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NASA NTRS1994

The Rb 780-nanometer Faraday anomalous dispersion optical filter: Theory and experiment

The Faraday anomalous dispersion optical filter may provide ultra-high background noise rejection for free-space laser communications systems. The theoretical model for the filter is reported. The experimental measurements and their comparison with theoretical results are discussed. The results show that the filter can provide a 56-dB solar background noise rejection with about a 2-GHz transmission bandwidth and no image degradation. To further increase the background noise rejection, a composite Zeeman and Faraday anomalous dispersion optical filter is designed and experimentally demonstrated.

Yin, B.↗

NASA NTRS1994

Filter parameter tuning analysis for operational orbit determination support

The use of an extended Kalman filter (EKF) for operational orbit determination support is being considered by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). To support that investigation, analysis was performed to determine how an EKF can be tuned for operational support of a set of earth-orbiting spacecraft. The objectives of this analysis were to design and test a general purpose scheme for filter tuning, evaluate the solution accuracies, and develop practical methods to test the consistency of the EKF solutions in an operational environment. The filter was found to be easily tuned to produce estimates that were consistent, agreed with results from batch estimation, and compared well among the common parameters estimated for several spacecraft. The analysis indicates that there is not a sharply defined 'best' tunable parameter set, especially when considering only the position estimates over the data arc. The comparison of the EKF estimates for the user spacecraft showed that the filter is capable of high-accuracy results and can easily meet the current accuracy requirements for the spacecraft included in the investigation. The conclusion is that the EKF is a viable option for FDD operational support.

Dunham, J.↗

NASA NTRS1994

The Stark anomalous dispersion optical filter: The theory

The Stark anomalous dispersion optical filter is a wide-frequency-tunable ultra-narrow-bandwidth optical filter. The first theoretical investigation of this filter matched to the wavelength of a doubled Nd:YAG laser is reported. The calculations show that such a filter may provide above 80 percent transmission, and a noise equivalent bandwidth of 3 GHz.

Yin, B.↗

NASA NTRS1995

A description of the solar wind-magnetosphere coupling based on nonlinear filters

A nonlinear filtering method is introduced for the study of the solar wind -- magnetosphere coupling and related to earlier linear techniques. The filters are derived from the magnetospheric state, a representation of the magnetospheric conditions in terms of a few global variables, here the auroral electrojet indices. The filters also couple to the input, a representation of the solar wind variables, here the rectified electric field. Filter-based iterative prediction of the indices has been obtained for up to 20 hours. The prediction is stable with respect to perturbations in the initial magnetospheric state; these decrease exponentially at the rate of 30/min. The performance of the method is examined for a wide range of parameters and is superior to that of other linear and nonlinear techniques. In the magnetospheric state representation the coupling is modeled as a small number of nonlinear equations under a time-dependent input.

Vassiliadis, D.↗

NASA NTRS1995

Determination of plasma temperatures and luminosities using multiple extreme-ultraviolet and X-ray filters

We carefully examine the techniques used to infer temperatures of stellar coronal plasmas from the count rates of several broadband instruments in the X-ray and extreme-ultraviolet spectral ranges. In particular, we determine to what extent temperatures can be constrained and the corresponding uncertainties in the luminosities and emission measures lowered by fitting simultaneously count rates from the Einstein imaging proportional counter (IPC), the ROSAT Position Sensitive Proportional Counter (PSPC), the ROSAT Wide Field Camera (WFC) (both filters), and the EXOSAT Low Energy Telescope (LET) with the 3-Lex filter. We use published plasma emissivities with solar photospheric abundances. Since it has been found that single-temperature plasmas do not fit IPC data well, we assume a two-temperature plasma model. We find that, even with count rates from all of the above filters and overly optimistic error estimates, it is still not possible to determine a unique two-temperature solution. However, since the use of count rates from many filters can reduce substantially the number of possible solutions, temperature solutions determined by other means can be tested. We carry out such an analysis on a set of 18 nearby late-type stars to determine possible two-temperature solutions using multifilter photometry, and we compare these results with the temperature solutions derived by Schmitt et al. (1990) using IPC spectral data. In general, the two-temperature fits derived from the IPC spectral data are inconsistent with our results, with our data implying that, for many stars, the two temperatures derived by the IPC may be too low by about a factor of 2. The EXOSAT transmission grating Spectrometer (TGS) spectra of capella and sigma(exp 2) CrB support this conclusion. For Procyon and 70 Oph, though, the presence of a temperature component cooler than a million degress (not detected by the IPC) is deduced. While our analysis suggests the existence of more than one temperature in the coronae of late-type stars, in many instances our WFC data appear to be inconsistent with the presence of significant emission measure over a broad temperature distribution. This, together with the success of two-temperature plasmas in fitting IPC and TGS data, implies that for many stars, the coronal emission measure distribution may in fact be dominated by two distinct temperature regimes.

Wood, Brian E.↗

NASA NTRS1996

Absorption Filter Based Optical Diagnostics in High Speed Flows

Two major regimes where laser light scattered by molecules or particles in a flow contains significant information about the flow are Mie scattering and Rayleigh scattering. Mie scattering is used to obtain only velocity information, while Rayleigh scattering can be used to measure both the velocity and the thermodynamic properties of the flow. Now, recently introduced (1990, 1991) absorption filter based diagnostic techniques have started a new era in flow visualization, simultaneous velocity and thermodynamic measurements, and planar velocity measurements. Using a filtered planar velocimetry (FPV) technique, we have modified the optically thick iodine filter profile of Miles, et al., and used it in the pressure-broaden regime which accommodates measurements in a wide range of velocity applications. Measuring velocity and thermodynamic properties simultaneously, using absorption filtered based Rayleigh scattering, involves not only the measurement of the Doppler shift, but also the spectral profile of the Rayleigh scattering signal. Using multiple observation angles, simultaneous measurement of one component velocity and thermodynamic properties in a supersonic jet were measured. Presently, the technique is being extended for simultaneous measurements of all three components of velocity and thermodynamic properties.

Samimy, Mo↗

NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗

NASA NTRS1996

YBCO High-Temperature Superconducting Filters on M-Plane Sapphire Substrates

Since the discovery of High Temperature Superconductors (HTS) in 1986, microwave circuits have been demonstrated using HTS films on various substrates. These HTS-based circuits have proven to operate with less power loss than their metallic film counterparts at 77 K. This translates into smaller and lighter microwave circuits for space communication systems such as multiplexer filter banks. High quality HTS films have conventionally been deposited on lanthanum aluminate (LaAlO3) substrates. However, LaAlO3 has a relative dielectric constant (epsilon(sub r)) of 24. With a epsilon(sub r) approx. 9.4-11.6, sapphire (Al2O3) would be a preferable substrate for the fabrication of HTS-based components since the lower dielectric constant would permit wider microstrip lines to be used in filter design, since the lower dielectric constant would permit wider microstrip lines to be used for a given characteristic impedance (Z(sub 0)), thus lowering the insertion losses and increasing the power handling capabilities of the devices. We report on the fabrication and characterization of YBa2Cu3O(7-delta) (YBCO) on M-plane sapphire bandpass filters at 4.0 GHz. For a YBCO 'hairpin' filter, a minimum insertion loss of 0.5 dB was measured at 77 K as compared with 1.4 dB for its gold counterpart. In an 'edge-coupled' configuration, the insertion loss went down from 0.9 dB for the gold film to 0.8 dB for the YBCO film at the same temperature.

Sabataitis, J. C.↗

NASA NTRS1997

Improvement in Suppression of Pulsed Nd:YAG Laser Light With Iodine Absorption Cells for Filtered Rayleigh Scattering Measurements

Filtered Rayleigh scattering using iodine absorption cells is an effective technique for obtaining density, temperature, and velocity measurements in high speed confined flows. By tuning a single frequency laser to a strong iodine absorption line, stray scattered laser light can be greatly suppressed. For example, the minimum transmission predicted by an iodine absorption model calculation is less than 10(exp -5) at the 18788.44/cm line using a 200 mm absorption cell containing iodine vapor at 0.46 T. Measurements obtained by other researches using a CW Nd:YAG laser agree with the model calculations. However, measurements made by us and by others using Q-switched, injection-seeded, frequency doubled Nd:YAG lasers only show minimum transmission of about 3 x 10(exp -3). This greatly reduces the applicability of the filtered Rayleigh scattering technique using these lasers in experiments having large amounts of stray scattered laser light. The purposes of the present study are to characterize the spectrum of the excess light transmitted by the iodine cell and to make changes to the laser to reduce the transmitted laser light. Transmission data as a function of laser frequency for the iodine absorption line at 18788.44/cm are presented. A planar mirror Fabry-Perot interferometer was used to characterize the frequency spectrum of the light passed through the cell. Measurements taken with the laser tuned to the center of the iodine absorption line show the light transmitted through the iodine cell to have a component with a bandwidth of about 40 GHz. This is probably caused by other modes in the laser that exist in spite of the single frequency injection beam. A second broadband component was also observed, possibly caused by the laser flash lamps or by fluorescence. An intracavity etalon was installed in the laser oscillator cavity to suppress the 40 GHz component. Measurements taken with the etalon tuned to the injection frequency showed a reduction in the transmitted laser light. This improvement allows the iodine cell to block significantly more of the stray laser light in filtered Rayleigh scattering experiments. Examples are given of filtered Rayleigh scattering measurements showing the effect of the etalon on measurements taken in a Mach 3 flow in the NASA Lewis 4 inch by 10 inch supersonic wind tunnel.

Seasholtz, Richard G.↗

NASA NTRS1998

Initial flight results of the TRMM Kalman filter

The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls attitude based on the Earth Sensor Assembly (ESA) output. After a potential single point failure in the ESA was identified, the contingency attitude determination method chosen to backup the ESA-based system was a sixth-order extended Kalman filter that uses magnetometer and digital sun sensor measurements. A brief description of the TRMM Kalman filter will be given, including some implementation issues and algorithm heritage. Operational aspects of the Kalman filter and some failure detection and correction will be described. The Kalman filter was tested in a sun pointing attitude and in a nadir pointing attitude during the in-orbit checkout period, and results from those tests will be presented. This paper will describe some lessons learned from the experience of the TRMM team.

Andrews, Stephen F.↗

NASA NTRS1998

Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation

A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.

Chang, Lang-Ping↗

NASA NTRS1996

Application of Consider Covariance to the Extended Kalman Filter

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Lundberg, John B.↗

NASA NTRS1998

Initial Flight Results of the TRMM Kalman Filter

Andrews, Stephen F.↗

NASA NTRS1998

The Dependence of Signal-To-Noise Ratio (S/N) Between Star Brightness and Background on the Filter Used in Images Taken by the Vulcan Photometric Planet Search Camera

The Vulcan Photometric Planet Search is the ground-based counterpart of Kepler Mission Proposal. The Kepler Proposal calls for the launch of telescope to look intently at a small patch of sky for four year. The mission is designed to look for extra-solar planets that transit sun-like stars. The Kepler Mission should be able to detect Earth-size planets. This goal requires an instrument and software capable of detecting photometric changes of several parts per hundred thousand in the flux of a star. The goal also requires the continuous monitoring of about a hundred thousand stars. The Kepler Mission is a NASA Discovery Class proposal similar in cost to the Lunar Prospector. The Vulcan Search is also a NASA project but based at Lick Observatory. A small wide-field telescope monitors various star fields successively during the year. Dozens of images, each containing tens of thousands of stars, are taken any night that weather permits. The images are then monitored for photometric changes of the order of one part in a thousand. These changes would reveal the transit of an inner-orbit Jupiter-size planet similar to those discovered recently in spectroscopic searches. In order to achieve a one part in one thousand photometric precision even the choice of a filter used in taking an exposure can be critical. The ultimate purpose of an filter is to increase the signal-to-noise ratio (S/N) of one's observation. Ideally, filters reduce the sky glow cause by street lights and, thereby, make the star images more distinct. The higher the S/N, the higher is the chance to observe a transit signal that indicates the presence of a new planet. It is, therefore, important to select the filter that maximizes the S/N.

Mena-Werth, Jose↗

NASA NTRS1999

An Adaptive Kalman Filter Using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.↗

NASA NTRS1999

An Adaptive Kalman Filter using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.↗

NASA NTRS1999

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Keppenne, Christian L.↗

NASA NTRS2000

Time Filtering in Large Eddy Simulations

An explicit time filter is applied to the Navier-Stokes equation prior to a space filter. The time filter is supposed to be smooth, and an exact expansion depending on the time derivatives of the velocity is derived for the associated stress tensor. On the contrary, the effect of the space filter is treated as usual and an eddy viscosity model is introduced in the LES equation. The total stress is thus represented using a new class of mixed models combining time and space derivatives of the LES field.

Carati, Daniele↗