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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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NASA NTRS1972

Space shuttle guidance, navigation and control equation document no. 4: Precision state and filter weighting matrix extrapolation

The Precision State and Filter Weighting Matrix Extrapolation Routine is described which provides the capability to extrapolate any spacecraft geocentric state vector either backwards or forwards in time through a force field consisting of the earth's primary central-force gravitational attraction and a superimposed perturbing acceleration. The routine also provides the capability of extrapolating the filter-weighting matrix along the precision trajectory. This matrix is a square root form of the error covariance matrix and contains statistical information relative to the accuracies of the state vectors and certain other optionally estimated quantities. The routine is a cooled algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of the spacecraft's center of mass and by the filter-weighting matrix.

Robertson, W. M.↗

NASA NTRS1985

A homotopy continuation method for general preliminary orbit determination and special application to the Tracking and Data Relay Satellite System

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The use of this technique, the homotopy continuation method, was motivated by the possible need to perform preliminary orbit determination in the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. In the formulation studied here, a set of six tracking observations is continuously transformed from a set with known solutions to the given set with unknown solutions, and the corresponding orbit state vector is followed from the a priori orbit state to the solution orbit states. A modular numerical algorithm is developed to follow the state vector. The technique is formulated and then tested, using both real and simulated tracking, with positive results. Direct comparisons show that the basic method has a much larger radius of convergence than standard or simply modified Newton-Raphson methods. An extension of the basic method is formulated that is expected to produce a global method.

Smith, R. L.↗

NASA NTRS1994

Overview of the MSTI 2 on-orbit alignment

The Miniature Sensor Technology Integration (MSTI) 2 Spacecraft is a small 3-axis stabilized spacecraft designed to track mid-range missiles and estimate their state vectors. In order to accurately estimate the target state vector, the MSTI 2 spacecraft must have highly accurate knowledge of its own attitude. Errors in its attitude knowledge arise primarily from the errors in its Attitude Control System (ACS) sensors. The ACS sensors on the spacecraft include a scanning Earth Sensor (ES), a Sun Sensor (SS), and two 2-axis gyros. The On-Orbit Alignment (OOA) generated an error map of the ES and estimated the biases of the SS and the misalignment of the gyros. This paper discusses some of the error sources, and the techniques used to reduce the effects of these errors. The payload carried by the MSTI2 spacecraft is a high fidelity camera, which was aimed at the target using gimballed mirrors. By aiming it at a celestial target, the payload was used as a high-accuracy single-axis attitude reference. This attitude reference was compared to the attitude reference of the ACS sensors, and the errors were attributed to the ACS sensors.

Rygaard, Christopher A.↗

DOE OSTI2025

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2010

The Fifteen-Year Attitude History of the Wide Field Planetary Camera 2 Radiator and Collection Efficiencies for Micrometeoroids and Orbital Debris

An examination of the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC-2) radiator assembly was conducted at NASA Goddard Space Flight Center (GSFC) during the summer of 2009. Immediately apparent was a distinct biasing of the largest 45 impact features towards one side of the radiator, in contrast to an approximately uniform distribution of smaller impacts. Such a distribution may be a consequence of the HST s attitude history and pointing requirements for the cold radiator, or of environmental effects, such as an anisotropic distribution of the responsible population in that size regime. Understanding the size-dependent spatial distribution of impact features is essential to the general analysis of these features. We have obtained from GSFC a 15 minute temporal resolution record of the state vector (Earth Centered Inertial position and velocity) and HST attitude, consisting of the orientation of the velocity and HST-sun vectors in HST body coordinates. This paper reviews the actual state vector and attitude history of the radiator in the context of the randomly tumbling plate assumption and assesses the statistical likelihood (or collection efficiency) of the radiator for the micrometeoroid and orbital debris environments. The NASA Marshall Space Flight Center s Meteoroid Environment Model is used to assess the micrometeoroid component. The NASA Orbital Debris Engineering Model (ORDEM) is used to model the orbital debris component. Modeling results are compared with observations of the impact feature spatial distribution, and the relative contribution of each environmental component are examined in detail.

Anz-Meador, Phillip D.↗

NASA NTRS1991

Structural control design based on reduced-order observer

An observer-based structural control design method is proposed in this paper. The method is a semi-inverse design procedure in that the control law is not designed before the observer system, but is a result that comes from the observer design. However, the observer design is not completely independent of the control design either, but seeks to yield a control law that is close to a prescribed control law. First, the observer design problem is considered as the reconstruction of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the optimal feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. The semi-inverse design procedure can yield a reduced-order observer with dimension considerably smaller than that of the system. Two examples are used to demonstrate the proposed design procedure.

Su, Tzu-Jeng↗

NASA NTRS1992

Control design based on a linear state function observer

An approach to the design of low-order controllers for large scale systems is proposed. The method is derived from the theory of linear state function observers. First, the realization of a state feedback control law is interpreted as the observation of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. A four-disk system and a lightly damped beam are presented as examples to demonstrate the applicability and efficacy of the proposed method.

Su, Tzu-Jeng↗

NASA NTRS1986

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

Smith, R. L.↗

NASA NTRS2010

SPOT Program

A Spacecraft Position Optimal Tracking (SPOT) program was developed to process Global Positioning System (GPS) data, sent via telemetry from a spacecraft, to generate accurate navigation estimates of the vehicle position and velocity (state vector) using a Kalman filter. This program uses the GPS onboard receiver measurements to sequentially calculate the vehicle state vectors and provide this information to ground flight controllers. It is the first real-time ground-based shuttle navigation application using onboard sensors. The program is compact, portable, self-contained, and can run on a variety of UNIX or Linux computers. The program has a modular objec-toriented design that supports application-specific plugins such as data corruption remediation pre-processing and remote graphics display. The Kalman filter is extensible to additional sensor types or force models. The Kalman filter design is also strong against data dropouts because it uses physical models from state and covariance propagation in the absence of data. The design of this program separates the functionalities of SPOT into six different executable processes. This allows for the individual processes to be connected in an a la carte manner, making the feature set and executable complexity of SPOT adaptable to the needs of the user. Also, these processes need not be executed on the same workstation. This allows for communications between SPOT processes executing on the same Local Area Network (LAN). Thus, SPOT can be executed in a distributed sense with the capability for a team of flight controllers to efficiently share the same trajectory information currently being computed by the program. SPOT is used in the Mission Control Center (MCC) for Space Shuttle Program (SSP) and International Space Station Program (ISSP) operations, and can also be used as a post -flight analysis tool. It is primarily used for situational awareness, and for contingency situations.

Smith, Jason T.↗

NASA NTRS2007

A Slow Retrieval Algorithm for Satellite and Surface Based Instruments

We present results of a retrieval algorithm for satellite and ground based instruments using the Arizona radiative transfer code. A state vector describing the atmospheric and surface condition is iteratively modified until the calculated radiances match the observed values. Elements of the state vector include: aerosol concentrations, radius, optical properties, mass-weighted altitudes, chlorophyll concentration and wind speed. While computationally expensive, many assumptions used in other retrieval algorithms are not invoked. We present co-located retrievals for MODIS, SEAWIFS and nearby AERONET sites. MODIS AQUA and SEA WIFS: Ten MODIS (.412 - 2.110 microns) and eight SEA WIFS (.412-.865 microns) radiances (.412-.865 microns) include channels where aerosols absorb and reflect radiation. We focus on retrieving bio-mass burning aerosols that are advected over open ocean. Since chlorophyll absorbs at frequencies where black carbon absorbs, our retrieval algorithm accounts for chlorophyll absorption by simultaneously retrieving both aerosol and chlorophyll amount. Our retrieved chlorophyll concentrations are similar to those from the Ocean Color Group. AERONET: Both Almucantar and Principle plane radiances are used to retrieve the state of the atmosphere and ocean conditions. Our retrieved aerosol size distributions and optical properties are consistent with the aerosol inversions from the AERONET group.

Weaver, C.↗

NASA NTRS1973

Rendezvous targeting

Revisions to be included in 'Space Shuttle Guidance, Navigation and Control Design Equations' are reported. Technical changes include: (1) a plane change maneuver was incorporated in the program's logic; (2) in the search for an apsidal crossing, program checks were included to update through intervals of pi in the case of near circular orbits or close proximity to an apsidal point; (3) following an astronaut overwrite of a Lambert maneuver, the state vector was updated to establish a new target vector for use in the powered flight routine; and (4) following the computation of each maneuver, the position vector of the primary vehicle was offset - to help compensate for the effects of the finite maneuver - prior to the update of the state vector to the next maneuver point. Input and output variables, detailed flow diagrams a functional flow diagram, and a description of equations are presented.

Tempelman, W. H.↗

NASA NTRS1977

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.↗

NASA NTRS1991

A method for computing instantaneous downtrack error from TDRS Doppler residuals

A simple method has been developed which calculates the instantaneous downtrack error in an orbiting vehicle's state vector from TDRS (Tracking and Data Relay Satellite) Doppler observation residuals. The downtrack error is expressed as a delta-time correction to the timetag of the vehicle's state vector. The method requires only a few easily obtained parameters and is easy to implement. This paper details the derivation of computing a delta-time correction from TDRS Doppler observation residuals and evaluates the method's assumptions and limitations. The results presented show that typically the method computes delta-time corrections that are less than five percent off from the true timetag error for Doppler observation residuals within twenty minutes of closest approach to the TDRS.

Haas, Franklin M., Jr.↗

NASA NTRS2003

Optimal Feedback Control of Thermal Networks

An improved approach to the mathematical modeling of feedback control of thermal networks has been devised. Heretofore software for feedback control of thermal networks has been developed by time-consuming trial-and-error methods that depend on engineers expertise. In contrast, the present approach is a systematic means of developing algorithms for feedback control that is optimal in the sense that it combines performance with low cost of implementation. An additional advantage of the present approach is that a thermal engineer need not be expert in control theory. Thermal networks are lumped-parameter approximations used to represent complex thermal systems. Thermal networks are closely related to electrical networks commonly represented by lumped-parameter circuit diagrams. Like such electrical circuits, thermal networks are mathematically modeled by systems of differential-algebraic equations (DAEs) that is, ordinary differential equations subject to a set of algebraic constraints. In the present approach, emphasis is placed on applications in which thermal networks are subject to constant disturbances and, therefore, integral control action is necessary to obtain steady-state responses. The mathematical development of the present approach begins with the derivation of optimal integral-control laws via minimization of an appropriate cost functional that involves augmented state vectors. Subsequently, classical variational arguments provide optimality conditions in the form of the Hamiltonian equations for the standard linear-quadratic-regulator (LQR) problem. These equations are reduced to an algebraic Riccati equation (ARE) with respect to the augmented state vector. The solution of the ARE leads to the direct computation of the optimal proportional- and integral-feedback control gains. In cases of very complex networks, large numbers of state variables make it difficult to implement optimal controllers in the manner described in the preceding paragraph.

Papalexandris, Miltiadis↗

DOE OSTI2023

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Benefits Derived From Laser Ranging Measurements for Orbit Determination of the GPS Satellite Orbit

While navigation systems for the determination of the orbit of the Global Position System (GPS) have proven to be very effective, the current research is examining methods to lower the error in the GPS satellite ephemerides below their current level. Two GPS satellites that are currently in orbit carry retro-reflectors onboard. One notion to reduce the error in the satellite ephemerides is to utilize the retro-reflectors via laser ranging measurements taken from multiple Earth ground stations. Analysis has been performed to determine the level of reduction in the semi-major axis covariance of the GPS satellites, when laser ranging measurements are supplemented to the radiometric station keeping, which the satellites undergo. Six ground tracking systems are studied to estimate the performance of the satellite. The first system is the baseline current system approach which provides pseudo-range and integrated Doppler measurements from six ground stations. The remaining five ground tracking systems utilize all measurements from the current system and laser ranging measurements from the additional ground stations utilized within those systems. Station locations for the additional ground sites were taken from a listing of laser ranging ground stations from the International Laser Ranging Service. Results show reductions in state covariance estimates when utilizing laser ranging measurements to solve for the satellite s position component of the state vector. Results also show dependency on the number of ground stations providing laser ranging measurements, orientation of the satellite to the ground stations, and the initial covariance of the satellite's state vector.

Welch, Bryan W.↗

NASA NTRS1980

Level B/C software ground navigation program. Delta-T processor

The Delta-T Processor (DTP) computes the instantaneous downtrack error in a specified orbiter onboard navigation state vector recovered via downlink telemetry. The downtrack error, expressed in units of time, is computed based on current incoming Earth based range and Doppler navigation tracking data and the ground selected onboard navigation state vector. The computed time difference when used to modify the timetag of the vector used for onboard navigation reduces the instantaneous downtrack error in this vector to within the threshold of the DTP, the input data, and the onboard software. This threshold is currently estimated to be approximately 2 to 4 nautical miles. The DTP is not restricted to using only onboard vectors. Any vector, either input via the manual entry device or accessible via the vector administration table, may be used. The DTP does not require that both data types be available.

Source record↗

NASA NTRS1987

Differential sampling for fast frequency acquisition via adaptive extended least squares algorithm

This paper presents a differential signal model along with appropriate sampling techinques for least squares estimation of the frequency and frequency derivatives and possibly the phase and amplitude of a sinusoid received in the presence of noise. The proposed algorithm is recursive in mesurements and thus the computational requirement increases only linearly with the number of measurements. The dimension of the state vector in the proposed algorithm does not depend upon the number of measurements and is quite small, typically around four. This is an advantage when compared to previous algorithms wherein the dimension of the state vector increases monotonically with the product of the frequency uncertainty and the observation period. Such a computational simplification may possibly result in some loss of optimality. However, by applying the sampling techniques of the paper such a possible loss in optimality can made small.

Kumar, Rajendra↗