Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “STATE 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.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Real-time shipboard orbit determination using Kalman filtering techniques

The real-time tracking and orbit determination program used on board the NASA tracking ship, the USNS Vanguard, is described in this paper. The computer program uses a variety of filtering algorithms, including an extended Kalman filter, to derive real-time orbit determinations (position-velocity state vectors) from shipboard tracking and navigation data. Results from Apollo missions are given to show that orbital parameters can be estimated quickly and accurately using these methods.

Brammer, R. F.↗
NASA NTRS1974

State equations for an n-body spacecraft

Considerable attention, in the open literature, is being focused on the problem of developing a suitable set of deterministic dynamical equations for a complex spacecraft. The present paper addresses the problem of determining a set of state equations for an n-body spacecraft. The approach used in obtaining the state equations involves the application and interpretation of advanced dynamical principles. This set of state equations can be effectively used in the development of a stochastic controller for the spacecraft (in this latter development, the deterministic model developed in the present paper will be appropriately corrupted by plant noise). The major effort in the paper revolves around the determination of the plant matrices and the specification of the state vector and the control vector.

Larson, V.↗
NASA NTRS1974

Autonomous target relative navigation

The present work outlines eight candidate navigation systems for autonomous target relative navigation near a comet, asteroid, or planet. An analytic model is developed for each system, showing how the solution of the relative state vector is obtained from measurement data.

Brock, H. I.↗
NASA NTRS1975

FCAP - A new tool for the evaluation of active control technology

A computer program has been developed for the evaluation of flight control systems designed for flexible aircraft. This Flight Control Analysis Program (FCAP) is designed in a modular fashion to incorporate sensor, actuator, and control logic element dynamics as well as aircraft dynamics and aerodynamics for complex configurations. Formulation of the total aircraft dynamic system is accomplished in matrix form by casting the equations in state vector format. The system stability and performance are determined in either the frequency or time domain using classical analysis techniques. The aerodynamic method used also permits evaluation of the flutter characteristics of the aircraft.

Noll, R. B.↗
NASA NTRS1975

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Choudhury, A. K.↗
NASA NTRS1975

Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Kaufman, H.↗
NASA NTRS1976

Reduced state feedback gain computation

Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Kaufman, H.↗
NASA NTRS1975

Dispersion analysis for baseline reference mission 1

A dispersion analysis considering 3 sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the baseline reference mission (BRM) 1 of the space shuttle orbiter. The dispersion analysis is based on the nominal trajectory for the BRM 1. State vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties were studied. The dispersions were determined at major mission events and fixed times from lift-off (time slices) and the results will be used to evaluate the capability of the vehicle to perform the mission within a 3 sigma level of confidence and to determine flight performance reserves. A computer program is given that was used for dynamic flight simulations of the space shuttle orbiter.

Kuhn, A. E.↗
NASA NTRS1975

Dispersion analysis for baseline reference mission 2

A dispersion analysis considering uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for baseline reference mission (BRM) 2. The dispersion analysis is based on the nominal trajectory for BRM 2. The analysis was performed to determine state vector and performance dispersions (or variations) which result from the indicated uncertainties. The dispersions are determined at major mission events and fixed times from liftoff (time slices). The dispersion results will be used to evaluate the capability of the vehicle to perform the mission within a specified level of confidence and to determine flight performance reserves.

Snow, L. S.↗
NASA NTRS1975

Solution of an optimal control lifting body entry problem by an improved method of perturbation functions

This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.

Garcia, F., Jr.↗
NASA NTRS1975

Minimum-fuel rocket trajectories involving intermediate-thrust arcs

The optimal trajectories in the neighborhood of an optimal intermediate-thrust arc are investigated for the minimum-fuel orbit rendezvous problem with fixed specific impulse. Since such an arc is singular, the thrust acceleration magnitude being the singular control component, a second-variation analysis leads to the identification of a field of neighboring, singular arcs in a state space of dimension four rather than six, provided that a suitable Jacobi condition is met. A given neighboring initial six-dimensional state vector does not generally lie on a neighboring singular arc, and junction onto the appropriate singular arc must be accomplished by a short period of strong variations in the acceleration. The neighboring singular arc meets the final condition in 4 dimensions, rather than 6 dimensions, and rendezvous must be completed by another, terminal short period of strong variations in the acceleration. Implications for midcourse guidance near a singular arc are discussed.

Breakwell, J. V.↗
NASA NTRS1975

Onboard navigation of the Space Shuttle

This paper discusses the Kalman filter used in the navigation software of the Space Shuttle. The form of the filter will be discussed: the standard Kalman filter versus the square-root version of this filter. Both of these filters have severe nonlinearity problems. Two successful solutions of the nonlinearity problem are presented. A real-time program must have a good method of editing bad data. The data editing scheme is discussed. Those elements of the Kalman filter state vector which are random variables will be discussed.

Lear, W. M.↗
NASA NTRS1976

Parametric study of predictor accuracy impact on OFT rendezvous targeting

A parametric study was made to quantitatively define the effects of errors in the state vector predictor used by the Operational Flight Trainer (OFT) rendezvous targeting algorithms. The effect of the predictor accuracy on the OFT rendezvous profile is shown by the sensitivity of various critical rendezvous parameters with respect to downrange and radial predictor error rates. The effect of both inertial (same errors on both vehicles) and relative (differential errors on one vehicle with respect to the other) errors were considered. Relative radial error rates had the largest impact on the rendezvous followed by relative downrange errors, radial inertial errors and downrange inertial errors.

Glenn, S. W.↗
NASA NTRS1977

Space shuttle engineering and operations support: Dispersion analysis for the first orbital flight test (OFT-1) mission

A dispersion analysis considering 3—sigma (3σ) uncertainties (or perturbations) in platform, vehicle, and environmental parameters has been performed for the first orbital flight test (OFT-1) mission. The dispersion analysis is based on the nominal trajectory for the OFT-1 reference flight profile (RFP) which is described in Reference 1. The analysis has been performed to determine state vector and performance dispersions (or variations) which result from the indicated 3σ uncertainties. The dispersions are determined at major mission events and fixed times from Liftoff (time slices). The dispersion results will be used to evaluate the capability of the vehicle to perform the mission within a 3σ Level of confidence and to determine flight performance reserves. (FPR).

L.S. Snow↗
NASA NTRS1977

Updated dispersion analysis for the first Orbital Flight Test (OFT-1) mission

A dispersion analysis considering 3-sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the first orbital flight test (OFT-1) mission. The dispersion analysis is based on the nominal trajectory for the OFT-1 reference flight profile and was performed to determine state vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties. The dispersions are determined at major mission events and fixed times from liftoff (time slices). Principal error contributors to the covariance matrix are listed. The dispersion data indicates that the largest position error occurs in the down range component. At main engine cutoff and circularization, the vehicle performance uncertainties are the major contributors to down range error.

Snow, L. S.↗
NASA NTRS1975

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗
NASA NTRS1977

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗