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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

CORRELATED ERRORS IN EARTH POINTING MISSIONS

Two different Earth-pointing missions dealing with attitude control and dynamics changes illustrate concerns with correlated error sources and coupled effects that can occur. On the OrbView-2 (OV-2) spacecraft, the assumption of a nearly-inertially-fixed momentum axis was called into question when a residual dipole bias apparently changed magnitude. The possibility that alignment adjustments and/or sensor calibration errors may compensate for actual motions of the spacecraft is discussed, and uncertainties in the dynamics are considered. Particular consideration is given to basic orbit frequency and twice orbit frequency effects and their high correlation over the short science observation data span. On the Tropical Rainfall Measuring Mission (TRMM) spacecraft, the switch to a contingency Kalman filter control mode created changes in the pointing error patterns. Results from independent checks on the TRMM attitude using science instrument data are reported, and bias shifts and error correlations are discussed. Various orbit frequency effects are common with the flight geometry for Earth pointing instruments. In both dual-spin momentum stabilized spacecraft (like OV-2) and three axis stabilized spacecraft with gyros (like TRMM under Kalman filter control), changes in the initial attitude state propagate into orbit frequency variations in attitude and some sensor measurements. At the same time, orbit frequency measurement effects can arise from dynamics assumptions, environment variations, attitude sensor calibrations, or ephemeris errors. Also, constant environment torques for dual spin spacecraft have similar effects to gyro biases on three axis stabilized spacecraft, effectively shifting the one-revolution-per-orbit (1-RPO) body rotation axis. Highly correlated effects can create a risk for estimation errors particularly when a mission switches an operating mode or changes its normal flight environment. Some error effects will not be obvious from attitude sensor measurement residuals, so some independent checks using imaging sensors are essential and derived science instrument attitude measurements can prove quite valuable in assessing the attitude accuracy.

Steve Bilanow↗
NASA NTRS1979

A navigation algorithm for single channel low-cost GPS receiver

A sequential navigation algorithm for a navigator using the Global Positioning System satellites is developed and tested for both noise-free and noisy system models. Data from a six-hour flight from California to Hawaii (C5A aircraft) simulates a true user to test the accuracy of the user's position for a sequential navigation system. For error reduction in the user's position in the sequential navigation system (considering 100 m as a maximum average error tolerated by any low-cost GPS user) an analysis of error sources in the sequential system has led to the use of range-ephemeris rate to translate ranges to a common point in time and to use velocity aiding at the time of a satellite disappearance. To reduce the user's position and velocity errors in a noisy navigation system an 'alpha-beta' two-pole filter is implemented whose optimum alpha is obtained experimentally. A user's position error of 73 m at noise range error of 30.48 (1sigma) is achieved.

Parsiani, H.↗
NASA NTRSDate not supplied

Hybrid Flush and Synthetic Air Data Filter for Entry Vehicle Atmospheric State Estimation

A hybrid flush/synthetic air data sensing filter for entry vehicle atmosphere estimation is developed. The approach makes use of a Kalman-Schmidt and Rauch-Tung-Streibel smoother. The filter/smoother blends information from pressure sensors distributed on the heatshield with pseudo-measurements of the vehicle aerodynamic forces and moments computed from mass properties and inertial measurement unit data, and prior estimates of the atmosphere. The filter produces estimates of the atmospheric conditions along the entry trajectory, and systematic error estimates to reconcile differences between the pressure and aerodynamic data sources. The filter is applied to data acquired during the Mars 2020 entry, descent, and landing at Jezero crater on February 18th, 2021. The final paper will also include results from the Mars Science Laboratory entry, descent, and landing.

Chris D. Karlgaard↗
NASA NTRS1995

Experiments with explicit filtering for LES using a finite-difference method

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Lund, T. S.↗
NASA NTRS2011

Model-Based Wavefront Control for CCAT

The 25-m aperture CCAT submillimeter-wave telescope will have a primary mirror that is divided into 162 individual segments, each of which is provided with 3 positioning actuators. CCAT will be equipped with innovative Imaging Displacement Sensors (IDS) inexpensive optical edge sensors capable of accurately measuring all segment relative motions. These measurements are used in a Kalman-filter-based Optical State Estimator to estimate wavefront errors, permitting use of a minimum-wavefront controller without direct wavefront measurement. This controller corrects the optical impact of errors in 6 degrees of freedom per segment, including lateral translations of the segments, using only the 3 actuated degrees of freedom per segment. The global motions of the Primary and Secondary Mirrors are not measured by the edge sensors. These are controlled using a gravity-sag look-up table. Predicted performance is illustrated by simulated response to errors such as gravity sag.

edge sensor↗
NASA NTRS1986

Design of robust failure detection filters

An essential aspect of the design of control systems for large, flexible spacecraft is fault tolerance. Because it is anticipated that a large number of sensors and actuators will be required to realize good control over these assemblies, the detection and isolation of component failures cannot be based on direct comparisons among replicated components. Instead, the notion of 'analytic redundancy' must be employed for the FDI function. Unfortunately this makes the FDI function sensitive to modeling errors which are certain to exist in the large space structure problem due to model truncation and parameter uncertainty. This paper addresses the robustness to model error of one method of FDI residual generation - the failure detection filter. Initial designs were found to be extremely sensitive to modeling error. The sources of this sensitivity are analyzed and modifications to the design are suggested. The improved filter is shown to have much better visibility of the failure signatures relative to the background due to modeling error.

San Martin, A. M.↗
NASA NTRS1989

Extended Kalman filter for attitude estimation of the earth radiation budget satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗
NASA NTRS1990

Extended Kalman Filter for attitude estimation of the Earth Radiation Budget Satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗
NASA NTRS1982

Evaluation of LANDSAT-D Orbit Determination Using a Filter/Smoother (PREFER)

Simulated range and range rate data for five tracking stations were first generated using batch least squares orbit determination (GTDS). Then GTDS was used (in the differential correction mode) to produce a nominal trajectory which was input to PREFER. The GTDS differential correction (DC) run was made using models which differed from those used to produce the simulated data. These model differences were chosen to be fairly realistic approximations to the errors in the models actually used for operational orbit determination. Several different simulation runs were made with different types of model errors in order to determine the sensitivity to these errors. The nominal trajectory and the simulated measurement data were input to PREFER to produce a smoothed ephemeris file. Numerous runs of PREFER were made in which parameters describing the statistics of the model errors were varied. The likelihood function computed by the Kalman filter determined the ""best'' choice of input parameters. There was strong negative correlation between the likelihood function and the errors in the smoothed ephemeris.

Gibbs, B. P.↗
NASA NTRS2010

SEU/SET Tolerant Phase-Locked Loops

The phase-locked loop (PLL) is an old and widely used circuit for frequency and phase demodulation, carrier and clock recovery, and frequency synthesis [1]. Its implementations range from discrete components to fully integrated circuits and even to firmware or software. Often the PLL is a highly critical component of a system, as for example when it is used to derive the on-chip clock, but as of this writing no definitive single-event upset (SET)/single-event transient (SET) tolerant PLL circuit has been described. This chapter hopes to rectify that situation, at least in regard to PLLs that are used to generate clocks. Older literature on fault-tolerant PLLs deals with detection of a hard failure, which is recovered by replacement, repair, or manual restart of discrete component systems. Several patents exist along these lines (6349391, 6272647, and 7089442). A newer approach is to harden the parts of a PLL system, to one degree or another, such as by using a voltage-based charge pump or a triple modular redundant (TMR) voted voltage-controlled oscillator (VCO). A more comprehensive approach is to harden by triplication and voting (TMR) all the digital pieces (primarily the divider) of a frequency synthesis PLL, but this still leaves room for errors in the VCO and the loop filter. Instead of hardening or voting pieces of a system, such as a frequency synthesis system (i.e., clock multiplier), we will show how the entire system can be voted. There are two main ways of doing this, each with advantages and drawbacks. We will show how each has advantages in certain areas, depending on the lock acquisition and tracking characteristics of the PLL. Because of this dependency on PLL characteristics, we will briefly revisit the theory of PLLs. But first we will describe the characteristics of voters and their correct application, as some literature does not follow the voting procedure that guarantees elimination of errors. Additionally, we will find that voting clocks is a bit trickier than voting data where an infallible clock is assumed. It is our job here to produce (or recover) that assumed infallible clock!

Shuler, Robert L., Jr.↗
NASA NTRS1998

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗
NASA NTRS1976

Simulated performance of coded PCM/FM modem on Rician fading channel

This paper describes a simulation approach to characterizing the performance of a coded PCM/FM modem operating on the classical Rician fading channel. In particular, we consider the performance of short constraint length convolutional codes in conjunction with Viterbi maximum likelihood decoding. The receiver consists of a narrowband filter followed by an ideal limiter/discriminator. Primary interest is in the bit error probability performance parameterized by both the fading channel and receiver parameters. Particular attention is given to simulating the impulse noise appearing at the discriminator output. This is the 'click' noise caused by encirclements of the origin by the instantaneous signal-plus-noise phasor. Results include the effects of channel memory and narrowband receiver filtering effects on overall bit error probability.

Modestino, J. W.↗
NASA NTRS2005

Hardware in-the-Loop Demonstration of Real-Time Orbit Determination in High Earth Orbits

This paper presents results from a study conducted at Goddard Space Flight Center (GSFC) to assess the real-time orbit determination accuracy of GPS-based navigation in a number of different high Earth orbital regimes. Measurements collected from a GPS receiver (connected to a GPS radio frequency (RF) signal simulator) were processed in a navigation filter in real-time, and resulting errors in the estimated states were assessed. For the most challenging orbit simulated, a 12 hour Molniya orbit with an apogee of approximately 39,000 km, mean total position and velocity errors were approximately 7 meters and 3 mm/s respectively. The study also makes direct comparisons between the results from the above hardware in-the-loop tests and results obtained by processing GPS measurements generated from software simulations. Care was taken to use the same models and assumptions in the generation of both the real-time and software simulated measurements, in order that the real-time data could be used to help validate the assumptions and models used in the software simulations. The study makes use of the unique capabilities of the Formation Flying Test Bed at GSFC, which provides a capability to interface with different GPS receivers and to produce real-time, filtered orbit solutions even when less than four satellites are visible. The result is a powerful tool for assessing onboard navigation performance in a wide range of orbital regimes, and a test-bed for developing software and procedures for use in real spacecraft applications.

Moreau, Michael↗
NASA NTRS1999

The Impact of Anisotropic Error Correlation Modelling

Most data assimilation systems assume isotropic forecast error correlations, but results from two dimensional Kalman Filter experiments indicate that the correlations can be far from isotropic. In this paper we use a simple two-dimensional data assimilation system, which analyses trace chemical species such as ozone, to assess different approaches to modelling the error correlations. We compare assimilation results using isotropic correlations with results obtained using different approaches to modelling anisotropic correlations: first, using correlations based on the concentrations of the trace chemicals, and secondly using an advective correlation model. We show that these relatively cheap ways of modelling anisotropic correlations give objectively better results than using isotropic correlations. We discuss the possible extension of these approaches to a full 3-D meteorological data assimilation system.

Swinbank, R.↗
NASA NTRS2012

Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗
NASA NTRS1991

Phase ambiguity resolution for offset QPSK modulation systems

A demodulator for Offset Quaternary Phase Shift Keyed (OQPSK) signals modulated with two words resolves eight possible combinations of phase ambiguity which may produce data error by first processing received I(sub R) and Q(sub R) data in an integrated carrier loop/symbol synchronizer using a digital Costas loop with matched filters for correcting four of eight possible phase lock errors, and then the remaining four using a phase ambiguity resolver which detects the words to not only reverse the received I(sub R) and Q(sub R) data channels, but to also invert (complement) the I(sub R) and/or Q(sub R) data, or to at least complement the I(sub R) and Q(sub R) data for systems using nontransparent codes that do not have rotation direction ambiguity.

Nguyen, Tien M.↗
NASA NTRS1972

Nonlinear and adaptive estimation in reentry.

The problem of real-time estimation of a lifting reentry vehicle trajectory of the shuttle orbiter type is considered. Simulations feature large position and velocity uncertainties at radar acquisition and realistic model errors in lift, drag and other model parameters. Radar tracking and accelerometer data are simulated. Significant nonlinearities are found to exist on spacecraft acquisition. An iterated nonlinear filter is shown to perform optimally during the radar acquisition phase. An adaptive filter is shown to track time-varying model errors, such as errors in the lift and drag coefficients, down to the noise level. Such real-time model tracking (identification) is frequently required for guidance and control implementation.

Jazwinski, A. H.↗