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At least 127 records · Page 7

Model Adaptation for Prognostics in a Particle Filtering Framework

One of the key motivating factors for using particle filters for prognostics is the ability to include model parameters as part of the state vector to be estimated. This performs model adaptation in conjunction with state tracking, and thus, produces a tuned model that can used for long term predictions. This feature of particle filters works in most part due to the fact that they are not subject to the "curse of dimensionality", i.e. the exponential growth of computational complexity with state dimension. However, in practice, this property holds for "well-designed" particle filters only as dimensionality increases. This paper explores the notion of wellness of design in the context of predicting remaining useful life for individual discharge cycles of Li-ion batteries. Prognostic metrics are used to analyze the tradeoff between different model designs and prediction performance. Results demonstrate how sensitivity analysis may be used to arrive at a well-designed prognostic model that can take advantage of the model adaptation properties of a particle filter.

Saha, Bhaskar

Improved Stratospheric Temperature Retrievals for Climate Reanalysis

The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.

Rokke, L.

Orion Optical Navigation Progress Toward Exploration: Mission 1

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. It shares a history with the "method of lunar distances" that was used in the 18th century and gained some notoriety after its use by Captain James Cook during his 1768 Pacific voyage of the HMS Endeavor. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is being worked as a Government Furnished Equipment (GFE) project delivered as an application within the Core Flight Software of the Orion camera controller module. The mathematical formulation behind the initial ellipse fit in the image processing is detailed in Christian. The non-linear least squares refinement then follows the technique of Mortari as an estimation process of the planetary limb using the sigmoid function. The Orion optical navigation system uses a body fixed camera, a decision that was driven by mass and mechanism constraints. The general concept of operations involves a 2-hour pass once every 24 hours, with passes specifically placed before all maneuvers to supply accurate navigation information to guidance and targeting. The pass lengths are limited by thermal constraints on the vehicle since the OpNav attitude generally deviates from the thermally stable tail-to-sun attitude maintained during the rest of the orbit coast phase. Calibration is scheduled prior to every pass due to the unknown nature of thermal effects on the lens distortion and the mounting platform deformations between the camera and star trackers. The calibration technique is described in detail by Christian, et al. and simultaneously estimates the Brown-Conrady coefficients and the Star Tracker/Camera interlock angles. Accurate attitude information is provided by the star trackers during each pass. Figure 1 shows the various phases of lunar return navigation when the vehicle is in autonomous operation with lost ground communication. The midcourse maneuvers are placed to control the entry interface conditions to the desired corridor for safe landing. The general form of optical navigation on Orion is where still images of the Moon or Earth are processed to find the apparent angular diameter and centroid in the camera focal plane. This raw data is transformed into range and bearing angle measurements using planetary data and precise star tracker inertial attitude. The measurements are then sent to the main flight computer's Kalman filter to update the onboard state vector. The images are, of course, collected over an arc to converge the state and estimate velocity. The same basic technique was used by Apollo to satisfy loss-of-comm, but Apollo used manual crew sightings with a vehicle-integral sextant instead of autonomously processing optical imagery. The software development is past its Critical Design Review, and is progressing through test and certification for human rating. In support of this, a hardware-in-the-loop test rig was developed in the Johnson Space Center Electro-Optics Lab to exercise the OpNav system prior to integrated testing on the Orion vehicle. Figure 2 shows the rig, which the test team has dubbed OCILOT (Orion Camera In the Loop Optical Testbed). Analysis performed to date shows a delivery that satisfies an allowable entry corridor as shown in Figure 3.

Holt, Greg N.

Efficient Optimization of Low-Thrust Spacecraft Trajectories

A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.

Lee, Seungwon

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Navigation and meteorological error equations for some aerodynamic parameters

Mathematical equations for the analysis of the errors that are expected in a set of postflight aerodynamic parameters are presented. The errors are due to inaccuracies in the Shuttle best estimate trajectory and in the meteorological data obtained in support of the flights. The error analysis shows that the parameter vector, Z, and its associated error covariance matrix, C sub Z, is calculated from a given state vector, X, and its associated covariance matrix, C sub X.

Krikorian, M. J.

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Source record

Parameter adaptive control of multivariable systems

Model reference adaptive controllers for multivariable plants are designed using only input and output signals rather than the complete state vector. The design is based on Liapunov's direct method, and the Meyer-Kalman-Yacubovich lemma. State variable filters are employed to avoid differentiating output signals. Augmented error signals are used in deriving stable adaptive control laws which assure that the normally used response error signals approach zero asymptotically.

Monopoli, R. V.

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis

Procedures for generation and reduction of linear models of a turbofan engine

A real time hybrid simulation of the Pratt & Whitney F100-PW-F100 turbofan engine was used for linear-model generation. The linear models were used to analyze the effect of disturbances about an operating point on the dynamic performance of the engine. A procedure that disturbs, samples, and records the state and control variables was developed. For large systems, such as the F100 engine, the state vector is large and may contain high-frequency information not required for control. This, reducing the full-state to a reduced-order model may be a practicable approach to simplifying the control design. A reduction technique was developed to generate reduced-order models. Selected linear and nonlinear output responses to exhaust-nozzle area and main-burner fuel flow disturbances are presented for comparison.

Seldner, K.

Optimal landing of a helicopter in autorotation

The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. A unique feature in the present formulation is the addition of path inequality constraints on both the control and the state vectors. The control variable inequality constraint is a reflection of the limitation on the rotor thrust coefficient. The state-variable inequality constraint is an upper bound on the vertical sink-rate of the helicopter during descent. Optimal trajectories are calculated for entry conditions well within the height-velocity (H-V) restriction curve, with the helicopter initially in hover or in forward flight. The optimal solutions exhibited control techniques similar to those used by helicopter pilots in actual autorotational landings. The study indicates that, subject to pilot acceptability, a substantial reduction could be made in the H-V restriction zone using optimal control techniques.

Lee, A. Y.

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Deutsch, Ivan H.

Reduced Vector Preisach Model

A new vector Preisach model, called the Reduced Vector Preisach model (RVPM), was developed for fast computations. This model, derived from the Simplified Vector Preisach model (SVPM), has individual components that like the SVPM are calculated independently using coupled selection rules for the state vector computation. However, the RVPM does not require the rotational correction. Therefore, it provides a practical alternative for computing the magnetic susceptibility using a differential approach. A vector version, using the framework of the DOK model, is implemented. Simulation results for the reduced vector Preisach model are also presented.

Patel, Umesh D.

Kalman Filtering of Angular-Momentum-Based Attitude Parameters

This paper presents an extended Kalman filter using an attitude parameterization that is advantageous for attitude estimation of spinning spacecraft. The parameters are the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. To avoid the singularity of the 7x7 covariance of this state vector arising from the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames, the Kalman filter employs the nonsingular 6x6 covariance of a reduced error state. Three of the components of this six-component error state are the usual infinitesimal attitude error angles, so the usual 3x3 attitude covariance matrix is a submatrix of the 6x6 covariance. The performance of the resulting filter is compared with that of a quaternion-based filter.

Markley, F. Landis

The primer vector in linear, relative-motion equations

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

Source record

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS