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At least 379 records · Page 21

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DOE OSTI2025

On the Error Covariance Correction Step of an ESKF Attitude Update

The attitude states of an error-state Kalman filter (ESKF) behave differently than most other states in the system due to their multiplicative (rather than additive) nature. One way in which they differ is an error covariance correction step after an ESKF error reset, which is not required for, for example, position and velocity states. This covariance correction step is not intuitive, and it has only been recently derived for coordinate transform matrices. The author of this memo, however, found the provided derivation in [1] confusing due to a lack of clarity surrounding the invoked reference frames, and clarity is required as there are at least 4 different ways to parameterize small-angle attitude errors in an ESKF. Furthermore, while reproducing the work, the author of this memo found a more straightforward derivation that provides additional insight into the correction step. This memo offers a derivation of the attitude error covariance correction step of an ESKF, which pays specific attention to the coordinate reference frames.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

A Monte Carlo error analysis program for near-Mars, finite-burn, orbital transfer maneuvers

A computer program was developed which performs an error analysis of a minimum-fuel, finite-thrust, transfer maneuver between two Keplerian orbits in the vicinity of Mars. The method of analysis is the Monte Carlo approach where each off-nominal initial orbit is targeted to the desired final orbit. The errors in the initial orbit are described by two covariance matrices of state deviations and tracking errors. The function of the program is to relate these errors to the resulting errors in the final orbit. The equations of motion for the transfer trajectory are those of a spacecraft maneuvering with constant thrust and mass-flow rate in the neighborhood of a single body. The thrust vector is allowed to rotate in a plane with a constant pitch rate. The transfer trajectory is characterized by six control parameters and the final orbit is defined, or partially defined, by the desired target parameters. The program is applicable to the deboost maneuver (hyperbola to ellipse), orbital trim maneuver (ellipse to ellipse), fly-by maneuver (hyperbola to hyperbola), escape maneuvers (ellipse to hyperbola), and deorbit maneuver.

Green, R. N.↗

NASA NTRS1971

Arithmetic error codes - Cost and effectiveness studies for application in digital system design.

The application of error-detecting or error-correcting codes in digital computer design requires studies of cost and effectiveness tradeoffs to supplement the knowledge of their theoretical properties. General criteria for cost and effectiveness studies of error codes are developed, and results are presented for arithmetic error codes with the low-cost check modulus 2 super a - 1. Both separate (residue) and nonseparate (AN) codes are considered. The class of multiple arithmetic error codes is developed as an extension of low-cost single codes.

Avizienis, A.↗

NASA NTRS1972

Dynamic errors in a tuned flexure-mounted strapdown gyro

Motion induced errors in a tuned, flexure-mounted strapdown gyro are investigated. Analytic expressions are developed for errors induced by linear vibrations, angular motion, and detuning. Sensor-level errors (gyro drift rate) and system-level errors (navigation errors) that are stimulated by an actual dynamic motion environment are computed.

Bortz, J. E., Sr.↗

NASA NTRS1972

Error model for the SAO 1969 standard earth.

A method is developed for estimating an error model for geopotential coefficients using satellite tracking data. A single station's apparent timing error for each pass is attributed to geopotential errors. The root sum of the residuals for each station also depends on the geopotential errors, and these are used to select an error model. The model chosen is 1/4 of the difference between the SAO M1 and the APL 3.5 geopotential.

Martin, C. F.↗

NASA NTRS1973

Effect of photogrammetric reading error on slope-frequency distributions

The effect of reading error on two hypothetical slope frequency distributions and two slope frequency distributions from actual lunar data in order to ensure that these errors do not cause excessive overestimates of algebraic standard deviations for the slope frequency distributions. The errors introduced are insignificant when the reading error is small and the slope length is large. A method for correcting the errors in slope frequency distributions is presented and applied to 11 distributions obtained from Apollo 15, 16, and 17 panoramic camera photographs and Apollo 16 metric camera photographs.

Moore, H. J.↗

NASA NTRS1974

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Long, S. A. T.↗

NASA NTRS1974

Error protection capability of space shuttle data bus designs

Error protection assurance in the reliability of digital data communications is discussed. The need for error protection on the space shuttle data bus system has been recognized and specified as a hardware requirement. The error protection techniques of particular concern are those designed into the Shuttle Main Engine Interface (MEI) and the Orbiter Multiplex Interface Adapter (MIA). The techniques and circuit design details proposed for these hardware are analyzed in this report to determine their error protection capability. The capability is calculated in terms of the probability of an undetected word error. Calculated results are reported for a noise environment that ranges from the nominal noise level stated in the hardware specifications to burst levels which may occur in extreme or anomalous conditions.

Proch, G. E.↗

NASA NTRS1974

Optimizing signal-to-error ratio in standing wave ultrasonic measurements

Standing wave ultrasonic techniques for the measurement of very small changes in acoustic attenuation and phase velocity are discussed. Enhanced sensitivity to these small changes was achieved by making the specimen part of a composite ultrasonic resonator. It was found that a point of maximum sensitivity on the response of such an ultrasonic resonator need not coincide with a point of maximum signal-to-error ratio. A model is presented and analyzed which takes into account error due to long term (low frequency) noise effects such as gain drifts and dc level shifts. This model yields a quantitative value for the signal-to-error ratio in which the signal is defined as the ideal change in the monitored response and the error as the difference between the experimentally measured change and the signal. The specific frequency dependent forms for the ultrasonic response and the sensitivity enhancement factor were used to predict the operating point on a mechanical resonance corresponding to maximum signal-to-error ratio.

Brown, J. J.↗

NASA NTRS1975

The influence of radio altimeter errors on pilot performance during the final approach and landing phase of an RPV mission

Due to the fact that remotely piloted vehicles (RPV's) are currently being flown from fixed base control centers, kinesthetic and real world peripheral vision cues are absent. The absence of these cues complicates the piloting task, particularly during the final approach and landing phase of a mission. The pilot's task is futher complicated by errors in the displayed altitude information. To determine the influence of these errors on pilot performance during the final approach and landing phase of a mission, an experiment was conducted in which pilot subjects were asked to fly a fixed base simulation of a Piper PA-30 aircraft, using degraded altitude information. For this experiment, the chevron component of the display configuration was driven by a radio altimeter. Four altimeters were used, each with a different error characteristic, but within the range specified for the Sperry series of radio altimeters. Results indicate that for range of errors considered, there is no significant difference in landing performance that can be attributed to errors in altitude information.

Howard, J. C.↗

NASA NTRS1975

An analysis of spacecraft data time tagging errors

An indepth examination of the timing and telemetry in just one spacecraft points out the genesis of various types of timing errors and serves as a guide in the design of future timing/telemetry systems. The principal sources of timing errors are examined carefully and are described in detail. Estimates of these errors are also made and presented. It is found that the timing errors within the telemetry system are larger than the total timing errors resulting from all other sources.

Fang, A. C.↗

NASA NTRS1976

Development of a methodology for classifying software errors

A mathematical formalization of the intuition behind classification of software errors is devised and then extended to a classification discipline: Every classification scheme should have an easily discernible mathematical structure and certain properties of the scheme should be decidable (although whether or not these properties hold is relative to the intended use of the scheme). Classification of errors then becomes an iterative process of generalization from actual errors to terms defining the errors together with adjustment of definitions according to the classification discipline. Alternatively, whenever possible, small scale models may be built to give more substance to the definitions. The classification discipline and the difficulties of definition are illustrated by examples of classification schemes from the literature and a new study of observed errors in published papers of programming methodologies.

Gerhart, S. L.↗

NASA NTRS1975

Error Analysis of the Shuttle Reaction Control System Propellant Gaging Module

An investigation of the Shuttle Reaction Control System (RCS) propellant gaging module has revealed that the gaging errors due to the combined effects of random instrumentation measurement errors and propellant loading uncertainties are non-linear over the range of the propellant quantity gage (0-100%), with the largest error occurring at the zero point. When the RCS propellant tanks are filled to contain 100% of the maximum usable propellant, the largest gaging error was determined to be 3.9% for the fuel and 5.4% for the oxidizer. When the RCS propellant tanks initially contain 50% of the maximum usable propellant, the largest gaging error increases to 4.0% for the fuel and 5.6% for the oxidizer.

Duhon, D. D.↗

NASA NTRS1975

Dispersion analysis and linear error analysis capabilities of the space vehicle dynamics simulation program

Previous error analyses conducted by the Guidance and Dynamics Branch of NASA have used the Guidance Analysis Program (GAP) as the trajectory simulation tool. Plans are made to conduct all future error analyses using the Space Vehicle Dynamics Simulation (SVDS) program. A study was conducted to compare the inertial measurement unit (IMU) error simulations of the two programs. Results of the GAP/SVDS comparison are presented and problem areas encountered while attempting to simulate IMU errors, vehicle performance uncertainties and environmental uncertainties using SVDS are defined. An evaluation of the SVDS linear error analysis capability is also included.

Snow, L. S.↗

NASA NTRS1976

Techniques for correcting transmission errors in video adaptive delta modulation channels

We investigated the effects of channel errors on an adaptive delta modulator used to encode video signals. The investigation revealed that channel errors caused a permanent shift in the dc level of the delta modulator's estimate. Errors in the step size, on the other hand, were transitory and had no noticeable effect on the received pictures. We then presented three error correction schemes to minimize the visibility of the channel errors in the received picture. The first scheme required the transmitter to periodically send the correct dc level of the estimate to the receiver. The second method employed a leaky integrator, and the third method used line-to-line interpolation

Scheinberg, N.↗

NASA NTRS1975

Error Analysis of the Shuttle Orbital Maneuvering System P-V-T Propellant Gaging Module. Mission Planning, Mission Analysis and Software Formulation

An investigation of the shuttle orbital maneuvering system (OMS) pressure-volume-temperature (P-V-T) propellant gaging module has revealed that the gaging errors due to the combined effects of random instrumentation measurement errors, propellant loading uncertainties, and simplifying assumptions in the software are non-linear over the range of the usable propellant quantity gage (0-100%), with the largest error being at the zero point. When the OMS propellant tanks in the orbiter vehicle pods are filled to contain 100% of the maximum usable propellant, the gaging error at the zero point was determined to be 9.5% for the fuel and 9.5% for the oxidizer. When the OMS propellant tanks initially contain 50% of the maximum usable propellant, the largest gaging error is still 9.5% for the fuel and 9.5% for the oxidizer.

Duhon, D. D.↗

NASA NTRS1977

Effect of gyro verticality error on lateral autoland tracking performance for an inertially smoothed control law

The results of a simulation study performed to determine the effects of gyro verticality error on lateral autoland tracking and landing performance are presented. A first order vertical gyro error model was used to generate the measurement of the roll attitude feedback signal normally supplied by an inertial navigation system. The lateral autoland law used was an inertially smoothed control design. The effect of initial angular gyro tilt errors (2 deg, 3 deg, 4 deg, and 5 deg), introduced prior to localizer capture, were investigated by use of a small perturbation aircraft simulation. These errors represent the deviations which could occur in the conventional attitude sensor as a result of the maneuver-induced spin-axis misalinement and drift. Results showed that for a 1.05 deg per minute erection rate and a 5 deg initial tilt error, ON COURSE autoland control logic was not satisfied. Failure to attain the ON COURSE mode precluded high control loop gains and localizer beam path integration and resulted in unacceptable beam standoff at touchdown.

Thibodeaux, J. J.↗

NASA NTRS1977

Effects of tropospheric and ionospheric refraction errors in the utilization of GEOS-C altimeter data

The effects of tropospheric and ionospheric refraction errors are analyzed for the GEOS-C altimeter project in terms of their resultant effects on C-band orbits and the altimeter measurement itself. Operational procedures using surface meteorological measurements at ground stations and monthly means for ocean surface conditions are assumed, with no corrections made for ionospheric effects. Effects on the orbit height due to tropospheric errors are approximately 15 cm for single pass short arcs (such as for calibration) and 10 cm for global orbits of one revolution. Orbit height errors due to neglect of the ionosphere have an amplitude of approximately 40 cm when the orbits are determined from C-band range data with predominantly daylight tracking. Altimeter measurement errors are approximately 10 cm due to residual tropospheric refraction correction errors. Ionospheric effects on the altimeter range measurement are also on the order of 10 cm during the GEOS-C launch and early operation period.

Goad, C. C.↗