantly better performance than a second order phase locked loop.

Raez, C. A. P.↗