The state-variable approach to analog communication theory.
Approximate minimum mean square error estimates of Markovian state vector observed in nonlinearly imbedded stochastic signal, noting analog communication theory
Snyder, D. L.↗
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Results for “error vector”
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.
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Attitude determination and sensor alignment via weighted least squares affine transformations
Vehicle attitude determination and guidance sensor orientation by vector space matrix method, minimizing errors by weighted least squares affine transformation technique
Davenport, P. B.↗
In-flight calibration of the high-gain antenna pointing for the Mariner Venus-Mercury 1973 spacecraft
The methods used to in-flight calibrate the pointing direction of the Mariner Venus-Mercury 1973 spacecraft high gain antenna and the achieved antenna pointing accuracy are described. The overall pointing calibration was accomplished by performing calibration sequences at a number of points along the spacecraft trajectory. Each of these consisted of articulating the antenna about the expected spacecraft-earth vector to determine systematic pointing errors. The high gain antenna pointing system, the error model used in the calibration, and the calibration and pointing strategy and results are discussed.
Hardman, J. M.↗
Shuttle program: Ground tracking data program document shuttle OFT launch/landing
The equations for processing ground tracking data during a space shuttle ascent or entry, or any nonfree flight phase of a shuttle mission are given. The resulting computer program processes data from up to three stations simultaneously: C-band station number 1; C-band station number 2; and an S-band station. The C-band data consists of range, azimuth, and elevation angle measurements. The S-band data consists of range, two angles, and integrated Doppler data in the form of cycle counts. A nineteen element state vector is used in Kalman filter to process the measurements. The acceleration components of the shuttle are taken to be independent exponentially-correlated random variables. Nine elements of the state vector are the measurement bias errors associated with range and two angles for each tracking station. The biases are all modeled as exponentially-correlated random variables with a typical time constant of 108 seconds. All time constants are taken to be the same for all nine state variables. This simplifies the logic in propagating the state error covariance matrix ahead in time.
Lear, W. M.↗
The airborne laser ranging system, its capabilities and applications
The airborne laser ranging system is a multibeam short pulse laser ranging system on board an aircraft. It simultaneously measures the distances between the aircraft and six laser retroreflectors (targets) deployed on the Earth's surface. The system can interrogate over 100 targets distributed over an area of 25,000 sq, kilometers in a matter of hours. Potentially, a total of 1.3 million individual range measurements can be made in a six hour flight. The precision of these range measurements is approximately + or - 1 cm. These measurements are used in procedure which is basically an extension of trilateration techniques to derive the intersite vector between the laser ground targets. By repeating the estimation of the intersite vector, strain and strain rate errors can be estimated. These quantities are essential for crustal dynamic studies which include determination and monitoring of regional strain in the vicinity of active fault zones, land subsidence, and edifice building preceding volcanic eruptions.
Kahn, W. D.↗
The Airborne Laser Ranging System - Its capabilities and applications
The Airborne Laser Ranging System is a proposed multibeam short pulse laser ranging system on board an aircraft. It simultaneously measures the distances between the aircraft and six laser retroreflectors (targets) deployed on the earth's surface. Depending on the host aircraft and terrain characteristics, the system can interrogate hundreds of targets distributed over an area as large as 60,000 sq. km in a matter of hours. Potentially, a total of 1.3 million individual range measurements can be made in a 6 hr flight. The precision of these range measurements is approximately 1 cm. These measurements are then used in a procedure which is basically an extension of trilateration techniques to derive the intersite vector between the laser ground targets. By repeating the estimation of the intersite vector, strain and strain rate errors can be estimated. These quantities are essential for crustal dynamic studies which include determination and monitoring of regional strain in the vicinity of active fault zones, land subsidence, and edifice building preceding volcanic eruptions.
Kahn, W. D.↗
Hydraulic Calibrator for Strain-Gauge Balances
Instrument for calibrating strain-gauge balances uses hydraulic actuators and load cells. Eliminates effects of nonparallelism, nonperpendicularity, and changes of cable directions upon vector sums of applied forces. Errors due to cable stretching, pulley friction, and weight inaccuracy also eliminated. New instrument rugged and transportable. Set up quickly. Developed to apply known loads to wind-tunnel models with encapsulated strain-gauge balances, also adapted for use in calibrating dynamometers, load sensors on machinery and laboratory instruments.
Skelly, Kenneth↗
Pulse Vector-Excitation Speech Encoder
Proposed pulse vector-excitation speech encoder (PVXC) encodes analog speech signals into digital representation for transmission or storage at rates below 5 kilobits per second. Produces high quality of reconstructed speech, but with less computation than required by comparable speech-encoding systems. Has some characteristics of multipulse linear predictive coding (MPLPC) and of code-excited linear prediction (CELP). System uses mathematical model of vocal tract in conjunction with set of excitation vectors and perceptually-based error criterion to synthesize natural-sounding speech.
Davidson, Grant↗
Astrometry in local reference frames for deep space navigation
Future deep space missions will benefit from submilliarcsecond angular navigation accuracy (less than 25 km projected distance at Neptune). Conventional Very Long Baseline Interferometry (VLBI) measurement strategies entail observations of a radio source (RS) and spacecraft pair. To increase the 3-5 milliarcsecond accuracies currently attainable, instrumental improvements could be coupled with either of two methods: (1) use improved calibration measurements with the single RS as the spacecraft reference, or (2) use a reference frame established by a local network of RSs near the spacecraft to reduce the contribution of sky-dependent error sources. The demanding baseline vector (earth orientation) and tropospheric calibrations needed to realize submilliarcsecond accuracy with the single-source strategy would not be necessary with the multisource strategy. The two strategies are compared via a sample covariance analysis. In this analysis, the single-source method yields 1.5 milliarcseconds for the navigation accuracy, while the multisource method yields 0.5 milliarcseconds.
Treuhaft, R. N.↗
Application of a Monte Carlo accuracy assessment tool to TDRS and GPS
In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometric tracking accuracy. Initially, the tool was applied to the problem of determining optimal interferometric station siting for orbit determination of the Tracking and Data Relay Satellite (TDRS). Subsequently, the Orbit Determination Accuracy Estimator (ODAE) was expanded to model the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with measurement types including not only group and phase delay from radio interferometry, but also range, range rate, angular measurements, and satellite-to-satellite measurements. The user of ODAE specifies the statistical properties of error sources, including inherent observable imprecision, atmospheric delays, station location uncertainty, and measurement biases. Upon Monte Carlo simulation of the orbit determination process, ODAE calculates the statistical properties of the error in the satellite state vector and any other parameters for which a solution was obtained in the orbit determination. This paper presents results from ODAE application to two different problems: (1)determination of optimal geometry for interferometirc tracking of TDRS, and (2) expected orbit determination accuracy for Global Positioning System (GPS) tracking of low-earth orbit (LEO) satellites. Conclusions about optimal ground station locations for TDRS orbit determination by radio interferometry are presented, and the feasibility of GPS-based tracking for IRIDIUM, a LEO mobile satellite communications (MOBILSATCOM) system, is demonstrated.
Pavloff, Michael S.↗
A simple suboptimal least-squares algorithm for attitude determination with multiple sensors
Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.
Brozenec, Thomas F.↗
Correction of WindScat Scatterometric Measurements by Combining with AMSR Radiometric Data
The Seawinds scatterometer on the advanced Earth observing satellite-2 (ADEOS-2) will determine surface wind vectors by measuring the radar cross section. Multiple measurements will be made at different points in a wind-vector cell. When dense clouds and rain are present, the signal will be attenuated, thereby giving erroneous results for the wind. This report describes algorithms to use with the advanced mechanically scanned radiometer (AMSR) scanning radiometer on ADEOS-2 to correct for the attenuation. One can determine attenuation from a radiometer measurement based on the excess brightness temperature measured. This is the difference between the total measured brightness temperature and the contribution from surface emission. A major problem that the algorithm must address is determining the surface contribution. Two basic approaches were developed for this, one using the scattering coefficient measured along with the brightness temperature, and the other using the brightness temperature alone. For both methods, best results will occur if the wind from the preceding wind-vector cell can be used as an input to the algorithm. In the method based on the scattering coefficient, we need the wind direction from the preceding cell. In the method using brightness temperature alone, we need the wind speed from the preceding cell. If neither is available, the algorithm can work, but the corrections will be less accurate. Both correction methods require iterative solutions. Simulations show that the algorithms make significant improvements in the measured scattering coefficient and thus is the retrieved wind vector. For stratiform rains, the errors without correction can be quite large, so the correction makes a major improvement. For systems of separated convective cells, the initial error is smaller and the correction, although about the same percentage, has a smaller effect.
Song, S.↗
High-Performance Reaction Wheel Optimization for Fine-Pointing Space Platforms: Minimizing Induced Vibration Effects on Jitter Performance plus Lessons Learned from Hubble Space Telescope for Current and Future Spacecraft Applications
The Hubble Space Telescope (HST) applies large-diameter optics (2.5-m primary mirror) for diffraction-limited resolution spanning an extended wavelength range (approx. 100-2500 nm). Its Pointing Control System (PCS) Reaction Wheel Assemblies (RWAs), in the Support Systems Module (SSM), acquired an unprecedented set of high-sensitivity Induced Vibration (IV) data for 5 flight-certified RWAs: dwelling at set rotation rates. Focused on 4 key ratios, force and moment harmonic values (in 3 local principal directions) are extracted in the RWA operating range (0-3000 RPM). The IV test data, obtained under ambient lab conditions, are investigated in detail, evaluated, compiled, and curve-fitted; variational trends, core causes, and unforeseen anomalies are addressed. In aggregate, these values constitute a statistically-valid basis to quantify ground test-to-test variations and facilitate extrapolations to on-orbit conditions. Accumulated knowledge of bearing-rotor vibrational sources, corresponding harmonic contributions, and salient elements of IV key variability factors are discussed. An evolved methodology is presented for absolute assessments and relative comparisons of macro-level IV signal magnitude due to micro-level construction-assembly geometric details/imperfections stemming from both electrical drive and primary bearing design parameters. Based upon studies of same-size/similar-design momentum wheels' IV changes, upper estimates due to transitions from ground tests to orbital conditions are derived. Recommended HST RWA choices are discussed relative to system optimization/tradeoffs of Line-Of-Sight (LOS) vector-pointing focal-plane error driven by higher IV transmissibilities through low-damped structural dynamics that stimulate optical elements. Unique analytical disturbance results for orbital HST accelerations are described applicable to microgravity efforts. Conclusions, lessons learned, historical context/insights, and perspectives on future applications are given; these previously unpublished data and findings represents a valuable resource for fine-pointing spacecraft or space-based platforms using RWAs, Control Moment Gyros (CMGs), Momentum Wheels, or other ball-bearing-based rotational units.
Hasha, Martin D.↗
CORRELATED AND ZONAL ERRORS OF GLOBAL ASTROMETRIC MISSIONS: A SPHERICAL HARMONIC SOLUTION
We propose a computer-efficient and accurate method of estimating spatially correlated errors in astrometric positions, parallaxes, and proper motions obtained by space- and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects in space astrometry, such as SIM or JASMINE.
79 ASTRONOMY AND ASTROPHYSICS↗
Autonomous reconfigurable GPS/INS navigation and pointing system for rendezvous and docking
This paper describes the results of an integrated navigation and pointing system software development effort sponsored by the NASA MSFC through a SBIR Phase 2 Program. The integrated Global Positioning System (GPS)/Inertial Navigation System (INS) implements an autonomous navigation filter that is reconfigurable in real-time to accommodate mission contingencies. An onboard expert system monitors the spacecraft status and reconfigures the navigation filter accordingly, to optimize the system performance. The navigation filter is a multi-mode Kalman filter to estimate the spacecraft position, velocity, and attitude. Three different GPS-based attitude determination techniques, namely, velocity vector matching, attitude vector matching, and interferometric processing, are implemented to encompass different mission contingencies. The integrated GPS/INS navigation filter will use any of these techniques depending on the mission phase and the state of the sensors. The first technique, velocity vector matching, uses the GPS velocity measurement to estimate the INS velocity errors and exploits the correlation between INS velocity and attitude errors to estimate the attitude. The second technique, attitude vector matching, uses INS gyro measurements and GPS carrier phase (integrated Doppler) measurements during a spacecraft rotation maneuver to determine the attitude. Both of these techniques require only one GPS antenna onboard to determine the spacecraft attitude. The third technique, interferometric processing, requires use of multiple GPS antennae. In order to determine 3-axis body attitude, three GPS antennae (2 no-coplanor baselines) are required.
Upadhyay, Triveni N.↗
Minimizing distortion and internal forces in truss structures by simulated annealing
Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.
Kincaid, Rex K.↗
Smisc - A collection of miscellaneous functions
A collection of functions for statistical computing and data manipulation. These include routines for rapidly aggregating heterogeneous matrices, manipulating file names, loading R objects, sourcing multiple R files, formatting datetimes, multi-core parallel computing, stream editing, specialized plotting, etc. Smisc-package A collection of miscellaneous functions allMissing Identifies missing rows or columns in a data frame or matrix as.numericSilent Silent wrapper for coercing a vector to numeric comboList Produces all possible combinations of a set of linear model predictors cumMax Computes the maximum of the vector up to the current index cumsumNA Computes the cummulative sum of a vector without propogating NAs d2binom Probability functions for the sum of two independent binomials dataIn A flexible way to import data into R. dbb The Beta-Binomial Distribution df2list Row-wise conversion of a data frame to a list dfplapply Parallelized single row processing of a data frame dframeEquiv Examines the equivalence of two dataframes or matrices dkbinom Probability functions for the sum of k independent binomials factor2character Converts all factor variables in a dataframe to character variables findDepMat Identify linearly dependent rows or columns in a matrix formatDT Converts date or datetime strings into alternate formats getExtension Filename manipulations: remove the extension or path, extract the extension or path getPath Filename manipulations: remove the extension or path, extract the extension or path grabLast Filename manipulations: remove the extension or path, extract the extension or path ifelse1 Non-vectorized version of ifelse integ Simple numerical integration routine interactionPlot Two-way Interaction Plot with Error Bar linearMap Linear mapping of a numerical vector or scalar list2df Convert a list to a data frame loadObject Loads and returns the object(s) in an ".Rdata" file more Display the contents of a file to the R terminal movAvg2 Calculate the moving average using a 2-sided window openDevice Opens a graphics device based on the filename extension p2binom Probability functions for the sum of two independent binomials padZero Pad a vector of numbers with zeros parseJob Parses a collection of elements into (almost) equal sized groups pbb The Beta-Binomial Distribution pcbinom A continuous version of the binomial cdf pkbinom Probability functions for the sum of k independent binomials plapply Simple parallelization of lapply plotFun Plot one or more functions on a single plot PowerData An example of power data pvar Prints the name and value of one or more objects qbb The Beta-Binomial Distribution rbb And numerous others (space limits reporting).
Landon Sego, PNNL↗
Smisc - A collection of miscellaneous functions
A collection of functions for statistical computing and data manipulation. These include routines for rapidly aggregating heterogeneous matrices, manipulating file names, loading R objects, sourcing multiple R files, formatting datetimes, multi-core parallel computing, stream editing, specialized plotting, etc. Smisc-package A collection of miscellaneous functions allMissing Identifies missing rows or columns in a data frame or matrix as.numericSilent Silent wrapper for coercing a vector to numeric comboList Produces all possible combinations of a set of linear model predictors cumMax Computes the maximum of the vector up to the current index cumsumNA Computes the cummulative sum of a vector without propogating NAs d2binom Probability functions for the sum of two independent binomials dataIn A flexible way to import data into R. dbb The Beta-Binomial Distribution df2list Row-wise conversion of a data frame to a list dfplapply Parallelized single row processing of a data frame dframeEquiv Examines the equivalence of two dataframes or matrices dkbinom Probability functions for the sum of k independent binomials factor2character Converts all factor variables in a dataframe to character variables findDepMat Identify linearly dependent rows or columns in a matrix formatDT Converts date or datetime strings into alternate formats getExtension Filename manipulations: remove the extension or path, extract the extension or path getPath Filename manipulations: remove the extension or path, extract the extension or path grabLast Filename manipulations: remove the extension or path, extract the extension or path ifelse1 Non-vectorized version of ifelse integ Simple numerical integration routine interactionPlot Two-way Interaction Plot with Error Bar linearMap Linear mapping of a numerical vector or scalar list2df Convert a list to a data frame loadObject Loads and returns the object(s) in an ".Rdata" file more Display the contents of a file to the R terminal movAvg2 Calculate the moving average using a 2-sided window openDevice Opens a graphics device based on the filename extension p2binom Probability functions for the sum of two independent binomials padZero Pad a vector of numbers with zeros parseJob Parses a collection of elements into (almost) equal sized groups pbb The Beta-Binomial Distribution pcbinom A continuous version of the binomial cdf pkbinom Probability functions for the sum of k independent binomials plapply Simple parallelization of lapply plotFun Plot one or more functions on a single plot PowerData An example of power data pvar Prints the name and value of one or more objects qbb The Beta-Binomial Distribution rbb And numerous others (space limits reporting).
Landon Sego, PNNL↗