STATISTICAL FILTERING OF SPACE NAVIGATION MEASUREMENTS
Redundant measurements for space navigation - random variables, state vector, bayes estimator
BAYESIAN STATISTICS↗
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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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Four-body trajectory optimization
A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.
Pu, C. L.↗
Problems in space navigation and guidance.
Navigation and guidance problems involving flight path calculations and spacecraft state vector evaluation, using Mars midcourse navigation as example
FLIGHT PATH↗
Evaluation of the use of powered flight tracking and telemetry data in lunar orbit differential correction procedures
Powered flight maneuver data used to reduce state vector uncertainties for lunar satellite orbit differential correction
SPACECRAFT MANEUVER↗
Control of nonlinear multivariable systems.
Synthesis technique applying Liapunov theory for state vector tracking of nonlinear multivariable control systems illustrated by reactor control design
NONLINEAR SYSTEM↗
Lateral stability augmentation of supersonic aircraft using multichannel optimal feedback control.
Lateral stability augmentation of supersonic aircraft using linear multichannel state-vector optimal feedback control
OPTIMAL CONTROL↗
Vector magnetometer as an attitude determining instrument
The solid state vector magnetometer sensor system is presented for the accuracy and reliability of existing systems, and for providing independent measures of attitude. Since a large number of aircraft heading reference systems depend on measurement of the earth's magnetic field, it can be shown that by substituting a 3-axis magnetometer for the remote sensing unit, both heading and attitude measurement functions can be derived using common elements. Sample calculations are made using the earth's magnetic field data acquired during actual flight conditions.
Pietila, R.↗
State variable determination for digital control.
State vector determination for digital optimal control of system characterized by matrix equation
MATRIX ANALYSIS↗
An efficient method for calculating optimal free-space n-impulse trajectories.
Optimum central force transfer and rendezvous trajectories calculating technique, using primer-vector theory to determine time, number and state vector of all impulses
Jezewski, D. J.↗
Applicability of relative GPS to automated rendezvous between the space shuttle and space station
The purpose of this study is to determine the adequacy of the Global Positioning System (GPS) in providing relative navigation for automated rendezvous and proximity operations. The study was performed using the Proximity Operations Simulator (POS), Lockheed's high-fidelity, 6 degree of freedom simulation of the space shuttle and space station. This simulation includes identical models of GPS receivers for each vehicle. The navigation software in each vehicle includes identical Kalman filters. Each filter computes the absolute state of its vehicle, and the relative state vector is obtained by simply subtracting absolute states.
Clark, Fred D.↗
PatchworkWave: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe/Multimethod Simulations at Arbitrary Order
We present an extension of the PatchworkMHD code [1], itself an MHD-capable extension of thePatch-workcode [2], for which several algorithms presented here were co-developed. Its purpose is to create a“multipatch” scheme compatible with numerical simulations of arbitrary equations of motion at any dis-cretization order in space and time. In thePatchworkframework, the global simulation is comprised of anarbitrary number of moving, local meshes, or “patches”, which are free to employ their own resolution, co-ordinate system/topology, physics equations, reference frame, and in our new approach, numerical method.Each local patch exchanges boundary data with a single global patch on which all other patches residethrough a client-router-server parallelization model. In generalizingPatchworkto be compatible witharbitrary order time integration,PatchworkMHDandPatchworkWavehave significantly improved theinterpatch interpolation accuracy by removing an interpolation of interpolated data feedback present in theoriginalPatchworkcode. Furthermore, we extendPatchworkto bemultimethodby allowing multiplestate vectors to be updated simultaneously, with each state vector providing its own interpatch interpolationand transformation procedures. As such, our scheme is compatible with nearly any set of hyperbolic partialdifferential equations. We demonstrate our changes through the implementation of a scalar wave toy-modelthat is evolved on arbitrary, time dependent patch configurations at 4th order accuracy.
Dennis B Bowen↗
A vector autopilot system
Current technology has evolved low cost, highly reliable solid state vector magnetometers with excellent angular resolution. This paper discusses the role of a three-axis magnetometer as a new instrument for aircraft attitude determination. Using flight data acquired by an instrumented aircraft, attitude is calculated using the earth's magnetic field vector and compared to measured attitudes. The magnetic field alone is not adequate to resolve all attitude variations and the need for a second reference angle or vector is discussed. A system combining the functions of heading determination and attitude measurement is presented to show that both functions can be implemented with essentially the same component count required to measure heading alone. It is concluded that with the correlation achieved in calculated and measured attitude there is a potential application of vector magnetometry in attitude measurement systems.
Pietila, R.↗
Joint map data/phase sequence estimation for trellis phase codes
A unified estimation procedure is formulated for the coherent detection of trellis phase codes, including partial response FM codes and multi-h codes. The unknown carrier phase is imbedded in the system state vector, and by simple augmentation of the decoder's state space, joint data and carrier estimation may be accomplished. The procedure is general to all trellis phase codes analyzed thus far. The effect of a static phase error on detection performance is also treated.
Wilson, S. G.↗
Jupyter-notebook-for-antisymmetrization-circuits
Validation through explicit state-vector validation of the swap operations generated using Dicke-state construction to produce the antisymmetrized states of targets and projectiles for nuclear reaction simulations using quantum computing techniques.
Stetcu, Ionel [Los Alamos National Laboratory]↗
Star scanner attitude determination for the OSO-7 spacecraft.
Calculation of the inertial orientation of the OSO-7 spacecraft from the times at which known stars or planets transit planes fixed in the spacecraft. Both the reference planes and the timing information are provided by the star scanner instrument aboard the spacecraft, while the star identification and the statistical estimation of a set of parameters describing the spacecraft attitude are accomplished in a ground station computer facility. A recursive least-squares determination is made of a vector of first-order differential corrections to the attitude state vector. Preliminary analysis indicates the system accuracy to be 3 arc min in each attitude Euler angle.
Mackison, D. L.↗
The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits
Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.
Carpenter, J. Russell↗
Advanced Control Algorithms for Compensating the Phase Distortion Due to Transport Delay in Human-Machine Systems
The desire to create more complex visual scenes in modern flight simulators outpaces recent increases in processor speed. As a result, simulation transport delay remains a problem. New approaches for compensating the transport delay in a flight simulator have been developed and are presented in this report. The lead/lag filter, the McFarland compensator and the Sobiski/Cardullo state space filter are three prominent compensators. The lead/lag filter provides some phase lead, while introducing significant gain distortion in the same frequency interval. The McFarland predictor can compensate for much longer delay and cause smaller gain error in low frequencies than the lead/lag filter, but the gain distortion beyond the design frequency interval is still significant, and it also causes large spikes in prediction. Though, theoretically, the Sobiski/Cardullo predictor, a state space filter, can compensate the longest delay with the least gain distortion among the three, it has remained in laboratory use due to several limitations. The first novel compensator is an adaptive predictor that makes use of the Kalman filter algorithm in a unique manner. In this manner the predictor can accurately provide the desired amount of prediction, while significantly reducing the large spikes caused by the McFarland predictor. Among several simplified online adaptive predictors, this report illustrates mathematically why the stochastic approximation algorithm achieves the best compensation results. A second novel approach employed a reference aircraft dynamics model to implement a state space predictor on a flight simulator. The practical implementation formed the filter state vector from the operator s control input and the aircraft states. The relationship between the reference model and the compensator performance was investigated in great detail, and the best performing reference model was selected for implementation in the final tests. Theoretical analyses of data from offline simulations with time delay compensation show that both novel predictors effectively suppress the large spikes caused by the McFarland compensator. The phase errors of the three predictors are not significant. The adaptive predictor yields greater gain errors than the McFarland predictor for short delays (96 and 138 ms), but shows smaller errors for long delays (186 and 282 ms). The advantage of the adaptive predictor becomes more obvious for a longer time delay. Conversely, the state space predictor results in substantially smaller gain error than the other two predictors for all four delay cases.
Guo, Liwen↗
Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter
Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.
Keppenne, Christian↗