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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Finite Element Methods for real-time Haptic Feedback of Soft-Tissue Models in Virtual Reality Simulators

We have applied the linear elastic finite element method to compute haptic force feedback and domain deformations of soft tissue models for use in virtual reality simulators. Our results show that, for virtual object models of high-resolution 3D data (>10,000 nodes), haptic real time computations (>500 Hz) are not currently possible using traditional methods. Current research efforts are focused in the following areas: 1) efficient implementation of fully adaptive multi-resolution methods and 2) multi-resolution methods with specialized basis functions to capture the singularity at the haptic interface (point loading). To achieve real time computations, we propose parallel processing of a Jacobi preconditioned conjugate gradient method applied to a reduced system of equations resulting from surface domain decomposition. This can effectively be achieved using reconfigurable computing systems such as field programmable gate arrays (FPGA), thereby providing a flexible solution that allows for new FPGA implementations as improved algorithms become available. The resulting soft tissue simulation system would meet NASA Virtual Glovebox requirements and, at the same time, provide a generalized simulation engine for any immersive environment application, such as biomedical/surgical procedures or interactive scientific applications.

Frank, Andreas O.↗
NASA NTRS2011

NASA Tech Briefs, April 2011

Topics covered include: Amperometric Solid Electrolyte Oxygen Microsensors with Easy Batch Fabrication; Two-Axis Direct Fluid Shear Stress Sensor for Aerodynamic Applications; Target Assembly to Check Boresight Alignment of Active Sensors; Virtual Sensor Test Instrumentation; Evaluation of the Reflection Coefficient of Microstrip Elements for Reflectarray Antennas; Miniaturized Ka-Band Dual-Channel Radar; Continuous-Integration Laser Energy Lidar Monitor; Miniaturized Airborne Imaging Central Server System; Radiation-Tolerant, SpaceWire-Compatible Switching Fabric; Small Microprocessor for ASIC or FPGA Implementation; Source-Coupled, N-Channel, JFET-Based Digital Logic Gate Structure Using Resistive Level Shifters; High-Voltage-Input Level Translator Using Standard CMOS; Monitoring Digital Closed-Loop Feedback Systems; MASCOT - MATLAB Stability and Control Toolbox; MIRO Continuum Calibration for Asteroid Mode; GOATS Image Projection Component; Coded Modulation in C and MATLAB; Low-Dead-Volume Inlet for Vacuum Chamber; Thermal Control Method for High-Current Wire Bundles by Injecting a Thermally Conductive Filler; Method for Selective Cleaning of Mold Release from Composite Honeycomb Surfaces; Infrared-Bolometer Arrays with Reflective Backshorts; Commercialization of LARC (trade mark) -SI Polyimide Technology; Novel Low-Density Ablators Containing Hyperbranched Poly(azomethine)s; Carbon Nanotubes on Titanium Substrates for Stray Light Suppression; Monolithic, High-Speed Fiber-Optic Switching Array for Lidar; Grid-Tied Photovoltaic Power System; Spectroelectrochemical Instrument Measures TOC; A Miniaturized Video System for Monitoring Drosophila Behavior; Hydrofocusing Bioreactor Produces Anti-Cancer Alkaloids; Creep Measurement Video Extensometer; Radius of Curvature Measurement of Large Optics Using Interferometry and Laser Tracker n-B-pi-p Superlattice Infrared Detector; Safe Onboard Guidance and Control Under Probabilistic Uncertainty; General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets; Hidden Statistics of Schroedinger Equation; Optimal Padding for the Two-Dimensional Fast Fourier Transform; Spatial Query for Planetary Data; Higher Order Mode Coupling in Feed Waveguide of a Planar Slot Array Antenna; Evolutionary Computational Methods for Identifying Emergent Behavior in Autonomous Systems; Sampling Theorem in Terms of the Bandwidth and Sampling Interval; Meteoroid/Orbital Debris Shield Engineering Development Practice and Procedure; Self-Balancing, Optical-Center-Pivot, Fast-Steering Mirror; Wireless Orbiter Hang-Angle Inclinometer System; and Internal Electrostatic Discharge Monitor - IESDM.

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NASA NTRS2011

NASA Tech Briefs, July 2011

Topics covered include: 1) Collaborative Clustering for Sensor Networks; 2) Teleoperated Marsupial Mobile Sensor Platform Pair for Telepresence Insertion Into Challenging Structures; 3) Automated Verification of Spatial Resolution in Remotely Sensed Imagery; 4) Electrical Connector Mechanical Seating Sensor; 5) In Situ Aerosol Detector; 6) Multi-Parameter Aerosol Scattering Sensor; 7) MOSFET Switching Circuit Protects Shape Memory Alloy Actuators; 8) Optimized FPGA Implementation of Multi-Rate FIR Filters Through Thread Decomposition; 9) Circuit for Communication Over Power Lines; 10) High-Efficiency Ka-Band Waveguide Two-Way Asymmetric Power Combiner; 11) 10-100 Gbps Offload NIC for WAN, NLR, and Grid Computing; 12) Pulsed Laser System to Simulate Effects of Cosmic Rays in Semiconductor Devices; 13) Flight Planning in the Cloud; 14) MPS Editor; 15) Object-Oriented Multi Disciplinary Design, Analysis, and Optimization Tool; 16) Cryogenic-Compatible Winchester Connector Mount and Retaining System for Composite Tubes; 17) Development of Position-Sensitive Magnetic Calorimeters for X-Ray Astronomy; 18) Planar Rotary Piezoelectric Motor Using Ultrasonic Horns; 19) Self-Rupturing Hermetic Valve; 20) Explosive Bolt Dual-Initiated from One Side; 21) Dampers for Stationary Labyrinth Seals; 22) Two-Arm Flexible Thermal Strap; 23) Carbon Dioxide Removal via Passive Thermal Approaches; 24) Polymer Electrolyte-Based Ambient Temperature Oxygen Microsensors for Environmental Monitoring; 25) Pressure Shell Approach to Integrated Environmental Protection; 26) Image Quality Indicator for Infrared Inspections; 27) Micro-Slit Collimators for X-Ray/Gamma-Ray Imaging; 28) Scatterometer-Calibrated Stability Verification Method; 29) Test Port for Fiber-Optic-Coupled Laser Altimeter; 30) Phase Retrieval System for Assessing Diamond Turning and Optical Surface Defects; 31) Laser Oscillator Incorporating a Wedged Polarization Rotator and a Porro Prism as Cavity Mirror; 32) Generic, Extensible, Configurable Push-Pull Framework for Large-Scale Science Missions; 33) Dynamic Loads Generation for Multi-Point Vibration Excitation Problems; 34) Optimal Control via Self-Generated Stochasticity; 35) Space-Time Localization of Plasma Turbulence Using Multiple Spacecraft Radio Links; 36) Surface Contact Model for Comets and Asteroids; 37) Dust Mitigation Vehicle; 38) Optical Coating Performance for Heat Reflectors of the JWST-ISIM Electronic Component; 39) SpaceCube Demonstration Platform; 40) Aperture Mask for Unambiguous Parity Determination in Long Wavelength Imagers; 41) Spaceflight Ka-Band High-Rate Radiation-Hard Modulator; 42) Enabling Disabled Persons to Gain Access to Digital Media; 43) Cytometer on a Chip; 44) Principles, Techniques, and Applications of Tissue Microfluidics; and 45) Two-Stage Winch for Kites and Tethered Balloons or Blimps.

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NASA NTRS2009

SMAP's Radar OBP Algorithm Development

An approach for algorithm specifications and development is described for SMAP's radar onboard processor with multi-stage demodulation and decimation bandpass digital filter. Point target simulation is used to verify and validate the filter design with the usual radar performance parameters. Preliminary FPGA implementation is also discussed.

soil moisture↗
NASA NTRS2012

Fast and Adaptive Lossless Onboard Hyperspectral Data Compression System

Modern hyperspectral imaging systems are able to acquire far more data than can be downlinked from a spacecraft. Onboard data compression helps to alleviate this problem, but requires a system capable of power efficiency and high throughput. Software solutions have limited throughput performance and are power-hungry. Dedicated hardware solutions can provide both high throughput and power efficiency, while taking the load off of the main processor. Thus a hardware compression system was developed. The implementation uses a field-programmable gate array (FPGA). The implementation is based on the fast lossless (FL) compression algorithm reported in Fast Lossless Compression of Multispectral-Image Data (NPO-42517), NASA Tech Briefs, Vol. 30, No. 8 (August 2006), page 26, which achieves excellent compression performance and has low complexity. This algorithm performs predictive compression using an adaptive filtering method, and uses adaptive Golomb coding. The implementation also packetizes the coded data. The FL algorithm is well suited for implementation in hardware. In the FPGA implementation, one sample is compressed every clock cycle, which makes for a fast and practical realtime solution for space applications. Benefits of this implementation are: 1) The underlying algorithm achieves a combination of low complexity and compression effectiveness that exceeds that of techniques currently in use. 2) The algorithm requires no training data or other specific information about the nature of the spectral bands for a fixed instrument dynamic range. 3) Hardware acceleration provides a throughput improvement of 10 to 100 times vs. the software implementation. A prototype of the compressor is available in software, but it runs at a speed that does not meet spacecraft requirements. The hardware implementation targets the Xilinx Virtex IV FPGAs, and makes the use of this compressor practical for Earth satellites as well as beyond-Earth missions with hyperspectral instruments.

Aranki, Nazeeh I.↗
NASA NTRS1999

FPGA-Based Filterbank Implementation for Parallel Digital Signal Processing

One approach to parallel digital signal processing decomposes a high bandwidth signal into multiple lower bandwidth (rate) signals by an analysis bank. After processing, the subband signals are recombined into a fullband output signal by a synthesis bank. This paper describes an implementation of the analysis and synthesis banks using (Field Programmable Gate Arrays) FPGAs.

Berner, Stephan↗
NASA NTRS2009

Economical Implementation of a Filter Engine in an FPGA

A logic design has been conceived for a field-programmable gate array (FPGA) that would implement a complex system of multiple digital state-space filters. The main innovative aspect of this design lies in providing for reuse of parts of the FPGA hardware to perform different parts of the filter computations at different times, in such a manner as to enable the timely performance of all required computations in the face of limitations on available FPGA hardware resources. The implementation of the digital state-space filter involves matrix vector multiplications, which, in the absence of the present innovation, would ordinarily necessitate some multiplexing of vector elements and/or routing of data flows along multiple paths. The design concept calls for implementing vector registers as shift registers to simplify operand access to multipliers and accumulators, obviating both multiplexing and routing of data along multiple paths. Each vector register would be reused for different parts of a calculation. Outputs would always be drawn from the same register, and inputs would always be loaded into the same register. A simple state machine would control each filter. The output of a given filter would be passed to the next filter, accompanied by a "valid" signal, which would start the state machine of the next filter. Multiple filter modules would share a multiplication/accumulation arithmetic unit. The filter computations would be timed by use of a clock having a frequency high enough, relative to the input and output data rate, to provide enough cycles for matrix and vector arithmetic operations. This design concept could prove beneficial in numerous applications in which digital filters are used and/or vectors are multiplied by coefficient matrices. Examples of such applications include general signal processing, filtering of signals in control systems, processing of geophysical measurements, and medical imaging. For these and other applications, it could be advantageous to combine compact FPGA digital filter implementations with other application-specific logic implementations on single integrated-circuit chips. An FPGA could readily be tailored to implement a variety of filters because the filter coefficients would be loaded into memory at startup.

Kowalski, James E.↗
NASA NTRS2010

NASA Tech Briefs, September 2010

Topics covered include: Instrument for Measuring Thermal Conductivity of Materials at Low Temperatures; Multi-Axis Accelerometer Calibration System; Pupil Alignment Measuring Technique and Alignment Reference for Instruments or Optical Systems; Autonomous System for Monitoring the Integrity of Composite Fan Housings; A Safe, Self-Calibrating, Wireless System for Measuring Volume of Any Fuel at Non-Horizontal Orientation; Adaptation of the Camera Link Interface for Flight-Instrument Applications; High-Performance CCSDS Encapsulation Service Implementation in FPGA; High-Performance CCSDS AOS Protocol Implementation in FPGA; Advanced Flip Chips in Extreme Temperature Environments; Diffuse-Illumination Systems for Growing Plants; Microwave Plasma Hydrogen Recovery System; Producing Hydrogen by Plasma Pyrolysis of Methane; Self-Deployable Membrane Structures; Reactivation of a Tin-Oxide-Containing Catalys; Functionalization of Single-Wall Carbon Nanotubes by Photo-Oxidation; Miniature Piezoelectric Macro-Mass Balance; Acoustic Liner for Turbomachinery Applications; Metering Gas Strut for Separating Rocket Stages; Large-Flow-Area Flow-Selective Liquid/Gas Separator; Counterflowing Jet Subsystem Design; Water Tank with Capillary Air/Liquid Separation; True Shear Parallel Plate Viscometer; Focusing Diffraction Grating Element with Aberration Control; Universal Millimeter-Wave Radar Front End; Mode Selection for a Single-Frequency Fiber Laser; Qualification and Selection of Flight Diode Lasers for Space Applications; Plenoptic Imager for Automated Surface Navigation; Maglev Facility for Simulating Variable Gravity; Hybrid AlGaN-SiC Avalanche Photodiode for Deep-UV Photon Detection; High-Speed Operation of Interband Cascade Lasers; 3D GeoWall Analysis System for Shuttle External Tank Foreign Object Debris Events; Charge-Spot Model for Electrostatic Forces in Simulation of Fine Particulates; Hidden Statistics Approach to Quantum Simulations; Reconstituted Three-Dimensional Interactive Imaging; Determining Atmospheric-Density Profile of Titan; Digital Microfluidics Sample Analyzer; Radiation Protection Using Carbon Nanotube Derivatives; Process to Selectively Distinguish Viable from Non-Viable Bacterial Cells; and TEAMS Model Analyzer.

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NASA NTRS2006

Fault Tolerance Implementation within SRAM Based FPGA Designs based upon Single Event Upset Occurrence Rates

Emerging technology is enabling the design community to consistently expand the amount of functionality that can be implemented within Integrated Circuits (ICs). As the number of gates placed within an FPGA increases, the complexity of the design can grow exponentially. Consequently, the ability to create reliable circuits has become an incredibly difficult task. In order to ease the complexity of design completion, the commercial design community has developed a very rigid (but effective) design methodology based on synchronous circuit techniques. In order to create faster, smaller and lower power circuits, transistor geometries and core voltages have decreased. In environments that contain ionizing energy, such a combination will increase the probability of Single Event Upsets (SEUs) and will consequently affect the state space of a circuit. In order to combat the effects of radiation, the aerospace community has developed several "Hardened by Design" (fault tolerant) design schemes. This paper will address design mitigation schemes targeted for SRAM Based FPGA CMOS devices. Because some mitigation schemes may be over zealous (too much power, area, complexity, etc.. . .), the designer should be conscious that system requirements can ease the amount of mitigation necessary for acceptable operation. Therefore, various degrees of Fault Tolerance will be demonstrated along with an analysis of its effectiveness.

Berg, Melanie↗
NASA NTRS2011

FPGA Sequencer for Radar Altimeter Applications

A sequencer for a radar altimeter provides accurate attitude information for a reliable soft landing of the Mars Science Laboratory (MSL). This is a field-programmable- gate-array (FPGA)-only implementation. A table loaded externally into the FPGA controls timing, processing, and decision structures. Radar is memory-less and does not use previous acquisitions to assist in the current acquisition. All cycles complete in exactly 50 milliseconds, regardless of range or whether a target was found. A RAM (random access memory) within the FPGA holds instructions for up to 15 sets. For each set, timing is run, echoes are processed, and a comparison is made. If a target is seen, more detailed processing is run on that set. If no target is seen, the next set is tried. When all sets have been run, the FPGA terminates and waits for the next 50-millisecond event. This setup simplifies testing and improves reliability. A single vertex chip does the work of an entire assembly. Output products require minor processing to become range and velocity. This technology is the heart of the Terminal Descent Sensor, which is an integral part of the Entry Decent and Landing system for MSL. In addition, it is a strong candidate for manned landings on Mars or the Moon.

Berkun, Andrew C.↗
NASA NTRS2003

Design of an L-band Microwave Radiometer with Active Mitigation of Interference

Radio frequency interference (RFI) impairs L-band radiometry outside the protected 20 MHz frequency band around 1413 MHz. However, bandwidths of 100 MHz or more are desired for certain remote sensing applications as well as certain astronomy applications. Because much of the RFI in this band is from radars with pulse lengths on the order of microseconds, traditional radiometers (i.e., those which directly measure total power or power spectral density integrated over time scales of milliseconds or greater) are poorly-suited to this task. Simply reducing integration time and discarding contaminated outputs may not be a practical answer due to the wide variety of modulations and pulse lengths observed in L-band RFI signals, the dynamic and complex nature of the associated propagation channels, and the logistical effort associated with post-measurement data editing. This motivates the design and development of radiometers capable of coherent sampling and adaptive, real-time mitigation of interference. Such a radiometer will be described in this presentation. This design is capable of coherently-sampling up to 100 MHz bandwidth at L-band. RFI mitigation is implemented in FPGA components so that real-time suppression is achieved. The system currently uses a cascade of basic time- and frequency-domain detection and blanking techniques; more advanced algorithms are under consideration. The modular FPGA-based architecture provides other benefits, such as the ability to implement extremely stable digital filters and the ability to reconfigure the system "on the fly". An overview of the basic design along with on-the-air results from an initial implementation will be provided in the presentation. Related L-band RFI surveys will be described to illustrate the relevance of this approach in a variety of operating conditions.

Hampson, G. A.↗
NASA NTRS2003

Design of an L-band Microwave Radiometer with Active Mitigation of Interference

Radio frequency interference (RFI) impairs L-band radiometry outside the protected 20 MHz frequency band around 1413 MHz. However, bandwidths of 100 MHz or more are desired for certain remote sensing applications as well as certain astronomy applications. Because much of the RFI in this band is from radars with pulse lengths on the order of microseconds, traditional radiometers (i.e., those which directly measure total power or power spectral density integrated over time scales of milliseconds or greater) are poorly-suited to this task. Simply reducing integration time and discarding contaminated outputs may not be a practical answer due to the wide variety of modulations and pulse lengths observed in L-band RFI signals, the dynamic and complex nature of the associated propagation channels, and the logistical effort associated with post-measurement data editing. This motivates the design and development of radiometers capable of coherent sampling and adaptive, real-time mitigation of interference. Such a radiometer will be described in this presentation. This design is capable of coherently-sampling up to 100 MHz bandwidth at L-band. RFI mitigation is implemented in FPGA components so that real-time suppression is achieved. The system currently uses a cascade of basic time- and frequency- domain detection and blanking techniques; more advanced algorithms are un- der consideration. The modular FPGA-based architecture provides other benefits, such as the ability to implement extremely stable digital filters and the ability to reconfigure the system "on the fly". An overview of the basic design along with on-the-air results from an initial implementation will be provided in the presentation. Related L-band RFI surveys will be described to illustrate the relevance of this approach in a variety of operating conditions.

Ellingson, S. W.↗
NASA NTRS2007

JTRS/SCA and Custom/SDR Waveform Comparison

This paper compares two waveform implementations generating the same RF signal using the same SDR development system. Both waveforms implement a satellite modem using QPSK modulation at 1M BPS data rates with one half rate convolutional encoding. Both waveforms are partitioned the same across the general purpose processor (GPP) and the field programmable gate array (FPGA). Both waveforms implement the same equivalent set of radio functions on the GPP and FPGA. The GPP implements the majority of the radio functions and the FPGA implements the final digital RF modulator stage. One waveform is implemented directly on the SDR development system and the second waveform is implemented using the JTRS/SCA model. This paper contrasts the amount of resources to implement both waveforms and demonstrates the importance of waveform partitioning across the SDR development system.

Oldham, Daniel R.↗
NASA NTRS2016

An Efficient, FPGA-Based, Cluster Detection Algorithm Implementation for a Strip Detector Readout System in a Time Projection Chamber Polarimeter

A fundamental challenge in a spaceborne application of a gas-based Time Projection Chamber (TPC) for observation of X-ray polarization is handling the large amount of data collected. The TPC polarimeter described uses the APV-25 Application Specific Integrated Circuit (ASIC) to readout a strip detector. Two dimensional photoelectron track images are created with a time projection technique and used to determine the polarization of the incident X-rays. The detector produces a 128x30 pixel image per photon interaction with each pixel registering 12 bits of collected charge. This creates challenging requirements for data storage and downlink bandwidth with only a modest incidence of photons and can have a significant impact on the overall mission cost. An approach is described for locating and isolating the photoelectron track within the detector image, yielding a much smaller data product, typically between 8x8 pixels and 20x20 pixels. This approach is implemented using a Microsemi RT-ProASIC3-3000 Field-Programmable Gate Array (FPGA), clocked at 20 MHz and utilizing 10.7k logic gates (14% of FPGA), 20 Block RAMs (17% of FPGA), and no external RAM. Results will be presented, demonstrating successful photoelectron track cluster detection with minimal impact to detector dead-time.

Polarimeter↗
NASA NTRS2007

Optimizations of a Hardware Decoder for Deep-Space Optical Communications

The National Aeronautics and Space Administration has developed a capacity approaching modulation and coding scheme that comprises a serial concatenation of an inner accumulate pulse-position modulation (PPM) and an outer convolutional code [or serially concatenated PPM (SCPPM)] for deep-space optical communications. Decoding of this code uses the turbo principle. However, due to the nonbinary property of SCPPM, a straightforward application of classical turbo decoding is very inefficient. Here, we present various optimizations applicable in hardware implementation of the SCPPM decoder. More specifically, we feature a Super Gamma computation to efficiently handle parallel trellis edges, a pipeline-friendly 'maxstar top-2' circuit that reduces the max-only approximation penalty, a low-latency cyclic redundancy check circuit for window-based decoders, and a high-speed algorithmic polynomial interleaver that leads to memory savings. Using the featured optimizations, we implement a 6.72 megabits-per-second (Mbps) SCPPM decoder on a single field-programmable gate array (FPGA). Compared to the current data rate of 256 kilobits per second from Mars, the SCPPM coded scheme represents a throughput increase of more than twenty-six fold. Extension to a 50-Mbps decoder on a board with multiple FPGAs follows naturally. We show through hardware simulations that the SCPPM coded system can operate within 1 dB of the Shannon capacity at nominal operating conditions.

quadratic polynomial interleaver↗
NASA NTRS2006

Time Triggered Protocol (TTP) for Integrated Modular Avionics

Traditional avionics computing systems are federated, with each system provided on a number of dedicated hardware units. Federated applications are physically separated from one another and analysis of the systems is undertaken individually. Integrated Modular Avionics (IMA) takes these federated functions and integrates them on a common computing platform in a tightly deterministic distributed real-time network of computing modules in which the different applications can run. IMA supports different levels of criticality in the same computing resource and provides a platform for implementation of fault tolerance through hardware and application redundancy. Modular implementation has distinct benefits in design, testing and system maintainability. This paper covers the requirements for fault tolerant bus systems used to provide reliable communication between IMA computing modules. An overview of the Time Triggered Protocol (TTP) specification and implementation as a reliable solution for IMA systems is presented. Application examples in aircraft avionics and a development system for future space application are covered. The commercially available TTP controller can be also be implemented in an FPGA and the results from implementation studies are covered. Finally future direction for the application of TTP and related development activities are presented.

Motzet, Guenter↗
NASA NTRS2014

High-Speed On-Board Data Processing for Science Instruments

A new development of on-board data processing platform has been in progress at NASA Langley Research Center since April, 2012, and the overall review of such work is presented in this paper. The project is called High-Speed On-Board Data Processing for Science Instruments (HOPS) and focuses on a high-speed scalable data processing platform for three particular National Research Council's Decadal Survey missions such as Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS), Aerosol-Cloud-Ecosystems (ACE), and Doppler Aerosol Wind Lidar (DAWN) 3-D Winds. HOPS utilizes advanced general purpose computing with Field Programmable Gate Array (FPGA) based algorithm implementation techniques. The significance of HOPS is to enable high speed on-board data processing for current and future science missions with its reconfigurable and scalable data processing platform. A single HOPS processing board is expected to provide approximately 66 times faster data processing speed for ASCENDS, more than 70% reduction in both power and weight, and about two orders of cost reduction compared to the state-of-the-art (SOA) on-board data processing system. Such benchmark predictions are based on the data when HOPS was originally proposed in August, 2011. The details of these improvement measures are also presented. The two facets of HOPS development are identifying the most computationally intensive algorithm segments of each mission and implementing them in a FPGA-based data processing board. A general introduction of such facets is also the purpose of this paper.

Beyon, Jeffrey Y.↗