Search NASA⌕ Search

SEARCH · Search NASA

Results for “Optimal estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Northern and Southern Hemisphere Ground-Based Infrared Spectroscopic Measurements of Tropospheric Carbon Monoxide and Ethane

Time series of CO and C2H, measurements have been derived from high-resolution infrared solar spectra recorded in Lauder, New Zealand (45.0 degrees S, 169.7 degrees E, altitude 0.37 km), and at the U.S. National Solar Observatory (31.9 degrees N, 11, 1.6 degrees W, altitude 2.09 km) on Kitt Peak. Lauder observations were obtained between July 1993 and November 1997, while the Kitt Peak measurements were recorded between May 1977 and December 1997. Both databases were analyzed with spectroscopic parameters that included significant improvements for C2H6 relative to previous studies. Target CO and C2H6 lines were selected to achieve similar vertical samplings based on averaging kernels. These calculations show that partial columns from layers extending from the surface to the mean tropopause and from the mean tropopause to 100 km are nearly independent. Retrievals based on a semiempirical application of the Rodgers optimal estimation technique are reported for the lower layer, which has a broad maximum in sensitivity in the upper troposphere. The Lauder CO and C2H, partial columns exhibit highly asymmetrical seasonal cycles with minima in austral autumn and sharp peaks in austral spring. The spring maxima are the result of tropical biomass burning emissions followed by deep convective vertical transport to the upper troposphere and long-range horizontal transport. Significant year-to-year variations are observed for both CO and C2H6, but the measured trends, (+0.37 +/- 0.57)% yr(exp -1) and (-0.64 +/- 0.79)% yr(exp -1), I sigma, respectively, indicate no significant long-term changes. The Kitt Peak data also exhibit CO and C2H6, seasonal variations in the lower layer with trends equal to (-0.27 +/- 0.17)% yr(exp -1) and (-1.20 +/- 0.35)% yr(exp -1), 1 sigma, respectively. Hence a decrease in the Kitt Peak tropospheric C2H6 column has been detected, though the CO trend is not significant. Both measurement sets are compared with previous observations, reported trends, and three-dimensional model calculations.

Rinsland, Curtis P.↗

Development of a prototype algorithm for the operational retrieval of height-resolved products from GOME

Global ozone monitoring experiment (GOME) level 2 products of total ozone column amounts have been generated on a routine operational basis since July 1996. These products and the level 1 radiance products are the major outputs from the ERS-2 ground segment GOME data processor (GDP) at DLR in Germany. Off-line scientific work has already shown the feasibility of ozone profile retrieval from GOME. It is demonstrated how the retrievals can be performed in an operational context. Height-resolved retrieval is based on the optimal estimation technique, #and cloud-contaminated scenes are treated in an equivalent reflecting surface approximation. The prototype must be able to handle GOME measurements routinely on a global basis. Requirements for the major components of the algorithm are described: this incorporates an overall strategy for operational height-resolved retrieval from GOME.

Spurr, Robert J. D.↗

Northern and Southern Hemisphere Ground-Based Infrared Spectroscopic Measurements of Tropospheric Carbon Monoxide and Ethane

Time series of CO and C2H6 measurements have been derived from high resolution infrared solar spectra recorded in Lauder, New Zealand (45.0 deg S, 169.7 deg E, altitude 0.37 km) and at the U. S. National Solar Observatory (31.90 deg N, 111.6 deg W, altitude 2.09 km) on Kitt Peak. Lauder observations were obtained between July 1993 and November 1997 while the Kitt Peak measurements were recorded between May 1977 and December 1997. Both databases were analyzed with spectroscopic parameters that included significant improvements for C2H6 relative to previous studies. Target CO and C2H6 lines were selected to achieve similar vertical samplings based on averaging kernels. These calculations show that partial columns from layers extending from the surface to the mean tropopause and from the mean tropopause to 100 km are nearly independent. Retrievals based on a semiempirical application of the Rodgers optimal estimation technique are reported for the lower layer, which has a broad maximum in sensitivity in the upper troposphere. The Lauder CO and C2H6 partial columns exhibit highly asymmetrical seasonal cycles with minima in austral autumn and sharp peaks in austral spring. The spring maxima are the result of tropical biomass burning emissions followed by deep convective vertical transport to the upper troposphere and long-range horizontal transport. Significant year-to-year variations are observed for both CO and C2H6, but the measured trends, (+0.37 +/- 0.57)%/ yr and (-0.64 +/- 0.79)%/ yr, 1 sigma, respectively, indicate no significant long-term changes. The Kitt Peak data also exhibit CO and C2H6 seasonal variations in the lower layer with trends equal to (-0.27 +/- 0.17)%/ yr and (-1.20 +/- 0.35)%/ yr, 1 sigma, respectively. Hence, a decrease in the Kitt Peak tropospheric C2H6 column has been detected, though the CO trend is not significant. Both measurement sets are compared with previous observations, reported trends, and three-dimensional model calculations.

Rinsland, Curtis P.↗

Integrated INS/GPS Navigation from a Popular Perspective

Inertial navigation, blended with other navigation aids, Global Positioning System (GPS) in particular, has gained significance due to enhanced navigation and inertial reference performance and dissimilarity for fault tolerance and anti-jamming. Relatively new concepts based upon using Differential GPS (DGPS) blended with Inertial (and visual) Navigation Sensors (INS) offer the possibility of low cost, autonomous aircraft landing. The FAA has decided to implement the system in a sophisticated form as a new standard navigation tool during this decade. There have been a number of new inertial sensor concepts in the recent past that emphasize increased accuracy of INS/GPS versus INS and reliability of navigation, as well as lower size and weight, and higher power, fault tolerance, and long life. The principles of GPS are not discussed; rather the attention is directed towards general concepts and comparative advantages. A short introduction to the problems faced in kinematics is presented. The intention is to relate the basic principles of kinematics to probably the most used navigation method in the future-INS/GPS. An example of the airborne INS is presented, with emphasis on how it works. The discussion of the error types and sources in navigation, and of the role of filters in optimal estimation of the errors then follows. The main question this paper is trying to answer is 'What are the benefits of the integration of INS and GPS and how is this, navigation concept of the future achieved in reality?' The main goal is to communicate the idea about what stands behind a modern navigation method.

Omerbashich, Mensur↗

Description and Sensitivity Analysis of the SOLSE/LORE-2 and SAGE III Limb Scattering Ozone Retrieval Algorithms

The SOLSE (Shuttle Ozone Limb Sounding Experiment) and LORE (Limb Ozone Retrieval Experiment) instruments are scheduled for reflight on Space Shuttle flight STS-107 in July 2002. In addition, the SAGE III (Stratospheric Aerosol and Gas Experiment) instrument will begin to make limb scattering measurements during Spring 2002. The optimal estimation technique is used to analyze visible and ultraviolet limb scattered radiances and produce a retrieved ozone profile. The algorithm used to analyze data from the initial flight of the SOLSE/LORE instruments (on Space Shuttle flight STS-87 in November 1997) forms the basis of the current algorithms, with expansion to take advantage of the increased multispectral information provided by SOLSE/LORE-2 and SAGE III. We also present detailed sensitivity analysis for these ozone retrieval algorithms. The primary source of ozone retrieval error is tangent height misregistration (i.e., instrument pointing error), which is relevant throughout the altitude range of interest, and can produce retrieval errors on the order of 10-20 percent due to a tangent height registration error of 0.5 km at the tangent point. Other significant sources of error are sensitivity to stratospheric aerosol and sensitivity to error in the a priori ozone estimate (given assumed instrument signal-to-noise = 200). These can produce errors up to 10 percent for the ozone retrieval at altitudes less than 20 km, but produce little error above that level.

Loughman, R.↗

Retrievals of Jovian Tropospheric Phosphine from Cassini/CIRS

On December 30th 2000, the Cassini-Huygens spacecraft reached the perijove milestone on its continuing journey to the Saturnian system. During an extended six-month encounter, the Composite Infrared Spectrometer (CIRS) returned spectra of the Jovian atmosphere, rings and satellites from 10-1400 cm(exp -1) (1000-7 microns) at a programmable spectral resolution of 0.5 to 15 cm(exp -1). The improved spectral resolution of CIRS over previous IR instrument-missions to Jupiter, the extended spectral range, and higher signal-to-noise performance provide significant advantages over previous data sets. CIRS global observations of the mid-infrared spectrum of Jupiter at medium resolution (2.5 cm(exp -1)) have been analysed both with a radiance differencing scheme and an optimal estimation retrieval model to retrieve the spatial variation of phosphine and ammonia fractional scale height in the troposphere between 60 deg S and 60 deg N at a spatial resolution of 6 deg. The ammonia fractional scale height appears to be high over the Equatorial Zone (EZ) but low over the North Equatorial Belt (NEB) and South Equatorial Belt (SEB) indicating rapid uplift or strong vertical mixing in the EZ. The abundance of phosphine shows a similar strong latitudinal variation which generally matches that of the ammonia fractional scale height. However while the ammonia fractional scale height distribution is to a first order symmetric in latitude, the phosphine distribution shows a North/South asymmetry at mid latitudes with higher amounts detected at 40 deg N than 40 deg S. In addition the data show that while the ammonia fractional scale height at this spatial resolution appears to be low over the Great Red Spot (GRS), indicating reduced vertical mixing above the approx. 500 mb level, the abundance of phosphine at deeper levels may be enhanced at the northern edge of the GRS indicating upwelling.

Irwin, P. G. J.↗

Cirrus Clouds Optical, Microphysical and Radiative Properties Observed During Crystal-Face Experiment: I. A Radar-Lidar Retrieval System

A method of retrieving cloud microphysical properties using combined observations from both cloud radar and lidar is introduced. This retrieval makes use of an improvement to the traditional optimal estimation retrieval method, whereby a series of corrections are applied to the state vector during the search for an iterative solution. This allows faster convergence to a solution and is less processor intensive. The method is first applied to a synthetic cloud t o demonstrate its validity, and it is shown that the retrieval reliably reproduces vertical profiles of ice water content. The retrieval method is then applied to radar and lidar observations from the CRYSTAL-FACE experiment, and vertical profiles of ice crystal diameter, number concentration, and ice water content are retrieved for a cirrus cloud layers observed one day of that experiment. The validity of the relationship between visible extinction coefficient and radar reflectivity was examined. While synthetic tests showed such a functional relationship, the measured data only partially supported such a conclusion. This is due to errors in the forward model (as explained above) as well as errors in the data sets, including possible mismatch between lidar and radar profiles or errors in the optical depth. Empirical relationships between number concentrations and mean particle diameter were also examined. The results indicate that a distinct and robust relationship exists between these retrieved quantities and it is argued that such a relationship is more than an artifact of the retrieval process offering insight into the nature of the microphysical processes taking place in cirrus.

Mitrescu, C.↗

Hubble Space Telescope Fine Guidance Sensor and Two-Gyro Control Law Design, Implementation, and On-Orbit Performance

For fifteen years, the science mission of the Hubble Space Telescope (HST) required using at least three rate gyros for n Controlling with alternate sensors to replace failing gyros can extend the HST science mission. A two-gyro control law has been designed and implemented using magnetometers, star trackers, and Fine Guidance Sensors (FGSs) to control vehicle rate about the missing gyro axis. The three aforementioned sensors are used in succession to reduce HST boresight jitter to less than 7 milli-arcseconds rms prior to science imaging. The Magnetometer and 2-Gyro (M2G) control law is used for large angle maneuvers and attitude control during earth. occultation of star trackers and FGSs. The Tracker and 2-Gyro (T2G) control law dampens M2G rates and controls attitude in preparation for guide star acquisition with the FGSs. The Fine Guidance Sensor and 2-Gyro (F2G) control law dampens T2G rates and controls HST attitude during science imaging. This paper describes the F2G control law. Details of F2G algorithms are presented, including computation of the FGS-measured star vector using non-linear equations, optimal estimation of HST body rate, design of the F2G control laws and gyro bias observer, SISO and MIMO linear stability analyses, and design of the F2G intramode transition and guide star acquisition logic. Results from an FGS flight spare ground test are presented that define acceptable HST jitter levels for successful guide star acquisition under two-gyro control. HST-specific disturbance and noise models are described that are based upon flight telemetry; these models are used in HSTSIM, a high-fidelity non-linear time domain simulation, to predict HST on-orbit disturbance responses and FGS interferometer Loss of Lock (LOL) characteristics under F2G control. Additional HSTSIM results are presented predicting HST quiescent boresight jitter performance, science maneuver performance, and observer configuration performance during F2G operation. Simulation results are compared to on-orbit data b m F2G flight tests performed in February 2005. Science images and point spread functions from the Advanced Camera for Surveys (ACS) High Resolution Camera (HRC) are presented that compare HST science performance under F2G versus three-gyro control. Images and flight telemetry show that HST boresight jitter with the new F2G control law is usually less than jitter using the three-gyro law, and HST boresight jitter during F2G operation is dependent upon guide star magnitude.

Clapp, Brian R.↗

The Short-Term Prediction of Universal Time and Length-Of-Day Using Atmospheric Angular Momemtum

Methods to combine the diverse set of geodetic measurements of Earth orientation that are currently available, and to interpolate and extrapolate these data to generate an optimal estimate of Earth orientation, have been under development at JPL for a number of years. The strategy currently in use is a Kalman filtering scheme based on Earth orentation parameters and their excitation functions that incorporates stochastic models of the important physical processes and takes into account the variable form, quality, and temporal density of the data provided by diffent measurement services.

Universal Time↗

On the Biases in AIRS Retrieval of Ozone (Work in Progress)

A viewgraph presentation on various biases in AIRS retrieval of ozone is given. The topics include: 1) AIRS captures UTLS ozone events; 2) Simplified AIRS retrieval of ozone; 3) How much is AIRS getting its skill in ozone from regression? biases are similar to ECMWF; 4) How does channel selection and damping affect the retrieval?; 5) Decreasing damping worsens results in upper"trop/lower"strat with current channel selection; 6) If results worse with decreased damping, let s give the retrieval more information; 7) Adding channels at current damping doesn't change anything.; 8) Adding channels and decreasing damping gives mixed results; 9) Let's look at the radiances and their uncertainties ; 10) Systematic biases in radiance uncertainties?; 11) Surface Temperature; 12) Temperature Profile; and 13) x vs Brightness Temperature Error Optimal Estimation Retrieval.

Atmospheric Infrared Sounder (AIRS)↗

SeaWinds Scatterometer Wind Vector Retrievals Within Hurricanes Using AMSR and NEXRAD to Perform Corrections for Precipitation Effects: Comparison of AMSR and NEXRAD Retrievals of Rain

The opportunity provided by satellite scatterometers to measure ocean surface winds in strong storms and hurricanes is diminished by the errors in the received backscatter (SIGMA-0) caused by the attenuation, scattering and surface roughening produced by heavy rain. Providing a good rain correction is a very challenging problem, particularly at Ku band (13.4 GHz) where rain effects are strong. Corrections to the scatterometer measurements of ocean surface winds can be pursued with either of two different methods: empirical or physical modeling. The latter method is employed in this study because of the availability of near simultaneous and collocated measurements provided by the MIDORI-II suite of instruments. The AMSR was designed to measure atmospheric water-related parameters on a spatial scale comparable to the SeaWinds scatterometer. These quantities can be converted into volumetric attenuation and scattering at the Ku-band frequency of SeaWinds. Optimal estimates of the volume backscatter and attenuation require a knowledge of the three dimensional distribution of reflectivity on a scale comparable to that of the precipitation. Studies selected near the US coastline enable the much higher resolution NEXRAD reflectivity measurements evaluate the AMSR estimates. We are also conducting research into the effects of different beam geometries and nonuniform beamfilling of precipitation within the field-of-view of the AMSR and the scatterometer. Furthermore, both AMSR and NEXRAD estimates of atmospheric correction can be used to produce corrected SIGMA-0s, which are then input to the JPL wind retrieval algorithm.

SeaWinds↗

Regional Comparison and Assimilation of GOCART and MODIS Aerosol Optical Depth across the Eastern U.S.

This study compares aerosol optical depths (AOD) products from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model and their integrated products with ground measurements across the eastern U.S. from March 1, 2000 to December 31, 2001. The Terra MODIS Level-3 (collection 4) AOD at 0.55 pm has better correlation, but consistently overestimates the values of the Aerosol Robotic Network (AERONET) measurements. GOCART has small biases for a 22-month integration, and slight positive biases are appeared for the cold season. These results are also supported by the comparison with the IMPROVE (Interagency Monitoring of Protected Visual Environments) light extinction index. The optimal interpolation improves the daily-scale RMSE from either MODIS or GOCART alone. However, the regional biases in the aerosol products constitute a major constraint to the optimal estimate of AOD.

Matsui, Toshihisa↗

SPARTAN: A High-Fidelity Simulation for Automated Rendezvous and Docking Applications

bd Systems (a subsidiary of SAIC) has developed the Simulation Package for Autonomous Rendezvous Test and ANalysis (SPARTAN), a high-fidelity on-orbit simulation featuring multiple six-degree-of-freedom (6DOF) vehicles. SPARTAN has been developed in a modular fashion in Matlab/Simulink to test next-generation automated rendezvous and docking guidance, navigation,and control algorithms for NASA's new Vision for Space Exploration. SPARTAN includes autonomous state-based mission manager algorithms responsible for sequencing the vehicle through various flight phases based on on-board sensor inputs and closed-loop guidance algorithms, including Lambert transfers, Clohessy-Wiltshire maneuvers, and glideslope approaches The guidance commands are implemented using an integrated translation and attitude control system to provide 6DOF control of each vehicle in the simulation. SPARTAN also includes high-fidelity representations of a variety of absolute and relative navigation sensors that maybe used for NASA missions, including radio frequency, lidar, and video-based rendezvous sensors. Proprietary navigation sensor fusion algorithms have been developed that allow the integration of these sensor measurements through an extended Kalman filter framework to create a single optimal estimate of the relative state of the vehicles. SPARTAN provides capability for Monte Carlo dispersion analysis, allowing for rigorous evaluation of the performance of the complete proposed AR&D system, including software, sensors, and mechanisms. SPARTAN also supports hardware-in-the-loop testing through conversion of the algorithms to C code using Real-Time Workshop in order to be hosted in a mission computer engineering development unit running an embedded real-time operating system. SPARTAN also contains both runtime TCP/IP socket interface and post-processing compatibility with bdStudio, a visualization tool developed by bd Systems, allowing for intuitive evaluation of simulation results. A description of the SPARTAN architecture and capabilities is provided, along with details on the models and algorithms utilized and results from representative missions.

Turbe, Michael A.↗

On the Long-Term Stability of Microwave Radiometers Using Noise Diodes for Calibration

Results are presented from the long-term monitoring and calibration of the National Aeronautics and Space Administration Jason Microwave Radiometer (JMR) on the Jason-1 ocean altimetry satellite and the ground-based Advanced Water Vapor Radiometers (AWVRs) developed for the Cassini Gravity Wave Experiment. Both radiometers retrieve the wet tropospheric path delay (PD) of the atmosphere and use internal noise diodes (NDs) for gain calibration. The JMR is the first radiometer to be flown in space that uses NDs for calibration. External calibration techniques are used to derive a time series of ND brightness for both instruments that is greater than four years. For the JMR, an optimal estimator is used to find the set of calibration coefficients that minimize the root-mean-square difference between the JMR brightness temperatures and the on-Earth hot and cold references. For the AWVR, continuous tip curves are used to derive the ND brightness. For the JMR and AWVR, both of which contain three redundant NDs per channel, it was observed that some NDs were very stable, whereas others experienced jumps and drifts in their effective brightness. Over the four-year time period, the ND stability ranged from 0.2% to 3% among the diodes for both instruments. The presented recalibration methodology demonstrates that long-term calibration stability can be achieved with frequent recalibration of the diodes using external calibration techniques. The JMR PD drift compared to ground truth over the four years since the launch was reduced from 3.9 to - 0.01 mm/year with the recalibrated ND time series. The JMR brightness temperature calibration stability is estimated to be 0.25 K over ten days.

noise diode (ND)↗

Precipitating Snow Retrievals from Combined Airborne Cloud Radar and Millimeter-Wave Radiometer Observations

An algorithm for retrieving snow over oceans from combined cloud radar and millimeter-wave radiometer observations is developed. The algorithm involves the use of physical models to simulate cloud radar and millimeter-wave radiometer observations from basic atmospheric variables such as hydrometeor content, temperature, and relative humidity profiles and is based on an optimal estimation technique to retrieve these variables from actual observations. A high-resolution simulation of a lake-effect snowstorm by a cloud-resolving model is used to test the algorithm. That is, synthetic observations are generated from the output of the cloud numerical model, and the retrieval algorithm is applied to the synthetic data. The algorithm performance is assessed by comparing the retrievals with the reference variables used in synthesizing the observations. The synthetic observation experiment indicates good performance of the retrieval algorithm. The algorithm is also applied to real observations from the Wakasa Bay field experiment that took place over the Sea of Japan in January and February 2003. The application of the retrieval algorithm to data from the field experiment yields snow estimates that are consistent with both the cloud radar and radiometer observations.

Grecu, Mircea↗

A New Technique for Retrieval of Tropospheric and Stratospheric Ozone Profiles using Sky Radiance Measurements at Multiple View Angles: Application to a Brewer Spectrometer

This paper describes and applies a new technique for retrieving diurnal variability in tropospheric ozone vertical distribution using ground-based measurements of ultraviolet sky radiances. The measured radiances are obtained by a polarization-insensitive modified Brewer double spectrometer located at Goddard Space Flight Center, in Greenbelt, Maryland, USA. Results demonstrate that the Brewer angular (0-72deg viewing zenith angle) and spectral (303-320 nm) measurements of sky radiance in the solar principal plane provide sufficient information to derive tropospheric ozone diurnal variability. In addition, the Brewer measurements provide stratospheric ozone vertical distributions at least twice per day near sunrise and sunset. Frequent measurements of total column ozone amounts from direct-sun observations are used as constraints in the retrieval. The vertical ozone profile resolution is shown in terms of averaging kernels to yield at least four points in the troposphere-low stratosphere, including good information in Umkehr layer 0 (0-5 km). The focus of this paper is on the derivation of stratospheric and tropospheric ozone profiles using both simulated and measured radiances. We briefly discuss the necessary modifications of the Brewer spectrometer that were used to eliminate instrumental polarization sensitivity so that accurate sky radiances can be obtained in the presence of strong Rayleigh scattering and aerosols. The results demonstrate that including a site-specific and time-dependent aerosol correction, based on Brewer direct-sun observations of aerosol optical thickness, is critical to minimize the sky radiance residuals as a function of observing angle in the optimal estimation inversion algorithm and improve the accuracy of the retrieved ozone profile.

Tzortziou, Maria↗

Detection, Identification, Location, and Remote Sensing Using SAW RFID Sensor Tags

The Electromagnetic Systems Branch (EV4) of the Avionic Systems Division at NASA Johnson Space Center in Houston, TX is studying the utility of surface acoustic wave (SAW) radiofrequency identification (RFID) tags for multiple wireless applications including detection, identification, tracking, and remote sensing of objects on the lunar surface, monitoring of environmental test facilities, structural shape and health monitoring, and nondestructive test and evaluation of assets. For all of these applications, it is anticipated that the system utilized to interrogate the SAW RFID tags may need to operate at fairly long range and in the presence of considerable multipath and multiple-access interference. Towards that end, EV4 is developing a prototype SAW RFID wireless interrogation system for use in such environments called the Passive Adaptive RFID Sensor Equipment (PARSED) system. The system utilizes a digitally beam-formed planar receiving antenna array to extend range and provide direction-of-arrival information coupled with an approximate maximum-likelihood signal processing algorithm to provide near-optimal estimation of both range and temperature. The system is capable of forming a large number of beams within the field of view and resolving the information from several tags within each beam. The combination of both spatial and waveform discrimination provides the capability to track and monitor telemetry from a large number of objects appearing simultaneously within the field of view of the receiving array. In this paper, we will consider the application of the PARSEQ system to the problem of simultaneous detection, identification, localization, and temperature estimation for multiple objects. We will summarize the overall design of the PARSEQ system and present a detailed description of the design and performance of the signal detection and estimation algorithms incorporated in the system. The system is currently configured only to measure temperature (jointly with range and tag ID), but future versions will be revised to measure parameters other than temperature as SAW tags capable of interfacing with external sensors become available. It is anticipated that the estimation of arbitrary parameters measured using SAW-based sensors will be based on techniques very similar to the joint range and temperature estimation techniques described in this paper.

Barton, Richard J.↗