Modeling errors in Kalman filters
Algorithms for error effects due to modeling errors in Kalman filter for continuous and discrete systems
Nishimura, T.↗
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Survey of digital filtering
A three part survey is made of the state-of-the-art in digital filtering. Part one presents background material including sampled data transformations and the discrete Fourier transform. Part two, digital filter theory, gives an in-depth coverage of filter categories, transfer function synthesis, quantization and other nonlinear errors, filter structures and computer aided design. Part three presents hardware mechanization techniques. Implementations by general purpose, mini-, and special-purpose computers are presented.
Nagle, H. T., Jr.↗
Tape Cassette Bacteria Detection System
The design, fabrication, and testing of an automatic bacteria detection system with a zero-g capability and based on the filter-capsule approach is described. This system is intended for monitoring the sterility of regenerated water in a spacecraft. The principle of detection is based on measuring the increase in chemiluminescence produced by the action of bacterial porphyrins (i.e., catalase, cytochromes, etc.) on a luminol-hydrogen peroxide mixture. Since viable as well as nonviable organisms initiate this luminescence, viable organisms are detected by comparing the signal of an incubated water sample with an unincubated control. Higher signals for the former indicate the presence of viable organisms. System features include disposable sealed sterile capsules, each containing a filter membrane, for processing discrete water samples and a tape transport for moving these capsules through a processing sequence which involves sample concentration, nutrient addition, incubation, a 4 Molar Urea wash and reaction with luminol-hydrogen peroxide in front of a photomultiplier tube. Liquids are introduced by means of a syringe needle which pierces a rubber septum contained in the wall of the capsule. Detection thresholds obtained with this unit towards E. coli and S. marcescens assuming a 400 ml water sample are indicated.
Source record↗
On the feasibility of real-time prediction of aircraft carrier motion at sea
The ability to predict the aircraft carrier's motion over an interval of several seconds within reasonable error bounds may allow an improvement in touchdown dispersion and a more certain value for ramp clearance due to a smoother aircraft trajectory. Also, improved information to the landing signal officer should decrease the number of waveoffs substantially. It is quantitatively shown that, based on the power density spectrum data for pitch and heave measured for various ships and sea conditions, the motion can be predicted well for up to 15 seconds. The zero crossover times for both pitch and heave motions can be predicted with impressive accuracy. The predictor was designed on the basis of Kalman's optimum filtering theory for the discrete time case, adapted for real-time digital computer operation.
Sidar, M.↗
Image coding by way of wavelets
The application of two wavelet transforms to image compression is discussed. It is noted that the Haar transform, with proper bit allocation, has performance that is visually superior to an algorithm based on a Daubechies filter and to the discrete cosine transform based Joint Photographic Experts Group (JPEG) algorithm at compression ratios exceeding 20:1. In terms of the root-mean-square error, the performance of the Haar transform method is basically comparable to that of the JPEG algorithm. The implementation of the Haar transform can be achieved in integer arithmetic, making it very suitable for applications requiring real-time performance.
Shahshahani, M.↗
Infrared Rugates by Molecular Beam Epitaxy
Rugates are optical structures that have a sinusoidal index of refraction (harmonic gradient-index field). As their discrete high/ low index filter counterparts, they can be used as narrow rejection band filters. However, since rugates do not have abrupt interfaces, they tend to have a smaller absorption, hence deliver a higher in band reflectivity. The absence of sharp interfaces makes rugates even more desirable for high-energy narrow band reflectors. In this application, the lack of a sharp interface at the maximum internal standing wave electric field results in higher breakdown strengths. Our method involves fabricating rugates, with molecular beam epitaxy, on GaAs wafers as an Al(x)Ga(1-x)As single-crystal film.
Rona, M.↗
Multiplexed Colorimetric Solid-Phase Extraction
Multiplexed colorimetric solid-phase extraction (MC-SPE) is an extension of colorimetric solid-phase extraction (C-SPE) an analytical platform that combines colorimetric reagents, solid phase extraction, and diffuse reflectance spectroscopy to quantify trace analytes in water. In CSPE, analytes are extracted and complexed on the surface of an extraction membrane impregnated with a colorimetric reagent. The analytes are then quantified directly on the membrane surface using a handheld diffuse reflectance spectrophotometer. Importantly, the use of solid-phase extraction membranes as the matrix for impregnation of the colorimetric reagents creates a concentration factor that enables the detection of low concentrations of analytes in small sample volumes. In extending C-SPE to a multiplexed format, a filter holder that incorporates discrete analysis channels and a jig that facilitates the concurrent operation of multiple sample syringes have been designed, enabling the simultaneous determination of multiple analytes. Separate, single analyte membranes, placed in a readout cartridge create unique, analyte-specific addresses at the exit of each channel. Following sample exposure, the diffuse reflectance spectrum of each address is collected serially and the Kubelka-Munk function is used to quantify each water quality parameter via calibration curves. In a demonstration, MC-SPE was used to measure the pH of a sample and quantitate Ag(I) and Ni(II).
Gazda, Daniel B.↗
PACE OCI Pre-launch ETU Spectral Characterization and Performance
The Ocean Color Instrument (OCI) is the primary sensor on the upcoming Plankton, Aerosol, Cloud ocean Ecosystem (PACE) mission. OCI is a new type of sensor compared to NASA’s ocean color heritage sensors VIIRS, MODIS, and SeaWiFs. Unlike its heritage sensors, OCI has two slit grating hyperspectral spectrographs in addition to a fiber-coupled multiband filter spectrograph. The two hyperspectral spectrographs provide continuous coverage from 340nm to 885nm in the UV to NIR range. These spectrographs use programmable CCD detectors that aggregate multiple CCD pixels that can effectively provide various spectral resolutions. The fiber-coupled multiband filter spectrograph provides seven discrete spectral bands from 940nm to 2260nm. OCI completed system level testing of the Engineering Test Unit (ETU) in June 2021 at the Goddard Space Flight Center (GSFC). The ETU contains one of the slit grating spectrographs (600nm to 885nm) and the fiber-coupled spectrograph. The ETU was tested in thermal vacuum (TVAC) in February 2020 and January 2021 to assess characterization and performance compliance to design requirements. This paper presents an overview of the spectral performance of the OCI ETU for relative spectral response (RSR), integrated Out-of-Band response (IOOB), system gain, band centers, and bandwidths.
PACE↗
Optimal application of Morrison's iterative noise removal for deconvolution. Appendices
Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.
Ioup, George E.↗
Multi-star processing and gyro filtering for the video inertial pointing system
The video inertial pointing (VIP) system is being developed to satisfy the acquisition and pointing requirements of astronomical telescopes. The VIP system uses a single video sensor to provide star position information that can be used to generate three-axis pointing error signals (multi-star processing) and for input to a cathode ray tube (CRT) display of the star field. The pointing error signals are used to update the telescope's gyro stabilization system (gyro filtering). The CRT display facilitates target acquisition and positioning of the telescope by a remote operator. Linearized small angle equations are used for the multistar processing and a consideration of error performance and singularities lead to star pair location restrictions and equation selection criteria. A discrete steady-state Kalman filter which uses the integration of the gyros is developed and analyzed. The filter includes unit time delays representing asynchronous operations of the VIP microprocessor and video sensor. A digital simulation of a typical gyro stabilized gimbal is developed and used to validate the approach to the gyro filtering.
Murphy, J. P.↗
Comparison of several techniques to obtain multiple-look SAR imagery
In order to improve image interpretability when SAR imagery is contaminated by coherent speckle noise, multiple look images are often generated. The performance levels of techniques for the generation of such multiple look imagery are presently assessed, with attention to the detailed impulse responses and signal-to-speckle noise ratios obtainable. The speckle-reduction technique considered are those of the discrete mixed integrator and the image domain filter. It is found that, by using several types of image domain filters, the signal-to-speckle noise ratio can be improved over the conventional discrete mixed integrator method's results while maintaining the equivalent rectangular resolution constant.
Li, F.-K.↗
Estimation Filter for Alignment of the Spitzer Space Telescope
A document presents a summary of an onboard estimation algorithm now being used to calibrate the alignment of the Spitzer Space Telescope (formerly known as the Space Infrared Telescope Facility). The algorithm, denoted the S2P calibration filter, recursively generates estimates of the alignment angles between a telescope reference frame and a star-tracker reference frame. At several discrete times during the day, the filter accepts, as input, attitude estimates from the star tracker and observations taken by the Pointing Control Reference Sensor (a sensor in the field of view of the telescope). The output of the filter is a calibrated quaternion that represents the best current mean-square estimate of the alignment angles between the telescope and the star tracker. The S2P calibration filter incorporates a Kalman filter that tracks six states - two for each of three orthogonal coordinate axes. Although, in principle, one state per axis is sufficient, the use of two states per axis makes it possible to model both short- and long-term behaviors. Specifically, the filter properly models transient learning, characteristic times and bounds of thermomechanical drift, and long-term steady-state statistics, whether calibration measurements are taken frequently or infrequently. These properties ensure that the S2P filter performance is optimal over a broad range of flight conditions, and can be confidently run autonomously over several years of in-flight operation without human intervention.
Bayard, David↗
The Foggy EUV Corona and Coronal Heating by MHD Waves from Explosive Reconnection Events
In 0.5 arcsec/pixel TRACE coronal EUV images, the corona rooted in active regions that are at the limb and are not flaring is seen to consist of (1) a complex array of discrete loops and plumes embedded in (2) a diffuse ambient component that shows no fine structure and gradually fades with height. For each of two not-flaring active regions, found that the diffuse component is (1) approximately isothermal and hydrostatic and (2) emits well over half of the total EUV luminosity of the active-region corona. Here, from a TRACE Fe XII coronal image of another not-flaring active region, the large sunspot active region AR 10652 when it was at the west limb on 30 July 2004, we separate the diffuse component from the discrete loop component by spatial filtering, and find that the diffuse component has about 60% of the total luminosity. If under much higher spatial resolution than that of TRACE (e. g., the 0.1 arcsec/pixel resolution of the Hi-C sounding-rocket experiment proposed by J. W. Cirtain et al), most of the diffuse component remains diffuse rather being resolved into very narrow loops and plumes, this will raise the possibility that the EUV corona in active regions consists of two basically different but comparably luminous components: one being the set of discrete bright loops and plumes and the other being a truly diffuse component filling the space between the discrete loops and plumes. This dichotomy would imply that there are two different but comparably powerful coronal heating mechanisms operating in active regions, one for the distinct loops and plumes and another for the diffuse component. We present a scenario in which (1) each discrete bright loop or plume is a flux tube that was recently reconnected in a burst of reconnection, and (2) the diffuse component is heated by MHD waves that are generated by these reconnection events and by other fine-scale explosive reconnection events, most of which occur in and below the base of the corona where they are seen as UV explosive events, EUV blinkers, and type II spicules. These MHD waves propagate across field lines and dissipate, heating the plasma in the field between the bright loops and plumes.
Moore, Ron L.↗
EUTERPE: A global gyrokinetic code for stellarator geometry
The current state of the EUTERPE code is described with emphasis on the implemented models and their numerical implementation. The code solves the multi-species electromagnetic gyrokinetic equations in the full volume of a three-dimensional domain. Noise reduction of the particle-in-cell method is achieved by using a δf-method and Fourier filters. The field equations are discretized with B-splines and the resulting system of equations is solved iteratively. For linear simulations a phase-factor transformation is applied in order to strongly reduce the necessary grid resolution. Apart from the full gyrokinetic model, other numerically less expensive hybrid models are also implemented. They are mainly tailored for comparison with fluid theory and for studying the interaction of the bulk plasma with fast particles. The code is parallelized for CPUs by particle and domain decomposition. Good scalability up to several thousand nodes is demonstrated.
97 MATHEMATICS AND COMPUTING↗
A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids
Discrete ordinate (S N ) and filtered spherical harmonics (FP N ) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. Here, the resulting method is then compared with both S N and FP N schemes using four test problems and is found to perform well when one of the other methods fail.
79 ASTRONOMY AND ASTROPHYSICS↗
Characterization and mathematical representation of line scanning image systems
Characterization and mathematical representation of line scanning image systems and evaluating system performance with discrete output signal and post filtering
Lee, S. Y.↗
Digital communications study
Research is reported dealing with problems of digital data transmission and computer communications networks. The results of four individual studies are presented which include: (1) signal processing with finite state machines, (2) signal parameter estimation from discrete-time observations, (3) digital filtering for radar signal processing applications, and (4) multiple server queues where all servers are not identical.
Boorstyn, R. R.↗
Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain
A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.
Klein, V.↗