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Orbit calculation including boundary value problem optimal solution with programming for circular and elliptical orbits, linear filter weighting, and modeling of gravity anomalies
This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of prediction accuracy and accumulated observation cost is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. It is shown that the optimal measurement policy and the associated matched Kalman-type filter can be precomputed.
An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.
Two schemes for reception of weak radio signals conveying digital data via phase modulation provide for mutual coupling of multiple receivers, and coherent combination of outputs of receivers. In both schemes, optimal mutual-coupling weights computed according to Kalman-filter theory, but differ in manner of transmission and combination of outputs of receivers.
Optimizing the Fisher ratio is well established in statistical pattern recognition as a means of discriminating between classes. I show how to optimize that ratio for optical correlation intensity by choice of filter on an arbitrary spatial light modulator (SLM). I include the case of additive noise of known power spectral density.
This paper describes the techniques, equipment, and results from the optimization of a two-axis traverse actuation system used to maintain concentricity between a sting-mounted fan and a wall-mounted nacelle in the 9 x 15 (9 Foot by 15 Foot Test Section) Low Speed Wind Tunnel (LSWT) at the NASA Glenn Research Center (GRC). The Rotor Alone Nacelle (RAN) system, developed at GRC by the Engineering Design and Analysis Division (EDAD) and the Acoustics Branch, used nacelle-mounted lasers and an automated control system to maintain concentricity as thermal and thrust operating loads displace the fan relative to the nacelle. This effort was critical to ensuring rig/facility safety and experimental consistency of the acoustic data from a statorless, externally supported nacelle configuration. Although the tip clearances were originally predicted to be about 0.020 in. at maximum rotor (fan) operating speed, proximity probe measurements showed that the nominal clearance was less than 0.004 in. As a result, the system was optimized through control-loop modifications, active laser cooling, data filtering and averaging, and the development of strict operational procedures. The resultant concentricity error of RAN was reduced to +/- 0.0031 in. in the Y-direction (horizontal) and +0.0035 in./-0.001 3 in. in the Z-direction (vertical), as determined by error analysis and experimental results. Based on the success of this project, the RAN system will be transitioned to other wind tunnel research programs at NASA GRC.
Freeze tape casting is a means of making preforms of ceramic sheets that, upon subsequent completion of fabrication processing, can have anisotropic and/or functionally graded properties that notably include aligned and graded porosity. Freeze tape casting was developed to enable optimization of the microstructures of porous ceramic components for use as solid oxide electrodes in fuel cells: Through alignment and grading of pores, one can tailor surface areas and diffusion channels for flows of gas and liquid species involved in fuel-cell reactions. Freeze tape casting offers similar benefits for fabrication of optimally porous ceramics for use as catalysts, gas sensors, and filters.
The James Webb Space Telescope is an infrared-optimized space telescope scheduled for launch in 201 3. Its 6.5-m diameter primary mirror will collect light from some of the first galaxies formed after the big bang. The Near Infrared camera (NIRCam) will detect the first light from these galaxies, provide the necessary tools for studying the formation of stars, aid in discovering planets around other stars, and adjust the wave front error on the primary mirror (Fig. 1). The instrument and its complement of mechanisms and optics will operate at a cryogenic temperature of 35 K. This paper describes tests and test results of the NIRCam Filter Wheel assembly prototype.
This paper presents a design method for digital self-reorganizing control systems which is optimally tolerant of failures in aircraft sensors. The functions of this system are accomplished with software instead of the popular and costly technique of hardware duplication. The theoretical development, based on M-ary hypothesis testing, results in a bank of M Kalman filters operating in parallel in the failure detection logic. A moving window of the innovations of each Kalman filter drives the detection logic to decide the failure state of the system. The detection logic also selects the optimal state estimate (for control logic) from the bank of Kalman filters. The design process is applied to the design of a self-reorganizing control system for a current configuration of the space shuttle orbiter at Mach 5 and 120,000 feet. The failure detection capabilities of the system are demonstrated using a real-time simulation of the system with noisy sensors.
Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.
Modern computational and experimental tools for aerodynamics and propulsion applications have matured to a stage where they can provide substantial insight into engineering processes involving fluid flows, and can be fruitfully utilized to help improve the design of practical devices. In particular, rapid and continuous development in aerospace engineering demands that new design concepts be regularly proposed to meet goals for increased performance, robustness and safety while concurrently decreasing cost. To date, the majority of the effort in design optimization of fluid dynamics has relied on gradient-based search algorithms. Global optimization methods can utilize the information collected from various sources and by different tools. These methods offer multi-criterion optimization, handle the existence of multiple design points and trade-offs via insight into the entire design space, can easily perform tasks in parallel, and are often effective in filtering the noise intrinsic to numerical and experimental data. However, a successful application of the global optimization method needs to address issues related to data requirements with an increase in the number of design variables, and methods for predicting the model performance. In this article, we review recent progress made in establishing suitable global optimization techniques employing neural network and polynomial-based response surface methodologies. Issues addressed include techniques for construction of the response surface, design of experiment techniques for supplying information in an economical manner, optimization procedures and multi-level techniques, and assessment of relative performance between polynomials and neural networks. Examples drawn from wing aerodynamics, turbulent diffuser flows, gas-gas injectors, and supersonic turbines are employed to help demonstrate the issues involved in an engineering design context. Both the usefulness of the existing knowledge to aid current design practices and the need for future research are identified.
Symmetrical phase-only filtering (SPOF) can be exploited to obtain substantial improvements in the results of data processing in particle-image velocimetry (PIV). In comparison with traditional PIV data processing, SPOF PIV data processing yields narrower and larger amplitude correlation peaks, thereby providing more-accurate velocity estimates. The higher signal-to-noise ratios associated with the higher amplitude correlation peaks afford greater robustness and reliability of processing. SPOF also affords superior performance in the presence of surface flare light and/or background light. SPOF algorithms can readily be incorporated into pre-existing algorithms used to process digitized image data in PIV, without significantly increasing processing times. A summary of PIV and traditional PIV data processing is prerequisite to a meaningful description of SPOF PIV processing. In PIV, a pulsed laser is used to illuminate a substantially planar region of a flowing fluid in which particles are entrained. An electronic camera records digital images of the particles at two instants of time. The components of velocity of the fluid in the illuminated plane can be obtained by determining the displacements of particles between the two illumination pulses. The objective in PIV data processing is to compute the particle displacements from the digital image data. In traditional PIV data processing, to which the present innovation applies, the two images are divided into a grid of subregions and the displacements determined from cross-correlations between the corresponding sub-regions in the first and second images. The cross-correlation process begins with the calculation of the Fourier transforms (or fast Fourier transforms) of the subregion portions of the images. The Fourier transforms from the corresponding subregions are multiplied, and this product is inverse Fourier transformed, yielding the cross-correlation intensity distribution. The average displacement of the particles across a subregion results in a displacement of the correlation peak from the center of the correlation plane. The velocity is then computed from the displacement of the correlation peak and the time between the recording of the two images. The process as described thus far is performed for all the subregions. The resulting set of velocities in grid cells amounts to a velocity vector map of the flow field recorded on the image plane. In traditional PIV processing, surface flare light and bright background light give rise to a large, broad correlation peak, at the center of the correlation plane, that can overwhelm the true particle- displacement correlation peak. This has made it necessary to resort to tedious image-masking and background-subtraction procedures to recover the relatively small amplitude particle-displacement correlation peak. SPOF is a variant of phase-only filtering (POF), which, in turn, is a variant of matched spatial filtering (MSF). In MSF, one projects a first image (denoted the input image) onto a second image (denoted the filter) as part of a computation to determine how much and what part of the filter is present in the input image. MSF is equivalent to cross-correlation. In POF, the frequency-domain content of the MSF filter is modified to produce a unitamplitude (phase-only) object. POF is implemented by normalizing the Fourier transform of the filter by its magnitude. The advantage of POFs is that they yield correlation peaks that are sharper and have higher signal-to-noise ratios than those obtained through traditional MSF. In the SPOF, these benefits of POF can be extended to PIV data processing. The SPOF yields even better performance than the POF approach, which is uniquely applicable to PIV type image data. In SPOF as now applied to PIV data processing, a subregion of the first image is treated as the input image and the corresponding subregion of the second image is treated as the filter. The Fourier transforms from both the firs and second- image subregions are normalized by the square roots of their respective magnitudes. This scheme yields optimal performance because the amounts of normalization applied to the spatial-frequency contents of the input and filter scenes are just enough to enhance their high-spatial-frequency contents while reducing their spurious low-spatial-frequency content. As a result, in SPOF PIV processing, particle-displacement correlation peaks can readily be detected above spurious background peaks, without need for masking or background subtraction.
A robust method of detecting Orion Multi ]Purpose Crew Vehicle (MPCV) splashdown is necessary to ensure crew and hardware safety during descent and after touchdown. The proposed method uses a triple redundant system to inhibit Reaction Control System (RCS) thruster firings, detach parachute risers from the vehicle, and transition to the post ]landing segment of the Flight Software (FSW). The vehicle crew is the prime input for touchdown detection, followed by an autonomous FSW algorithm, and finally a strictly time based backup timer. RCS thrusters must be inhibited before submersion in water to protect against possible damage due to firing these jets under water. In addition, neglecting to declare touchdown will not allow the vehicle to transition to post ]landing activities such as activating the Crew Module Up ]righting System (CMUS), resulting in possible loss of communication and difficult recovery. A previous AIAA paper gAssessment of an Automated Touchdown Detection Algorithm for the Orion Crew Module h concluded that a strictly Inertial Measurement Unit (IMU) based detection method using an acceleration spike algorithm had the highest safety margins and shortest detection times of other methods considered. That study utilized finite element simulations of vehicle splashdown, generated by LS ]DYNA, which were expanded to a larger set of results using a Kriging surface fit. The study also used the Decelerator Systems Simulation (DSS) to generate flight dynamics during vehicle descent under parachutes. Proto ]type IMU and FSW MATLAB models provided the basis for initial algorithm development and testing. This paper documents an in ]depth trade study, using the same dynamics data and MATLAB simulations as the earlier work, to further develop the acceleration detection method. By studying the combined effects of data rate, filtering on the rotational acceleration correction, data persistence limits and values of acceleration thresholds, an optimal configuration was determined. The lever arm calculation, which removes the centripetal acceleration caused by vehicle rotation, requires that the vehicle angular acceleration be derived from vehicle body rates, necessitating the addition of a 2nd order filter to smooth the data. It was determined that using 200 Hz data directly from the vehicle IMU outperforms the 40 Hz FSW data rate. Data persistence counter values and acceleration thresholds were balanced in order to meet desired safety and performance. The algorithm proved to exhibit ample safety margin against early detection while under parachutes, and adequate performance upon vehicle splashdown. Fall times from algorithm initiation were also studied, and a backup timer length was chosen to provide a large safety margin, yet still trigger detection before CMUS inflation. This timer serves as a backup to the primary acceleration detection method. Additionally, these parameters were tested for safety on actual flight test data, demonstrating expected safety margins.
A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed 'truth' into another run termed 'prediction'. At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.
The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.
Infimum principle for dynamic optimal control with nonscalar valued cost criteria, rederiving Kalman-Bucy filter
The problems in navigation and guidance encountered by aircraft in the initial transition period in changing from distance measuring equipment, VORTAC, and barometric instruments to the more precise microwave landing system data type navaids in the terminal area are investigated. The effects of the resulting discontinuities on the estimates of position and velocity for both optimal (Kalman type navigation schemes) and fixed gain (complementary type) navigation filters, and the effects of the errors in cross track, track angle, and altitude on the guidance equation and control commands during the critical landing phase are discussed. A method is presented to remove the discontinuities from the navigation loop and to reconstruct an RNAV path designed to land the aircraft with minimal turns and altitude changes.
The EUV Explorer (EUVE) mission is described, with emphasis on the overall capabilities of the instrumentation and the relevance of the mission to determining parameters of the local interstellar medium. The primary purpose of the mission is to search the celestial sphere for astronomical sources of EUV radiation (100-1000 A). The search will be accomplished with the use of three EUV telescopes, sensitive to different segments of the EUV band. A fourth telescope will perform a high-sensitivity search of a limited sample of the sky in the shortest-wavelength bands. The all-sky survey will be carried out in the first six months of the mission. The second six months of the mission, conducted entirely by Guest Investigators selected by NASA, will be devoted to spectroscopic observations of selected EUV sources. The instrumentation is now well developed. The best mirror has full-width/half-energy spread of 8 arcsec and a surface finish of 20 A. Prototype thin-film bandpass filters have been flown on the Space Shuttle and their performance optimized. Prototype detectors have been developed which have 600 by 600-pixel imaging capability and up to 80-percent quantum efficiency in parts of the EUV band.