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NASA NTRS2016

Exploiting Measurement Uncertainty Estimation in Evaluation of GOES-R ABI Image Navigation Accuracy Using Image Registration Techniques

In evaluating GOES-R Advanced Baseline Imager (ABI) image navigation quality, upsampled sub-images of ABI images are translated against downsampled Landsat 8 images of localized, high contrast earth scenes to determine the translations in the East-West and North-South directions that provide maximum correlation. The native Landsat resolution is much finer than that of ABI, and Landsat navigation accuracy is much better than ABI required navigation accuracy and expected performance. Therefore, Landsat images are considered to provide ground truth for comparison with ABI images, and the translations of ABI sub-images that produce maximum correlation with Landsat localized images are interpreted as ABI navigation errors. The measured local navigation errors from registration of numerous sub-images with the Landsat images are averaged to provide a statistically reliable measurement of the overall navigation error of the ABI image. The dispersion of the local navigation errors is also of great interest, since ABI navigation requirements are specified as bounds on the 99.73rd percentile of the magnitudes of per pixel navigation errors. However, the measurement uncertainty inherent in the use of image registration techniques tends to broaden the dispersion in measured local navigation errors, masking the true navigation performance of the ABI system. We have devised a novel and simple method for estimating the magnitude of the measurement uncertainty in registration error for any pair of images of the same earth scene. We use these measurement uncertainty estimates to filter out the higher quality measurements of local navigation error for inclusion in statistics. In so doing, we substantially reduce the dispersion in measured local navigation errors, thereby better approximating the true navigation performance of the ABI system.

navigation performance↗

NASA NTRS1974

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual

Development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). The program NOMNAL targets a transfer trajectory from Earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.

Byrnes, D. V.↗

NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows: Minimization of Delta * B Numerical Error - II

The generalization of a class of low-dissipative high order filter finite difference schemes for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been developed. The new scheme consists of a divergence free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta * B) numerical error in the sense that no standard divergence cleaning is required. Performance evaluation of these variants, and the key role that the proper treatment of their corresponding numerical boundary conditions can play will be illustrated. Many levels of grid refinement and detailed comparison with several commonly used compressible MHD shock-capturing schemes will be sought. For certain MHD 2-D test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Sjoegreen, Bjoern↗

NASA NTRS1992

A monitor for the laboratory evaluation of control integrity in digital control systems operating in harsh electromagnetic environments

This paper presents a strategy for dynamically monitoring digital controllers in the laboratory for susceptibility to electromagnetic disturbances that compromise control integrity. The integrity of digital control systems operating in harsh electromagnetic environments can be compromised by upsets caused by induced transient electrical signals. Digital system upset is a functional error mode that involves no component damage, can occur simultaneously in all channels of a redundant control computer, and is software dependent. The motivation for this work is the need to develop tools and techniques that can be used in the laboratory to validate and/or certify critical aircraft controllers operating in electromagnetically adverse environments that result from lightning, high-intensity radiated fields (HIRF), and nuclear electromagnetic pulses (NEMP). The detection strategy presented in this paper provides dynamic monitoring of a given control computer for degraded functional integrity resulting from redundancy management errors, control calculation errors, and control correctness/effectiveness errors. In particular, this paper discusses the use of Kalman filtering, data fusion, and statistical decision theory in monitoring a given digital controller for control calculation errors.

Belcastro, Celeste M.↗

NASA NTRS2011

Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation

An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.

Simon, Donald L.↗

NASA NTRS2009

Advances in Land Data Assimilation at the NASA Goddard Space Flight Center

Research in land surface data assimilation has grown rapidly over the last decade. In this presentation we provide a brief overview of key research contributions by the NASA Goddard Space Flight Center (GSFC). The GSFC contributions to land assimilation primarily include the continued development and application of the Land Information System (US) and the ensemble Kalman filter (EnKF). In particular, we have developed a method to generate perturbation fields that are correlated in space, time, and across variables and that permit the flexible modeling of errors in land surface models and observations, along with an adaptive filtering approach that estimates observation and model error input parameters. A percentile-based scaling method that addresses soil moisture biases in model and observational estimates opened the path to the successful application of land data assimilation to satellite retrievals of surface soil moisture. Assimilation of AMSR-E surface soil moisture retrievals into the NASA Catchment model provided superior surface and root zone assimilation products (when validated against in situ measurements and compared to the model estimates or satellite observations alone). The multi-model capabilities of US were used to investigate the role of subsurface physics in the assimilation of surface soil moisture observations. Results indicate that the potential of surface soil moisture assimilation to improve root zone information is higher when the surface to root zone coupling is stronger. Building on this experience, GSFC leads the development of the Level 4 Surface and Root-Zone Soil Moisture (L4_SM) product for the planned NASA Soil-Moisture-Active-Passive (SMAP) mission. A key milestone was the design and execution of an Observing System Simulation Experiment that quantified the contribution of soil moisture retrievals to land data assimilation products as a function of retrieval and land model skill and yielded an estimate of the error budget for the SMAP L4_SM product. Terrestrial water storage observations from GRACE satellite system were also successfully assimilated into the NASA Catchment model and provided improved estimates of groundwater variability when compared to the model estimates alone. Moreover, satellite-based land surface temperature (LST) observations from the ISCCP archive were assimilated using a bias estimation module that was specifically designed for LST assimilation. As with soil moisture, LST assimilation provides modest yet statistically significant improvements when compared to the model or satellite observations alone. To achieve the improvement, however, the LST assimilation algorithm must be adapted to the specific formulation of LST in the land model. An improved method for the assimilation of snow cover observations was also developed. Finally, the coupling of LIS to the mesoscale Weather Research and Forecasting (WRF) model enabled investigations into how the sensitivity of land-atmosphere interactions to the specific choice of planetary boundary layer scheme and land surface model varies across surface moisture regimes, and how it can be quantified and evaluated against observations. The on-going development and integration of land assimilation modules into the Land Information System will enable the use of GSFC software with a variety of land models and make it accessible to the research community.

Reichle, Rolf↗

NASA NTRS1983

Design, implementation and flight testing of PIF autopilots for general aviation aircraft

The designs of Proportional-Integrated-Filter (PIF) auto-pilots for a General Aviation (NAVION) aircraft are presented. The PIF autopilot uses the sampled-data regulator and command generator tracking to determine roll select, pitch select, heading select, altitude select and localizer/glideslope capture and hold autopilot modes. The PIF control law uses typical General Aviation sensors for state feedback, command error integration for command tracking, digital complementary filtering and analog prefiltering for sensor noise suppression, a control filter for computation delay accommodation and the incremental form to eliminate trim values in implementation. Theoretical developments described in detail, were needed to combine the sampled-data regulator with command generator tracking for use as a digital flight control system. The digital PIF autopilots are evaluated using closed-loop eigenvalues and linear simulations. The implementation of the PIF autopilots in a digital flight computer using a high order language (FORTRAN) is briefly described. The successful flight test results for each PIF autopilot mode is presented.

Broussard, J. R.↗

NASA NTRS2018

Evaluation of Inflow Turbulence Methods in Large-Eddy Simulations of a Supersonic Boundary Layer

In the context of Large- Eddy Simulations (LES), Boundary-layer inflow turbulence is simulated using both the Synthetic Eddy Model (SEM) and Digital Filtering (DF). The effects of the projection error are investigated. The effect of the prescribed length scales on the adjustment region was found to be negligible for length scales less than one-tenth of the boundary-layer thickness. While it was conjectured that one method of the two might be more robust than the other, our results show that both the Digital Filtering Method and the Synthetic Eddy Method accurately replicate the boundary layer while successfully accounting for inflow turbulence.

Synthetic Eddy↗

NASA NTRS1987

Simplified solution for a class of fading memory filters

A fading memory filter is a least squares estimator (LSE) that applies an exponentially decaying weight to past measurements. When compared with a standard Kalman filter, its key advantages are asymptotic stability and reduced sensitivity to modeling errors. This paper derives a simple solution for a class of fading memory filters, resulting in a reduction in computational complexity. Steady state filter solutions are obtained for second- and third-order filters used in a global positioning system (GPS) receiver for high dynamic vehicles.

Statman, Joseph I.↗

NASA NTRS1988

Relative error covariance analysis techniques and application

A technique for computing the error covariance of the difference between two estimators derived from different (possibly overlapping) data arcs is presented. The relative error covariance is useful for predicting the achievable consistency between Kalman-Bucy filtered estimates generated from two (not necessarily disjoint) data sets. The relative error covariance analysis technique is then applied to a Venus Orbiter simulation.

Wolff, Peter, J.↗

NASA NTRS1998

Pulse Shaped 8-PSK Bandwidth Efficiency and Spectral Spike Elimination

The most bandwidth-efficient communication methods are imperative to cope with the congested frequency bands. Pulse shaping methods have excellent effects on narrowing bandwidth and increasing band utilization. The position of the baseband filters for the pulse shaping is crucial. Post-modulation pulse shaping (a low pass filter is located after the modulator) can change signals from constant envelope to non-constant envelope, and non-constant envelope signals through non-linear device (a SSPA or TWT) can further spread the power spectra. Pre-modulation pulse shaping (a filter is located before the modulator) will have constant envelope. These two pulse shaping methods have different effects on narrowing the bandwidth and producing bit errors. This report studied the effect of various pre-modulation pulse shaping filters with respect to bandwidth, spectral spikes and bit error rate. A pre-modulation pulse shaped 8-ary Phase Shift Keying (8PSK) modulation was used throughout the simulations. In addition to traditional pulse shaping filters, such as Bessel, Butterworth and Square Root Raised Cosine (SRRC), other kinds of filters or pulse waveforms were also studied in the pre-modulation pulse shaping method. Simulations were conducted by using the Signal Processing Worksystem (SPW) software package on HP workstations which simulated the power spectral density of pulse shaped 8-PSK signals, end to end system performance and bit error rates (BERS) as a function of Eb/No using pulse shaping in an AWGN channel. These results are compared with the post-modulation pulse shaped 8-PSK results. The simulations indicate traditional pulse shaping filters used in pre-modulation pulse shaping may produce narrower bandwidth, but with worse BER than those in post-modulation pulse shaping. Theory and simulations show pre- modulation pulse shaping could also produce discrete line power spectra (spikes) at regular frequency intervals. These spikes may cause interference with adjacent channel and reduce power efficiency. Some particular pulses (filters), such as trapezoid and pulses with different transits (such as weighted raised cosine transit) were found to reduce bandwidth and not generate spectral spikes. Although a solid state power amplifier (SSPA) was simulated in the non-linear (saturation) region, output power spectra did not spread due to the constant envelope 8-PSK signals.

Tao, Jian-Ping↗

NASA NTRS2006

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↗

NASA NTRS1983

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Schlesinger, R. E.↗

NASA NTRS1995

Wind gust models derived from field data

Wind data measured during a field experiment were used to verify the analytical model of wind gusts. Good coincidence was observed; the only discrepancy occurred for the azimuth error in the front and back winds, where the simulated errors were smaller than the measured ones. This happened because of the assumption of the spatial coherence of the wind gust model, which generated a symmetric antenna load and, in consequence, a low azimuth servo error. This result indicates a need for upgrading the wind gust model to a spatially incoherent one that will reflect the real gusts in a more accurate manner. In order to design a controller with wind disturbance rejection properties, the wind disturbance should be known at the input to the antenna rate loop model. The second task, therefore, consists of developing a digital filter that simulates the wind gusts at the antenna rate input. This filter matches the spectrum of the measured servo errors. In this scenario, the wind gusts are generated by introducing white noise to the filter input.

Gawronski, W.↗

NASA NTRS2004

Semimajor Axis Estimation Strategies

This paper extends previous analysis on the impact of sensing noise for the navigation and control aspects of formation flying spacecraft. We analyze the use of Carrier-phase Differential GPS (CDGPS) in relative navigation filters, with a particular focus on the filter correlation coefficient. This work was motivated by previous publications which suggested that a "good" navigation filter would have a strong correlation (i.e., coefficient near -1) to reduce the semimajor axis (SMA) error, and therefore, the overall fuel use. However, practical experience with CDGPS-based filters has shown this strong correlation seldom occurs (typical correlations approx. -0.1), even when the estimation accuracies are very good. We derive an analytic estimate of the filter correlation coefficient and demonstrate that, for the process and sensor noises levels expected with CDGPS, the expected value will be very low. It is also demonstrated that this correlation can be improved by increasing the time step of the discrete Kalman filter, but since the balance condition is not satisfied, the SMA error also increases. These observations are verified with several linear simulations. The combination of these simulations and analysis provide new insights on the crucial role of the process noise in determining the semimajor axis knowledge.

How, Jonathan P.↗

NASA NTRS1995

Assimilation of TOPEX Sea Level Measurements with a Reduced-Gravity, Shallow Water Model of the Tropical Pacific Ocean

Sea surface height variability measured by TOPEX is analyzed in the tropical Pacific Ocean by way of assimilation into a wind-driven, reduced-gravity, shallow water model using an approximate Kalman filter and smoother. The analysis results in an optimal fit of the dynamic model to the observations, providing it dynamically consistent interpolation of sea level and estimation of the circulation. Nearly 80% of the expected signal variance is accounted for by the model within 20 deg of the equator, and estimation uncertainty is substantially reduced by the voluminous observation. Notable features resolved by the analysis include seasonal changes associated with the North Equatorial Countercurrent and equatorial Kelvin and Rossby waves. Significant discrepancies are also found between the estimate and TOPEX measurements, especially near the eastern boundary. Improvements in the estimate made by the assimilation are validated by comparisons with independent tide gauge and current meter observations. The employed filter and smoother are based on approximately computed estimation error covariance matrices, utilizing a spatial transformation and an symptotic approximation. The analysis demonstrates the practical utility of a quasi-optimal filter and smoother.

Fukumori, Ichiro↗

NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗

NASA NTRS1998

Application of Least Mean Square Algorithms to Spacecraft Vibration Compensation

This paper describes the application of the Least Mean Square (LMS) algorithm in tandem with the Filtered-X Least Mean Square algorithm for controlling a science instrument's line-of-sight pointing. Pointing error is caused by a periodic disturbance and spacecraft vibration. A least mean square algorithm is used on-orbit to produce the transfer function between the instrument's servo-mechanism and error sensor. The result is a set of adaptive transversal filter weights tuned to the transfer function. The Filtered-X LMS algorithm, which is an extension of the LMS, tunes a set of transversal filter weights to the transfer function between the disturbance source and the servo-mechanism's actuation signal. The servo-mechanism's resulting actuation counters the disturbance response and thus maintains accurate science instrumental pointing. A simulation model of the Upper Atmosphere Research Satellite is used to demonstrate the algorithms.

Woodard , Stanley E.↗