TBERR - Two-body error analysis program
Two-body error analysis computer program to evaluate resulting state vector and covariance matrix for orbiter after one coast and one burn maneuver
Muhonen, D. P.↗
SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Spatial variations of ocean wave directional spectra from the Seasat synthetic aperture radar
Seasat synthetic aperture radar ocean wave spectra for a 900-km pass are analyzed and interpreted in the context of both their probable generation sources and their surface current and bathymetric modifiers. Systematic vector wavenumber variations of several times the standard error of determination (about 1.5 percent in magnitude and 0.9 deg in direction) occur along the entire 900-km pass. The large-scale spatial variation of a 200-m swell system can be accurately accounted for as a result of dispersion from a distant storm. The more local variations are qualitatively well correlated in position with known currents and bathymetry but show systematic biases that appear partly due to an environmentally dependent instrument transfer function in the regions of high current and highest sea state. There is also substantial evidence that a large angular deviation in the center of the pass is the result of a mesoscale eddy just to the east.
Beal, R. C.↗
A comparison of in situ measurements of vector-E and - vector-V x vector-B from Dynamics Explorer 2
Dynamics Explorer-2 provided the first opportunity to make a direct comparison of in situ measurements of the high-latitude convection electric field by two distinctly different techniques. The vector electric field instrument (VEFI) used antennae to measure the intrinsic electric fields and the ion drift meter (IDM) and retarding potential analyzer (RPA) measured the ion drift velocity vector, from which the convection electric field can be deduced. The data from three orbits having large electric fields at high latitude are presented, one at high, one at medium, and one at low altitudes. The general agreement between the two measurements of electric field is very good, with typical differences at high latitudes of the order of a few millivolts per meter, but there are some regions where the particle fluxes are extremely large (e.g., the cusp) and the disagreement is worse, probably because of IDM difficulties. The auroral zone potential patterns derived from the two devices are in excellent agreement for two of the cases, but not in the third, where bad attitude data may be the problem. At low latitudes there are persistent differences in the measurements of a few millivolts per meter, though these differences are quite constant from orbit to orbit. This problem seems to arise from some shortcoming in the VEFI measurments. Overall, however, these measurements confirm the concept of `frozen-in' plasma that drifts with velocity vector-E x vector-B/B(exp 2) within the measurement errors of the two techniques.
Hanson, W. B.↗
Spacecraft attitude and velocity control system
A spacecraft attitude and/or velocity control system includes a controller which responds to at least attitude errors to produce command signals representing a force vector F and a torque vector T, each having three orthogonal components, which represent the forces and torques which are to be generated by the thrusters. The thrusters may include magnetic torquer or reaction wheels. Six difference equations are generated, three having the form ##EQU1## where a.sub.j is the maximum torque which the j.sup.th thruster can produce, b.sub.j is the maximum force which the j.sup.th thruster can produce, and .alpha..sub.j is a variable representing the throttling factor of the j.sup.th thruster, which may range from zero to unity. The six equations are summed to produce a single scalar equation relating variables .alpha..sub.j to a performance index Z: ##EQU2## Those values of .alpha. which maximize the value of Z are determined by a method for solving linear equations, such as a linear programming method. The Simplex method may be used. The values of .alpha..sub.j are applied to control the corresponding thrusters.
Paluszek, Michael A.↗
An Empirical State Error Covariance Matrix Orbit Determination Example
State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.
Frisbee, Joseph H., Jr.↗
Achieving unequal error protection with convolutional codes
This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.
Mills, D. G.↗
Compact Midwave Imaging System: Results from an Airborne Demonstration
The Compact Midwave Imaging System (CMIS) is a wide field of view, multi-angle, multi-spectral push frame imager that relies on the forward motion of the satellite to create a two-dimensional (2D) image swath. An airborne demonstration of CMIS was successfully completed in January-February 2021 on the NASA Langley Research Center Gulfstream III. The primary objective of the four-flight campaign was to demonstrate the capability of this unique instrument to perform stereo observations of clouds and other particulates (e.g. smoke) in the atmosphere. It is shown that the midwave infrared (MWIR) spectral bands of CMIS provide a unique 24/7 capability with high resolution for accurate stereo sensing.The instrument relies on new focal plane array (FPA) technology, which provides excellent sensitivity at much warmer detector temperatures than traditional technologies. This capability enabled a compact, low-cost design that can provide atmospheric motion vectors and cloud heights to support requirements for atmospheric winds in the 2017-2027 Earth Science Decadal Survey. Applications include day/night observations of the planetary boundary layer, severe weather, and wildfires. A comparison with current space-based earth science instruments demonstrates that the SWIR/MWIR multi-spectral capability of CMIS is competitive with larger, more expensive instrumentation. Imagery obtained over a controlled burn and operating nuclear power plant demonstrated the sensitivity of the instrument to temperature variations. The system relies on a mature stereoscopic imaging technique applied to the same scene from two independent platforms to unambiguously retrieve atmospheric motion vectors (AMVs) with accurate height assignment.This capability has been successfully applied to geostationary and low-earth orbit satellites to achieve excellent accuracy. When applied to a ground-point validation case, the accuracy for the CMIS aircraft observations was 20 m and 0.3 m/s for cloud heights and motion vectors, respectively. This result was confirmed by a detailed error analysis with analytical and covariance models. The results for CMIS cases with under flights of Aeolus, CALIPSO and Aqua provided a good validation of expected accuracies. The paper also showed the feasibility of accommodating CMIS on CubeSats to enable multiple instruments to be flown in a leader-follower mode.
stereo winds↗
Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise
Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.
Sedlak, J.↗
Autonomous frequency domain identification: Theory and experiment
The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability.
Yam, Yeung↗
Improved Stratospheric Temperature Retrievals for Climate Reanalysis
The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.
Rokke, L.↗
A Systematic Approach for Model-Based Aircraft Engine Performance Estimation
A requirement for effective aircraft engine performance estimation is the ability to account for engine degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. This paper presents a linear point design methodology for minimizing the degradation-induced error in model-based aircraft engine performance estimation applications. The technique specifically focuses on the underdetermined estimation problem, where there are more unknown health parameters than available sensor measurements. A condition for Kalman filter-based estimation is that the number of health parameters estimated cannot exceed the number of sensed measurements. In this paper, the estimated health parameter vector will be replaced by a reduced order tuner vector whose dimension is equivalent to the sensed measurement vector. The reduced order tuner vector is systematically selected to minimize the theoretical mean squared estimation error of a maximum a posteriori estimator formulation. This paper derives theoretical estimation errors at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the estimation accuracy achieved through conventional maximum a posteriori and Kalman filter estimation approaches. Maximum a posteriori estimation results demonstrate that reduced order tuning parameter vectors can be found that approximate the accuracy of estimating all health parameters directly. Kalman filter estimation results based on the same reduced order tuning parameter vectors demonstrate that significantly improved estimation accuracy can be achieved over the conventional approach of selecting a subset of health parameters to serve as the tuner vector. However, additional development is necessary to fully extend the methodology to Kalman filter-based estimation applications.
Simon, Donald L.↗
Adaptation and optimization of a line-by-line radiative transfer program for the STAR-100 (STARSMART)
A program to calculate upwelling infrared radiation was modified to operate efficiently on the STAR-100. The modified software processes specific test cases significantly faster than the initial STAR-100 code. For example, a midlatitude summer atmospheric model is executed in less than 2% of the time originally required on the STAR-100. Furthermore, the optimized program performs extra operations to save the calculated absorption coefficients. Some of the advantages and pitfalls of virtual memory and vector processing are discussed along with strategies used to avoid loss of accuracy and computing power. Results from the vectorized code, in terms of speed, cost, and relative error with respect to serial code solutions are encouraging.
Rarig, P. L.↗
Recursive linearization of multibody dynamics equations of motion
The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.
Lin, Tsung-Chieh↗
Neural-Network Simulator
F77NNS (FORTRAN 77 Neural Network Simulator) computer program simulates popular back-error-propagation neural network. Designed to take advantage of vectorization when used on computers having this capability, also used on any computer equipped with ANSI-77 FORTRAN Compiler. Problems involving matching of patterns or mathematical modeling of systems fit class of problems F77NNS designed to solve. Program has restart capability so neural network solved in stages suitable to user's resources and desires. Enables user to customize patterns of connections between layers of network. Size of neural network F77NNS applied to limited only by amount of random-access memory available to user.
Mitchell, Paul H.↗
A method of determining attitude from magnetometer data only
Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.
Natanson, G. A.↗
Optimization of lateral-directional dynamics for an aircraft operating at high angle of attack
In this paper, the control laws for the lateral-directional dynamics of a supermaneuverable aircraft is analyzed with a view to reducing the levels of lateral acceleration and sideslip, which are encountered during aggressive rolling maneuvers at high angles of attack. The analysis uses a linearized model of the lateral-directional dynamics and thus H-free-flow techniques can be applied. It is shown that trade-offs exist between simultaneously minimizing lateral acceleration measured at the pilot's station, ny(p), minimizing sideslip and minimizing tracking errors between the roll-rate about the velocity vector and its command. The paper concludes that a significant reduction in ny(p) is only attainable by compromising the roll-rate performance.
Snell, S. A.↗
The effect of sensor sheltering and averaging techniques on wind measurements at the Shuttle Landing Facility
This document presents results of a field study of the effect of sheltering of wind sensors by nearby foliage on the validity of wind measurements at the Space Shuttle Landing Facility (SLF). Standard measurements are made at one second intervals from 30-feet (9.1-m) towers located 500 feet (152 m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. A companion study, Merceret (1995), quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. This work examines the effect of nearby foliage on the accuracy of the measurements made by any one sensor, and the effects of averaging on interpretation of the measurements. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions as a function of distance from the obstructing foliage. Appropriate statistics were computed. The results suggest that accurate measurements require foliage be cut back to OFCM standards. Analysis of averaging techniques showed that there is no significant difference between vector and scalar averages. Longer averaging periods reduce measurement error but do not otherwise change the measurement in reasonably steady flow regimes. In rapidly changing conditions, shorter averaging periods may be required to capture trends.
Merceret, Francis J.↗
An Error Analysis of the Phased Array Antenna Pointing Algorithm for STARS Flight Demonstration No. 2
STARS is a multicenter NASA project to determine the feasibility of using space-based assets, such as the Tracking and Data Relay Satellite System (TDRSS) and Global Positioning System (GPS), to increase flexibility (e.g. increase the number of possible launch locations and manage simultaneous operations) and to reduce operational costs by decreasing the need for ground-based range assets and infrastructure. The STARS project includes two major systems: the Range Safety and Range User systems. The latter system uses broadband communications (125 kbps to 500 kbps) for voice, video, and vehicle/payload data. Flight Demonstration #1 revealed the need to increase the data rate of the Range User system. During Flight Demo #2, a Ku-band antenna will generate a higher data rate and will be designed with an embedded pointing algorithm to guarantee that the antenna is pointed directly at TDRS. This algorithm will utilize the onboard position and attitude data to point the antenna to TDRS within a 2-degree full-angle beamwidth. This report investigates how errors in aircraft position and attitude, along with errors in satellite position, propagate into the overall pointing vector.
Carney, Michael P.↗