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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Filtering Methods for Error Reduction in Spacecraft Attitude Estimation Using Quaternion Star Trackers

Precision attitude determination for recent and planned space missions typically includes quaternion star trackers (ST) and a three-axis inertial reference unit (IRU). Sensor selection is based on estimates of knowledge accuracy attainable from a Kalman filter (KF), which provides the optimal solution for the case of linear dynamics with measurement and process errors characterized by random Gaussian noise with white spectrum. Non-Gaussian systematic errors in quaternion STs are often quite large and have an unpredictable time-varying nature, particularly when used in non-inertial pointing applications. Two filtering methods are proposed to reduce the attitude estimation error resulting from ST systematic errors, 1) extended Kalman filter (EKF) augmented with Markov states, 2) Unscented Kalman filter (UKF) with a periodic measurement model. Realistic assessments of the attitude estimation performance gains are demonstrated with both simulation and flight telemetry data from the Lunar Reconnaissance Orbiter.

Calhoun, Philip C.↗
NASA NTRS2005

Attitude Estimation for Large Field-of-View Sensors

The QUEST measurement noise model for unit vector observations has been widely used in spacecraft attitude estimation for more than twenty years. It was derived under the approximation that the noise lies in the tangent plane of the respective unit vector and is axially symmetrically distributed about the vector. For large field-of-view sensors, however, this approximation may be poor, especially when the measurement falls near the edge of the field of view. In this paper a new measurement noise model is derived based on a realistic noise distribution in the focal-plane of a large field-of-view sensor, which shows significant differences from the QUEST model for unit vector observations far away from the sensor boresight. An extended Kalman filter for attitude estimation is then designed with the new measurement noise model. Simulation results show that with the new measurement model the extended Kalman filter achieves better estimation performance using large field-of-view sensor observations.

Cheng, Yang↗
NASA NTRS1976

Computer simulation results of attitude estimation of earth orbiting satellites

Computer simulation results of attitude estimation of Earth-orbiting satellites (including Space Telescope) subjected to environmental disturbances and noises are presented. Decomposed linear recursive filter and Kalman filter were used as estimation tools. Six programs were developed for this simulation, and all were written in the basic language and were run on HP 9830A and HP 9866A computers. Simulation results show that a decomposed linear recursive filter is accurate in estimation and fast in response time. Furthermore, for higher order systems, this filter has computational advantages (i.e., less integration errors and roundoff errors) over a Kalman filter.

Kou, S. R.↗
NASA NTRS1991

An extended Kalman filter for spinning spacecraft attitude estimation

An extended Kalman filter for real-time ground attitude estimation of a gyro-less spinning spacecraft was developed and tested. The filter state vector includes the angular momentum direction, phase angle, inertial nutation angle, and inertial and body nutation rates. The filter solves for the nutating three-axis attitude and accounts for effects due to principle axes offset from the body axes. The attitude is propagated using the kinematics of a rigid body symmetric about the principle spin axis; disturbance torques are assumed to be small. Filter updates consist only of the measured angles between celestial objects (Sun, Earth, etc.) and the nominal spin axis, and the times these angles were measured. Both simulated data and real data from the Dynamics Explorer -A (DE-A) spacecraft were used to test the filter; the results are presented. Convergence was achieved rapidly from a wide range of a priori state estimates, and sub-degree accuracy was attained. Systematic errors affecting the solution accuracy are discussed, as are the results of an attempt to solve for sensor measurement angle biases in the state vector.

Baker, David F.↗
NASA NTRS2009

Necessary and Sufficient Conditions for Attitude Estimation in Fractionated Spacecraft Systems

This paper addresses the problem of attitude estimation in fractionated spacecraft clusters. Each module in the cluster may have either a star-tracker, a relative attitude sensor, or both. Using results in nonlinear ob- servability theory, we provide graph-theoretic sufficient conditions for the attitude of every module to be observable. In particular we show that the attitude of every module in the cluster can be observed if every module has either a star tracker with non-collinear stars, or there is a path through the sensing network from a module with a star tracker to the module without a star tracker, and each of the relative measurements along the path has either multiple non-collinear beacons or a single beacon that is not parallel to the rotation vector of the target module.

Blackmore, Lars↗
NASA NTRSDate not supplied

Optical Navigation Attitude Estimation and Calibration Performance Improvement using Outlier Rejection

Spacecraft optical navigation (OpNav) systems process a sequence of images of celestial bodies against a starfield background to estimate the position and velocity of the vehicle. While attitude is sometimes available from an onboard star tracker, it is often desirable to recognize the background stars in the OpNav images to better align the image. While many image processing algorithms exist for finding stars, efficiency and reliability remain key issues in the presence of extended bodies(e.g. the Moon, Earth), especially when attempting to solve the full lost-in-space problem. Some star outliers(stars identified with high residuals)could appear in the camera field of view, however using them in the attitude estimation or camera calibration would lead to less accurate results. Therefore, we require new and robust approaches to remove these outliers before any further processing. The emphasis of the work is on developing a simple and robust iterative technique to detect and reject the outliers which could be found in any frame during the lost in space attitude determination or during the camera calibration. These outliers are determined based on the residuals of the centroids of the detected stars and the corresponding location using the star catalog. If the residuals exceed a predetermined threshold value, the object will be detected as an outlier and will be removed before another attitude determination and calibration iteration is performed. The performance for both attitude determination and on-orbit camera calibration are improved by an almost two-fold increase in accuracy when applying this outlier rejection technique.

OpNav↗
NASA NTRS2000

Analytic Steady-State Accuracy of a Spacecraft Attitude Estimator

This paper extends Farrenkopf's analysis of a single-axis spacecraft attitude estimator using gyro and angle sensor data to include the angle output white noise of a rate-integrating gyro. Analytic expressions are derived for the steady-state pre-update and post-update angle and drift bias variances and for the state update equations. It is shown that only part of the state update resulting from the angle sensor measurement is propagated to future times.

Markley, F. Landis↗
NASA NTRS2005

Wilkinson Microwave Anisotropy Probe (WMAP) Attitude Estimation Filter Comparison

The Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft was launched in June of 2001. The sensor complement of WMAP consists of two Autonomous Star Trackers (ASTs), two Fine Sun Sensors (FSSs), and a gyro package which contains redundancy about one of the WMAP body axes. The onboard attitude estimation filter consists of an extended Kalman filter (EKF) solving for attitude and gyro bias errors which are then resolved into a spacecraft attitude quaternion and gyro bias. A pseudo-linear Kalman filter has been developed which directly estimates the spacecraft attitude quaternion, rate, and gyro bias. In this paper, the performance of the two filters is compared for the two major control modes of WMAP: inertial mode and observation mode.

Harman, Richard R.↗
NASA NTRS1993

Analysis of the Command and Control Segment (CCS) attitude estimation algorithm

This paper categorizes the qualitative behavior of the Command and Control Segment (CCS) differential correction algorithm as applied to attitude estimation using simultaneous spin axis sun angle and Earth cord length measurements. The categories of interest are the domains of convergence, divergence, and their boundaries. Three series of plots are discussed that show the dependence of the estimation algorithm on the vehicle radius, the sun/Earth angle, and the spacecraft attitude. Common qualitative dynamics to all three series are tabulated and discussed. Out-of-limits conditions for the estimation algorithm are identified and discussed.

Stockwell, Catherine↗
NASA NTRS1979

Multiple scene attitude estimator performance for LANDSAT-1

Initial results are presented to demonstrate the performance of a linear sequential estimator (Kalman Filter) used to estimate a LANDSAT 1 spacecraft attitude time series defined for four scenes. With the revised estimator a GCP poor scene - a scene with no usable geodetic control points (GCPs) - can be rectified to higher accuracies than otherwise based on the use of GCPs in adjacent scenes. Attitude estimation errors was determined by the use of GCPs located in the GCP-poor test scene, but which are not used to update the Kalman filter. Initial results achieved indicate that errors of 500m (rms) can be attained for the GCP-poor scenes. Operational factors are related to various scenarios.

Rifman, S. S.↗
NASA NTRS1982

Kalman filtering for spacecraft attitude estimation

Several schemes in current use for sequential estimation of spacecraft attitude using Kalman filters are examined. These differ according to their treatment of the attitude error, namely: using the complete four-component quaternion; using a truncated quaternion in which one of the components has been eliminated; or using a quaternion referred to approximate body-fixed axes. These schemes are examined for the case of a spacecraft carrying line-of-sight attitude sensors and three-axis gyros whose measurements are corrupted by noise on both the drift rate and the drift-rate ramp. The analysis of the covariance is carried out in detail. The historical development of Kalman filtering of attitude is reviewed.

Lefferts, E. J.↗
NASA NTRS1997

Estimating Attitude, Trajectory, and Gyro Biases in an Extended Kalman Filter using Earth Magnetic Field Data from the Rossi X-Ray Timing Explorer

Traditionally satellite attitude and trajectory have been estimated with completely separate systems, using different measurement data. The estimation of both trajectory and attitude for low earth orbit satellites has been successfully demonstrated in ground software using magnetometer and gyroscope data. Since the earth's magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed and measured magnetic field components, as measured by the magnetometers throughout the entire spacecraft orbit, are a function of both the spacecraft trajectory and attitude errors. Therefore, these errors can be used to estimate both trajectory and attitude. This work further tests the single augmented Extended Kalman Filter (EKF) which simultaneously and autonomously estimates spacecraft trajectory and attitude with data from the Rossi X-Ray Timing Explorer (RXTE) magnetometer and gyro-measured body rates. In addition, gyro biases are added to the state and the filter's ability to estimate them is presented.

Deutschmann, Julie↗
NASA NTRS1990

Comparison and testing of extended Kalman filters for attitude estimation of the Earth radiation budget satellite

The testing and comparison of two Extended Kalman Filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS) is described. One EKF updates the attitude quaternion using a four component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. A brief development of the multiplicative algorithm is included. The mathematical development of the additive EKF was presented in the 1989 Flight Mechanics/Estimation Theory Symposium along with some preliminary testing results using real spacecraft data. A summary of the additive EKF algorithm is included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases. Sensitivity studies are performed on the estimation of sensor calibration states. The potential application of the EKF for real time and non-real time ground attitude determination and sensor calibration for future missions such as the Gamma Ray Observatory (GRO) and the Small Explorer Mission (SMEX) is also presented.

Deutschmann, Julie↗
NASA NTRS2018

High Fidelity Reconstructed Attitude Estimation Using Cassini Flight Telemetry

The Cassini Grand Finale capped the 20 year Cassini mission with 22 one-week-long orbits each with periapsis inside the ring plane just above Saturn’s cloud tops. One aspect of these remarkable orbits was unprecedented measurements of Saturn’s magnetic field very close to the planet. Processing this data required precise estimates of Cassini’s orientation during these ring plane crossings. These periods coincided with planned gyro-only attitude propagation due to the enormous bright bodies in the star tracker field-of-view. This paper describes how attitude reacquisition information, when the star tracker reacquires an absolute inertial reference, can be used to correct errors introduced during gyro-only propagation. The resulting high fidelity reconstruction significantly improves the extraction of Saturn’s magnetic field from the raw data obtained during gyro-only periods when Cassini’s changing orientation makes precise attitude estimation a challenge.

Burk, Thomas A.↗
NASA NTRS2003

Effect of Variations in IRU Integration Time Interval On Accuracy of Aqua Attitude Estimation

During Aqua launch support, attitude analysts noticed several anomalies in Onboard Computer (OBC) rates and in rates computed by the ground Attitude Determination System (ADS). These included: 1) periodic jumps in the OBC pitch rate every 2 minutes; 2) spikes in ADS pitch rate every 4 minutes; 3) close agreement between pitch rates computed by ADS and those derived from telemetered OBC quaternions (in contrast to the step-wise pattern observed for telemetered OBC rates); 4) spikes of +/- 10 milliseconds in telemetered IRU integration time every 4 minutes (despite the fact that telemetered time tags of any two sequential IRU measurements were always 1 second apart from each other). An analysis presented in the paper explains this anomalous behavior by a small average offset of about 0.5 +/- 0.05 microsec in the time interval between two sequential accumulated angle measurements. It is shown that errors in the estimated pitch angle due to neglecting the aforementioned variations in the integration time interval by the OBC is within +/- 2 arcseconds. Ground attitude solutions are found to be accurate enough to see the effect of the variations on the accuracy of the estimated pitch angle.

Natanson, G. A.↗
NASA NTRS1990

Comparison and testing of extended Kalman filters for attitude estimation of the Earth Radiation Budget Satellite

This paper presents the testing and comparison of two extended Kalman filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS). One EKF updates the attitude quaternion using a four-component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. Brief developments of the algorithms are included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are tested with simulated ERBS sensor data in addition to real ERBS sensor data. The results of the two filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases.

Bar-Itzhack, Itzhack Y.↗
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↗