Maximum allowable lateral velocity errors during LM powered descent - Program Apollo
Lateral velocity error determination for lunar module descent guidance radar
Mc Swain, G.↗
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A Comprehensive Radial Velocity Error Budget for Next Generation Doppler Spectrometers
We describe a detailed radial velocity error budget for the NASA-NSF Extreme Precision Doppler Spectrometer instrument concept NEID (NN-explore Exoplanet Investigations with Doppler spectroscopy). Such an instrument performance budget is a necessity for both identifying the variety of noise sources currently limiting Doppler measurements, and estimating the achievable performance of next generation exoplanet hunting Doppler spectrometers. For these instruments, no single source of instrumental error is expected to set the overall measurement floor. Rather, the overall instrumental measurement precision is set by the contribution of many individual error sources. We use a combination of numerical simulations, educated estimates based on published materials, extrapolations of physical models, results from laboratory measurements of spectroscopic subsystems, and informed upper limits for a variety of error sources to identify likely sources of systematic error and construct our global instrument performance error budget. While natively focused on the performance of the NEID instrument, this modular performance budget is immediately adaptable to a number of current and future instruments. Such an approach is an important step in charting a path towards improving Doppler measurement precisions to the levels necessary for discovering Earth-like planets.
NASA-NSF Extreme Precision Doppler Spectrometer in↗
Application of Non-Uniform Beam Filling (NUBF) Doppler Velocity Error Correction on Airborne Radar Measurements
Non-uniform beam filling (NUBF) within an atmospheric radar sampling volume can cause significant Doppler velocity errors when the radar is located on a fast-moving platform. A case of strong NUBF errors was identified in ER-2 X-band Radar (EXRAD) data from the Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) 2020 field campaign. A basic NUBF correction was employed using an estimate of the along-track radar reflectivity gradient. The relationship is verified empirically using co-located Doppler velocity measurements from the higher resolution Cloud Radar System (CRS).
Matthew L. Walker McLinden↗
Global sensitivity to velocity errors at the libration points
The global effects on non-linear stability are investigated at and around the triangular libration points. The model of the circular restricted problem of three bodies is used, considering the earth and the moon as the primaries. Areas of the initial conditions in the configuration space leading to stability with zero initial velocity around the equilibrium points are compared to stable areas in the phase space with variable initial velocity and zero initial deviations at the equilibrium points. The behavior of the system concerning errors due to initial conditions in the configuration space is studied for 6 years and the effects of initial velocity errors are considered for 7.73 years.
Szebehely, V.↗
Reducing Spaceborne-Doppler-Radar Rainfall-Velocity Error
A combined frequency-time (CFT) spectral moment estimation technique has been devised for calculating rainfall velocity from measurement data acquired by a nadir-looking spaceborne Doppler weather radar system. Prior spectral moment estimation techniques used for this purpose are based partly on the assumption that the radar resolution volume is uniformly filled with rainfall. The assumption is unrealistic in general but introduces negligible error in application to airborne radar systems. However, for spaceborne systems, the combination of this assumption and inhomogeneities in rainfall [denoted non-uniform beam filling (NUBF)] can result in velocity measurement errors of several meters per second. The present CFT spectral moment estimation technique includes coherent processing of a series of Doppler spectra generated in a standard manner from data over measurement volumes that are partially overlapping in the along-track direction. Performance simulation of this technique using high-resolution data from an airborne rain-mapping radar shows that a spaceborne Ku-band Doppler radar operating at signal-to-noise ratios greater than 10 dB can achieve root-mean-square accuracy between 0.5 and 0.6 m/s in vertical-velocity estimates.
Tanelli, Simone↗
The effect of atmospheric drag on position and velocity errors of orbiting spacecraft
A model, in closed form, of position and velocity changes due to atmospheric drag of a spacecraft in orbit about a planetary body is presented, considering primarily the effects of a two-body force field. Calculations for both elliptical and circular geometries indicate that the simplifying assumptions in the analysis make the theory more accurate (to less than 1 percent error) for lengthier mappings, when the drag effect becomes quite significant. The downtrack error demonstrates a quadratic growth, while the radial error demonstrates a linear growth.
Russell, R. Kent↗
Jet stream velocity errors in general circulation models
The longitude and time dependence of excessive wind speed errors above subtropical jets in current GCM forecasts is studied for 14 five-day winter forecasts using the NASA Goddard Laboratory for Atmospheres fourth-order GCM. Several distinct phenomena, which may be divided into four categories, are found to contribute to the excess winds. These categories are: (1) error growth above the jet near the Himalayas; (2) error growth above the jet initiated elsewhere followed by advection; (3) tropical moisture bursts appearing in equatorial regions and migrating northeastward to merge with and distort the jet; and (4) undulatory growth of waves in the meridional component of the jet stream velocity. The results of additional sensitivity studies of the Himalayan region error are also reported.
Tenenbaum, J.↗
Application of a two-body analysis of position or velocity error propagation.
First order perturbation solution for transition matrix relating errors at one point of two-body orbit to errors at later point
TWO-BODY ORBIT↗
The Effect of Compressibility on the Pressure Reading of a Prandtl Pitot Tube at Subsonic Flow Velocity
Errors arising from yawed flow were also determined up to 20 degrees angle of attack. In axial flow, the Prandtl pitot tube begins at w/a approx. = 0.8 to give an incorrect static pressure reading, while it records the tank pressure correctly, as anticipated, up to sonic velocity. Owing to the compressibility of the air, the Prandtl pitot tube manifests compression shocks when the air speed approaches velocity of sound. This affects the pressure reading of the instrument. Because of the increasing importance of high speed in aviation, this compressibility effect is investigated in detail.
Walchner, O↗
Laser Doppler anemometer measurements using nonorthogonal velocity components - Error estimates
Laser Doppler anemometers (LDAs) that are arranged to measure nonorthogonal velocity components (from which orthogonal components are computed through transformation equations) are more susceptible to calibration and sampling errors than are systems with uncoupled channels. In this paper uncertainty methods and estimation theory are used to evaluate, respectively, the systematic and statistical errors that are present when such devices are applied to the measurement of mean velocities in turbulent flows. Statistical errors are estimated for two-channel LDA data that are either correlated or uncorrelated. For uncorrelated data the directional uncertainty of the measured velocity vector is considered for applications where mean streamline patterns are desired.
Orloff, K. L.↗
VLBI Contribution to ITRF2000
The VLBI data set spanning Aug. 1919 to the present is a major constituent of ITRF2000 because of the time span, the geometric strength and the accuracy of the modeling. Formal velocity errors for the best stations are less than 0.3 mm/yr while the probable frame definition error for station velocities is approximately 0.4 mm/yr. The primary systematic errors are the troposphere and tidal loading (solid Earth and ocean). However, the scale of the VLBI TRF is probably only weakly affected because of continued improvements in the tropospheric mapping function and gradient estimation. There are some weaknesses in the spatial distribution of data, particularly in the southern hemisphere, and the quality of the mobile VLBI results is now suboptimal. The deployment of the TIGO system to Chile will improve the geometric coverage. The current state of the art of VLBI analysis will be discussed.
Ma, Chopo↗
Small Body GN&C Research Report: A G-Guidance Enhancement to Increase Mission Functionality
G-Guidance is a robust G&C (guidance and control) algorithm developed under the small-body GN&C task. The G-Guidance scheme utilizes a model predictive control approach, along with a convexification of the governing dynamics, control constraints, and trajectory/state constraints. This report details an enhancement to the FY2005 G-Guidance algorithm; the addition of a fire-second approach helps to nullify velocity errors and hit desired final velocities much more precisely than the original Fire-first scheme developed in FY2005. The enhancement preserves the primary benefit of the algorithm, which is to ensure required thruster silent times during trajectory maneuvers. The fire-second scheme increases the versatility of the algorithm for missions employing G-Guidance. For instance, a landing sequence could employ the fire-second scheme to ensure a null final velocity at landing, whereas an ascent sequence could utilize a fire-first scheme to ensure there is no drift of the spacecraft toward the ground at the beginning of the maneuver. Examples are provided within to demonstrate a fire-first versus fire-second guidance scheme. As in the existing G-Guidance algorithm, the examples and schemes incorporate gravity models and thruster firing times into discrete dynamics that are solved as a optimal control problem to minimize fuel consumption or thruster energy expenditure.
velocity errors↗
Reducing Errors in Velocity–Azimuth Display (VAD) Wind and Deformation Retrievals from Airborne Doppler Radars in Convective Environments
The present study describes methods to reduce the uncertainty of velocity–azimuth display (VAD) wind and deformation retrievals from downward-pointing, conically scanning, airborne Doppler radars. These retrievals have important applications in data assimilation and real-time data processing. Several error sources for VAD retrievals are considered here, including violations to the underlying wind field assumptions, Doppler velocity noise, data gaps, temporal variability, and the spatial weighting function of the VAD retrieval. Specific to airborne VAD retrievals, we also consider errors produced due to the radar scans occurring while the instrument platform is in motion. While VAD retrievals are typically performed using data from a single antenna revolution, other strategies for selecting data can be used to reduce retrieval errors. Four such data selection strategies for airborne VAD retrievals are evaluated here with respect to their effects on the errors. These methods are evaluated using the second hurricane nature run numerical simulation, analytic wind fields, and observed Doppler radar radial velocities. The proposed methods are shown to reduce the median absolute error of the VAD wind retrievals, especially in the vicinity of deep convection embedded in stratiform precipitation. The median absolute error due to wind field assumption violations for the along-track and for the across-track wind is reduced from 0.36 to 0.08 m s−1 and from 0.35 to 0.24 m s−1, respectively. Although the study focuses on Doppler radars, the results are equally applicable to conically scanning Doppler lidars as well.
Charles N Helms↗
Apollo 15 mission report: Apollo 15 guidance, navigation, and control system performance analysis report (supplement 1)
This report contains the results of additional studies which were conducted to confirm the conclusions of the MSC Mission Report and contains analyses which were not completed in time to meet the mission report deadline. The LM IMU data were examined during the lunar descent and ascent phases. Most of the PGNCS descent absolute velocity error was caused by platform misalignments. PGNCS radial velocity divergence from AGS during the early part of descent was partially caused by PGNCS gravity computation differences from AGS. The remainder of the differences between PGNCS and AGS velocity were easily attributable to attitude reference alignment differences and tolerable instrument errors. For ascent the PGNCS radial velocity error at insertion was examined. The total error of 10.8 ft/sec was well within mission constraints but larger than expected. Of the total error, 2.30 ft/sec was PIPA bias error, which was suspected to exist pre-lunar liftoff. The remaining 8.5 ft/sec is most probably satisified with a large pre-liftoff planform misalignment.
Source record↗
Delay compensation - Its effect in reducing sampling errors in Fourier spectroscopy
An approximate formula is derived for the spectrum ghosts caused by periodic drive speed variations in a Michelson interferometer. The solution represents the case of fringe-controlled sampling and is applicable when the reference fringes are delayed to compensate for the delay introduced by the electrical filter in the signal channel. Numerical results are worked out for several common low-pass filters. It is shown that the maximum relative ghost amplitude over the range of frequencies corresponding to the lower half of the filter band is typically 20 times smaller than the relative zero-to-peak velocity error, when delayed sampling is used. In the lowest quarter of the filter band it is more than 100 times smaller than the relative velocity error. These values are ten and forty times smaller, respectively, than they would be without delay compensation if the filter is a 6-pole Butterworth.
Zachor, A. S.↗
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.↗
An Analytical Approach to the Design of an Automatic Discontinuous Control System
An analytical investigation was conducted concerning the design of an attitude-stabilization system for stabilizing a vehicle experiencing negligible external moments. The system studied was an automatic discontinuous control system employing a linear switching function including effects of pure time delays, rise and decay time, and neutral zone. Equations were developed which generalize the transient and limit-cycle performance of the control system. understanding of how the physical constants of the system affect its performance, the equations enable the optimization of the system with regard to most considerations that can be expressed mathematically. Design charts are presented which enable rapid calculation of the best thrust level and switching-function coefficient for minimizing power required to stabilize the vehicle within some amplitude, minimizing attitude error, and minimizing angular-velocity error after a period of operation.
Taylor, Lawrence W., Jr.↗
Mariner IV midcourse propulsion system impulse and accuracy prediction.
Mariner IV midcourse 50-lb thrust pressure- controlled monopropellant hydrazine propellant system, predicting impulse and velocity error as function of burn time
SPECIFIC IMPULSE↗