Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sum of squares”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

One way and two way VHF ranging system performance for tracking and data relay applications

The trajectory of an orbiting spacecraft is determined from an orbit determination program. Two inputs to this program, among others, are the range and range rate relative to some known location. The arithmetic and measurement errors in the determinations of the range, range rate, and range differences were identified and evaluated. These uncertainties are tabulated for one way and two way systems. A comparison of the measurement error contributions illustrate the predominance of thermal noise effects under low power budget conditions, with the other error sources becoming relevent for the high power budget case. The evaluated uncertainties are summarized as root sum squared noise and bias errors.

Bryan, J. W.↗
NASA NTRS1975

Two self-test methods applied to an inertial system problem

The paper describes two self-test procedures applied to the problem of estimating the biases in accelerometers and gyroscopes on an inertial platform. The first technique is the weighted sum-squared residual (WSSR) test, with which accelerator bias jumps are easily isolated, but gyro bias jumps are difficult to isolate. The WSSR method does not take full advantage of the knowledge of system dynamics. The other technique is a multiple hypothesis method developed by Buxbaum and Haddad (1969). It has the advantage of directly providing jump isolation information, but suffers from computational problems. It might be possible to use the WSSR to detect state jumps and then switch to the BH system for jump isolation and estimate compensation.

Willsky, A. S.↗
NASA NTRS1975

Dispersion analysis techniques within the space vehicle dynamics simulation program

The Space Vehicle Dynamics Simulation (SVDS) program was evaluated as a dispersion analysis tool. The Linear Error Analysis (LEA) post processor was examined in detail and simulation techniques relative to conducting a dispersion analysis using the SVDS were considered. The LEA processor is a tool for correlating trajectory dispersion data developed by simulating 3 sigma uncertainties as single error source cases. The processor combines trajectory and performance deviations by a root-sum-square (RSS process) and develops a covariance matrix for the deviations. Results are used in dispersion analyses for the baseline reference and orbiter flight test missions. As a part of this study, LEA results were verified as follows: (A) Hand calculating the RSS data and the elements of the covariance matrix for comparison with the LEA processor computed data. (B) Comparing results with previous error analyses. The LEA comparisons and verification are made at main engine cutoff (MECO).

Snow, L. S.↗
NASA NTRS1981

Sensor failure detection system

Advanced concepts for detecting, isolating, and accommodating sensor failures were studied to determine their applicability to the gas turbine control problem. Five concepts were formulated based upon such techniques as Kalman filters and a screening process led to the selection of one advanced concept for further evaluation. The selected advanced concept uses a Kalman filter to generate residuals, a weighted sum square residuals technique to detect soft failures, likelihood ratio testing of a bank of Kalman filters for isolation, and reconfiguring of the normal mode Kalman filter by eliminating the failed input to accommodate the failure. The advanced concept was compared to a baseline parameter synthesis technique. The advanced concept was shown to be a viable concept for detecting, isolating, and accommodating sensor failures for the gas turbine applications.

Beattie, E. C.↗
NASA NTRS1983

Control techniques to improve Space Shuttle solid rocket booster separation

The present Space Shuttle's control system does not prevent the Orbiter's main engines from being in gimbal positions that are adverse to solid rocket booster separation. By eliminating the attitude error and attitude rate feedback just prior to solid rocket booster separation, the detrimental effects of the Orbiter's main engines can be reduced. In addition, if angular acceleration feedback is applied, the gimbal torques produced by the Orbiter's engines can reduce the detrimental effects of the aerodynamic torques. This paper develops these control techniques and compares the separation capability of the developed control systems. Currently with the worst case initial conditions and each Shuttle system dispersion aligned in the worst direction (which is more conservative than will be experienced in flight), the solid rocket booster has an interference with the Shuttle's external tank of 30 in. Elimination of the attitude error and attitude rate feedback reduces that interference to 19 in. Substitution of angular acceleration feedback reduces the interference to 6 in. The two latter interferences can be eliminated by atess conservative analysis techniques, that is, by using a root sum square of the system dispersions.

Tomlin, D. D.↗
NASA NTRS1984

An investigation into the probabilistic combination of quasi-static and random accelerations

The development of design load factors for aerospace and aircraft components and experiment support structures, which are subject to a simultaneous vehicle dynamic vibration (quasi-static) and acoustically generated random vibration, require the selection of a combination methodology. Typically, the procedure is to define the quasi-static and the random generated response separately, and arithmetically add or root sum square to get combined accelerations. Since the combination of a probabilistic and a deterministic function yield a probabilistic function, a viable alternate approach would be to determine the characteristics of the combined acceleration probability density function and select an appropriate percentile level for the combined acceleration. The following paper develops this mechanism and provides graphical data to select combined accelerations for most popular percentile levels.

Schock, R. W.↗
NASA NTRS1985

A class of optimum digital phase locked loops for the DSN advanced receiver

A class of optimum digital filters for digital phase locked loop of the deep space network advanced receiver is discussed. The filter minimizes a weighted combination of the variance of the random component of the phase error and the sum square of the deterministic dynamic component of phase error at the output of the numerically controlled oscillator (NCO). By varying the weighting coefficient over a suitable range of values, a wide set of filters are obtained such that, for any specified value of the equivalent loop-noise bandwidth, there corresponds a unique filter in this class. This filter thus has the property of having the best transient response over all possible filters of the same bandwidth and type. The optimum filters are also evaluated in terms of their gain margin for stability and their steady-state error performance.

Hurd, W. J.↗
NASA NTRS1986

Ascent trajectory dispersion analysis for WTR heads-up space shuttle trajectory

The results of a Space Transportation System ascent trajectory dispersion analysis are discussed. The purpose is to provide critical trajectory parameter values for assessing the Space Shuttle in a heads-up configuration launched from the Western Test Range (STR). This analysis was conducted using a trajectory profile based on a launch from the WTR in December. The analysis consisted of the following steps: (1) nominal trajectories were simulated under the conditions as specified by baseline reference mission guidelines; (2) dispersion trajectories were simulated using predetermined parametric variations; (3) requirements for a system-related composite trajectory were determined by a root-sum-square (RSS) analysis of the positive deviations between values of the aerodynamic heating indicator (AHI) generated by the dispersion and nominal trajectories; (4) using the RSS assessment as a guideline, the system related composite trajectory was simulated by combinations of dispersion parameters which represented major contributors; (5) an assessment of environmental perturbations via a RSS analysis was made by the combination of plus or minus 2 sigma atmospheric density variation and 95% directional design wind dispersions; (6) maximum aerodynamic heating trajectories were simulated by variation of dispersion parameters which would emulate the summation of the system-related RSS and environmental RSS values of AHI. The maximum aerodynamic heating trajectories were simulated consistent with the directional winds used in the environmental analysis.

Source record↗
NASA NTRS1986

Viscoelastic deformation near active plate boundaries

Model deformations near the active plate boundaries of Western North America using space-based geodetic measurements as constraints are discussed. The first six months of this project were spent gaining familarity with space-based measurements, accessing the Crustal Dynamics Data Information Computer, and building time independent deformation models. The initial goal was to see how well the simplest elastic models can reproduce very long base interferometry (VLBI) baseline data. From the Crustal Dynamics Data Information Service, a total of 18 VLBI baselines are available which have been surveyed on four or more occasions. These data were fed into weighted and unweighted inversions to obtain baseline closure rates. Four of the better quality lines are illustrated. The deformation model assumes that the observed baseline rates result from a combination of rigid plate tectonic motions plus a component resulting from elastic strain build up due to a failure of the plate boundary to slip at the full plate tectonic rate. The elastic deformation resulting from the locked plate boundary is meant to portray interseismic strain accumulation. During and shortly after a large interplate earthquake, these strains are largely released, and points near the fault which were previously retarded suddenly catch up to the positions predicted by rigid plate models. Researchers judge the quality of fit by the sum squares of weighted residuals, termed total variance. The observed baseline closures have a total variance of 99 (cm/y)squared. When the RM2 velocities are assumed to model the data, the total variance increases to 154 (cm/y)squared.

Ward, S. N.↗
NASA NTRS1986

A comparison of methods for DPLL loop filter design

Four design methodologies for loop filters for a class of digital phase-locked loops (DPLLs) are presented. The first design maps an optimum analog filter into the digital domain; the second approach designs a filter that minimizes in discrete time weighted combination of the variance of the phase error due to noise and the sum square of the deterministic phase error component; the third method uses Kalman filter estimation theory to design a filter composed of a least squares fading memory estimator and a predictor. The last design relies on classical theory, including rules for the design of compensators. Linear analysis is used throughout the article to compare different designs, and includes stability, steady state performance and transient behavior of the loops. Design methodology is not critical when the loop update rate can be made high relative to loop bandwidth, as the performance approaches that of continuous time. For low update rates, however, the miminization method is significantly superior to the other methods.

Aguirre, S.↗
NASA NTRS1988

Designing Digital Filters

Digital Filter Design program presents method to compare desired and designed digital filters by minimizing sum-square error of differences in magnitude and phase angles. Written in FORTRAN IV.

Lin, Chiang↗
NASA NTRS1987

Spacecraft attitude determination using a second-order nonlinear filter

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

Vathsal, S.↗
NASA NTRS1990

Laboratory measurements of NO2 line parameters near 1600/cm for the interpretation of stratospheric spectra

Tunable diode laser laboratory measurements of infrared spectral parameters of selected NO2 lines near 1600/cm have been made to assess the contribution of uncertainties in these parameters to stratospheric measurements of NO2 made using the Balloon-Borne Laser In-Situ Sensor (BLISS) tunable diode laser spectrometer. Relative line intensities are measured to accuracies of better than 2 percent, with a root-sum-squared uncertainty in the absolute linestrengths of 4.5 percent. Air-broadening coefficients have been determined from measurements at total pressures in the range 20-100 Torr, at temperatures of 293 K and 214 K. These results are also discussed in the light of the discrepancies between infrared instruments flown in the 1982 and 1983 Balloon Intercomparison Campaigns.

May, R. D.↗
NASA NTRS1993

MASTRE trajectory code update to automate flight trajectory design, performance predictions, and vehicle sizing for support of shuttle and shuttle derived vehicles: Programmers manual

The information required by a programmer using the Minimum Hamiltonian AScent Trajectory Evaluation (MASTRE) Program is provided. This document enables the programmer to either modify the program or convert the program to computers other than the VAX computer. Documentation for each subroutine or function based on providing the definitions of the variables and a source listing are included. Questions concerning the equations, techniques, or input requirements should be answered by either the Engineering or User's manuals. Three appendices are also included which provide a listing of the Root-Sum-Square (RSS) program, a listing of subroutine names and definitions used in the MASTRE User Friendly Interface Program, and listing of the subroutine names and definitions used in the Mass Properties Program. The RSS Program is used to aid in the performance of dispersion analyses. The RSS program reads a file generated by the MASTRE Program, calculates dispersion parameters, and generates output tables and output plot files. UFI Program provides a screen user interface to aid the user in providing input to the model. The Mass Properties Program defines the mass properties data for the MASTRE program through the use of user interface software.

Source record↗
NASA NTRS1992

Normalization of cell responses in cat striate cortex

Simple cells in the striate cortex have been depicted as half-wave-rectified linear operators. Complex cells have been depicted as energy mechanisms, constructed from the squared sum of the outputs of quadrature pairs of linear operators. However, the linear/energy model falls short of a complete explanation of striate cell responses. In this paper, a modified version of the linear/energy model is presented in which striate cells mutually inhibit one another, effectively normalizing their responses with respect to stimulus contrast. This paper reviews experimental measurements of striate cell responses, and shows that the new model explains a significantly larger body of physiological data.

Heeger, D. J.↗
NASA NTRS1994

Evaluation of very long baseline interferometry atmospheric modeling improvements

We determine the improvement in baseline length precision and accuracy using new atmospheric delay mapping functions and MTT by analyzing the NASA Crustal Dynamics Project research and development (R&D) experiments and the International Radio Interferometric Surveying (IRIS) A experiments. These mapping functions reduce baseline length scatter by about 20% below that using the CfA2.2 dry and Chao wet mapping functions. With the newer mapping functions, average station vertical scatter inferred from observed length precision (given by length repeatabilites) is 11.4 mm for the 1987-1990 monthly R&D series of experiments and 5.6 mm for the 3-week-long extended research and development experiment (ERDE) series. The inferred monthly R&D station vertical scatter is reduced by 2 mm or by 7 mm is a root-sum-square (rss) sense. Length repeatabilities are optimum when observations below a 7-8 deg elevation cutoff are removed from the geodetic solution. Analyses of IRIS-A data from 1984 through 1991 and the monthly R&D experiments both yielded a nonatmospheric unmodeled station vertical error or about 8 mm. In addition, analysis of the IRIS-A exeriments revealed systematic effects in the evolution of some baseline length measurements. The length rate of change has an apparent acceleration, and the length evolution has a quasi-annual signature. We show that the origin of these effects is unlikely to be related to atmospheric modeling errors. Rates of change of the transatlantic Westford-Wettzell and Richmond-Wettzell baseline lengths calculated from 1988 through 1991 agree with the NUVEL-1 plate motion model (Argus and Gordon, 1991) to within 1 mm/yr. Short-term (less than 90 days) variations of IRIS-A baseline length measurements contribute more than 90% of the observed scatter about a best fit line, and this short-term scatter has large variations on an annual time scale.

Macmillan, D. S.↗
NASA NTRS1994

TOPEX/POSEIDON mission overview

TOPEX/POSEIDON is the first space mission specifically designed and conducted for studying the circulation of the world's oceans. A state-of-the-art radar altimetry system is used to measure the precise height of sea level, from which information on the ocean circulation is obtained. The satellite, launched on August 10, 1992, has been making observations of the global oceans with unprecedented accuracy since late September 1992. To meet the stringent measurement accuracy required for ocean circulation studies, a number of innovative improvements have been made to the mission design, including the first dual-frequency space-borne radar altimeter capable of retrieving the ionospheric delay of the radar signal, a three-frequency microwave radiometer for retrieving the signal delay caused by the water vapor in the troposphere, an optimal model of the Earth's gravity field and multiple satellite tracking systems for precision orbit determination. Additionally, the satellite also carries two experimental instruments to demonstrate new technologies: a single-frequency solid-state altimeter for the technology of low-power, low-weight altimeter and a Global Positioning System receiver for continuous,precise satellite tracking. The performance of the mission's measurement system has been tested by numerous verification studies. The results indicate that the root-sum-square accuracy of a single-pass sea level measurement is 4.7 cm for the TOPEX system and 5.1 cm for the POSEIDON system; both are more than a factor of 2 better than the requirement of 13.7 cm. This global data set is being analyzed to improve understanding of the global ocean circulation as well as the ocean tides, geodesy, and geodynamics, and ocean wind and waves. The mission is designed to last for at least 3 years with a possible extension to 6 years. The multiyear global data set will go a long way toward understanding the ocean circulation and its variability in relation to climate change. A summary of the mission's systems and their performance as well as the mission's science team is presented.

Fu, Lee-Lueng↗
NASA NTRS1994

Atmospheric pressure loading parameters from very long baseline interferometry observations

Atmospheric mass loading produces a primarily vertical displacement of the Earth's crust. This displacement is correlated with surface pressure and is large enough to be detected by very long baseline interferometry (VLBI) measurements. Using the measured surface pressure at VLBI stations, we have estimated the atmospheric loading term for each station location directly from VLBI data acquired from 1979 to 1992. Our estimates of the vertical sensitivity to change in pressure range from 0 to -0.6 mm/mbar depending on the station. These estimates agree with inverted barometer model calculations (Manabe et al., 1991; vanDam and Herring, 1994) of the vertical displacement sensitivity computed by convolving actual pressure distributions with loading Green's functions. The pressure sensitivity tends to be smaller for stations near the coast, which is consistent with the inverted barometer hypothesis. Applying this estimated pressure loading correction in standard VLBI geodetic analysis improves the repeatability of estimated lengths of 25 out of 37 baselines that were measured at least 50 times. In a root-sum-square (rss) sense, the improvement generally increases with baseline length at a rate of about 0.3 to 0.6 ppb depending on whether the baseline stations are close to the coast. For the 5998-km baseline from Westford, Massachusetts, to Wettzell, Germany, the rss improvement is about 3.6 mm out of 11.0 mm. The average rss reduction of the vertical scatter for inland stations ranges from 2.7 to 5.4 mm.

Macmillan, D. S.↗