Engineering topics

Bar-Itzhack, Itzhack Y.

Publications and source records attributed to Bar-Itzhack, Itzhack Y..

At least 19 records

NASA NTRS2007

A Novel Attitude Determination Algorithm for Spinning Spacecraft

This paper presents a single frame algorithm for the spin-axis orientation-determination of spinning spacecraft that encounters no ambiguity problems, as well as a simple Kalman filter for continuously estimating the full attitude of a spinning spacecraft. The later algorithm is comprised of two low order decoupled Kalman filters; one estimates the spin axis orientation, and the other estimates the spin rate and the spin (phase) angle. The filters are ambiguity free and do not rely on the spacecraft dynamics. They were successfully tested using data obtained from one of the ST5 satellites.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2004

Autonomous navigation system based on GPS and magnetometer data

This invention is drawn to an autonomous navigation system using Global Positioning System (GPS) and magnetometers for low Earth orbit satellites. As a magnetometer is reliable and always provides information on spacecraft attitude, rate, and orbit, the magnetometer-GPS configuration solves GPS initialization problem, decreasing the convergence time for navigation estimate and improving the overall accuracy. Eventually the magnetometer-GPS configuration enables the system to avoid costly and inherently less reliable gyro for rate estimation. Being autonomous, this invention would provide for black-box spacecraft navigation, producing attitude, orbit, and rate estimates without any ground input with high accuracy and reliability.

Julie, Thienel K.↗

NASA NTRS2004

Results of the Magnetometer Navigation (MAGNAV)lnflight Experiment

The Magnetometer Navigation (MAGNAV) algorithm is currently running as a flight experiment as part of the Wide Field Infrared Explorer (WIRE) Post-Science Engineering Testbed. Initialization of MAGNAV occurred on September 4, 2003. MAGNAV is designed to autonomously estimate the spacecraft orbit, attitude, and rate using magnetometer and sun sensor 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 magnetic field and measured magnetic field components, as measured by the magnetometer throughout the entire spacecraft orbit, are a function of the spacecraft trajectory and attitude errors. Therefore, these errors are used to estimate both trajectory and attitude. In addition, the time rate of change of the magnetic field vector is used to estimate the spacecraft rotation rate. The estimation of the attitude and trajectory is augmented with the rate estimation into an Extended Kalman filter blended with a pseudo-linear Kalman filter. Sun sensor data is also used to improve the accuracy and observability of the attitude and rate estimates. This test serves to validate MAGNAV as a single low cost navigation system which utilizes reliable, flight qualified sensors. MAGNAV is intended as a backup algorithm, an initialization algorithm, or possibly a prime navigation algorithm for a mission with coarse requirements. Results from the first six months of operation are presented.

Thienel, Julie K.↗

NASA NTRS2004

Pseudo Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler's equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate.

Harman, Richard R.↗

NASA NTRS2004

Schuler Period in LEO Satellites

This paper generalizes and extends the concept of the Schuler oscillation that occurs in the theory of inertial navigation systems, allowing one to see how the Schuler phenomenon affects inertial navigation systems operating in space. We show why a low earth orbit satellite's orbital period is identical to the period of the Schuler pendulum, which is the period of the errors for terrestrial inertial navigation systems. We also show that the generalized form of the Schuler oscillation takes the same form as the Hill-Clohessy-Wiltshire equations for satellite relative motion and that the period of the out-of-plane motion in neighboring satellite relative trajectories is the same as the Schuler period. Finally, we describe how INS gyro drift manifests itself in different coordinate systems for the orbital case. These results may assist orbital flight dynamics and attitude control systems engineers in the design and analysis of INS-equipped spacecraft

Carpenter, Russell J.↗

NASA NTRS2004

Implicit and Explicit Spacecraft Gyro Calibration

This paper presents a comparison between two approaches to sensor calibration. According to one approach, called explicit, an estimator compares the sensor readings to reference readings, and uses the difference between the two to estimate the calibration parameters. According to the other approach, called implicit, the sensor error is integrated to form a different entity, which is then compared with a reference quantity of this entity, and the calibration parameters are inferred from the difference. In particular this paper presents the comparison between these approaches when applied to in-flight spacecraft gyro calibration. Reference spacecraft rate is needed for gyro calibration when using the explicit approach; however, such reference rates are not readily available for in-flight calibration. Therefore the calibration parameter-estimator is expanded to include the estimation of that reference rate, which is based on attitude measurements in the form of attitude-quaternion. A comparison between the two approaches is made using simulated data. It is concluded that the performances of the two approaches are basically comparable. Sensitivity tests indicate that the explicit filter results are essentially insensitive to variations in given spacecraft dynamics model parameters.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2004

Pseudo-Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler s equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate. The performance of the two filters is examined using simulated data.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2003

The MAP Spacecraft Angular State Estimation After Sensor Failure

This work describes two algorithms for computing the angular rate and attitude in case of a gyro and a Star Tracker failure in the Microwave Anisotropy Probe (MAP) satellite, which was placed in the L2 parking point from where it collects data to determine the origin of the universe. The nature of the problem is described, two algorithms are suggested, an observability study is carried out and real MAP data are used to determine the merit of the algorithms. It is shown that one of the algorithms yields a good estimate of the rates but not of the attitude whereas the other algorithm yields a good estimate of the rate as well as two of the three attitude angles. The estimation of the third angle depends on the initial state estimate. There is a contradiction between this result and the outcome of the observability analysis. An explanation of this contradiction is given in the paper. Although this work treats a particular spacecraft, the conclusions have a far reaching consequence.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2003

On the Singularity in the Estimation of the Quaternion-of-Rotation

It has been claimed in the archival literature that the covariance matrix of a Kalman filter, which is designed to estimate the quaternion-of-rotation, is necessarily rank deficient because the normality constraint of the quaternion produces dependence between the quaternion elements. In reality, though, this phenomenon does not occur. The covariance matrix is not singular, and the filter is well behaved. Several simple examples are presented that demonstrate the regularity of the covariance matrix. First, estimation cases are presented where a relationship exists between the estimated variables, and yet the covariance matrix is not singular. Then the particular problem of quaternion estimation is analyzed. It is shown that the discrepancy stems from the fact that a functional relationship exists between the elements of the true quaternion but not between its estimated elements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2003

Implicit Spacecraft Gyro Calibration

This paper presents an implicit algorithm for spacecraft onboard instrument calibration, particularly to onboard gyro calibration. This work is an extension of previous work that was done where an explicit gyro calibration algorithm was applied to the AQUA spacecraft gyros. The algorithm presented in this paper was tested using simulated data and real data that were downloaded from the Microwave Anisotropy Probe (MAP) spacecraft. The calibration tests gave very good results. A comparison between the use of the implicit calibration algorithm used here with the explicit algorithm used for AQUA spacecraft indicates that both provide an excellent estimation of the gyro calibration parameters with similar accuracies.

Harman, Richard↗

NASA NTRS2003

The Effect of Sensor Failure on the Attitude and Rate Estimation of MAP Spacecraft

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2003

Pseudo Linear Gyro Calibration

Previous high fidelity onboard attitude algorithms estimated only the spacecraft attitude and gyro bias. The desire to promote spacecraft and ground autonomy and improvements in onboard computing power has spurred development of more sophisticated calibration algorithms. Namely, there is a desire to provide for sensor calibration through calibration parameter estimation onboard the spacecraft as well as autonomous estimation on the ground. Gyro calibration is a particularly challenging area of research. There are a variety of gyro devices available for any prospective mission ranging from inexpensive low fidelity gyros with potentially unstable scale factors to much more expensive extremely stable high fidelity units. Much research has been devoted to designing dedicated estimators such as particular Extended Kalman Filter (EKF) algorithms or Square Root Information Filters. This paper builds upon previous attitude, rate, and specialized gyro parameter estimation work performed with Pseudo Linear Kalman Filter (PSELIKA). The PSELIKA advantage is the use of the standard linear Kalman Filter algorithm. A PSELIKA algorithm for an orthogonal gyro set which includes estimates of attitude, rate, gyro misalignments, gyro scale factors, and gyro bias is developed and tested using simulated and flight data. The measurements PSELIKA uses include gyro and quaternion tracker data.

Harman, Richard↗

NASA NTRS2002

On the Singularity in the Estimation of the Quaternion-of-Rotation

It has been claimed in the archival literature that the covariance matrix of a Kalman filter, which is designed to estimate the quaternion-of-rotation, is necessarily rank, deficient because the normality constraint of the quaternion produces dependence between the quaternion elements. In reality, though, this phenomenon does not occur. The covariance matrix is not singular, and the filter is well behaved. Several simple examples are presented th at demonstrate the regularity of the covariance matrix. First, a Kalman filter is designed to estimate variables subject to a functional relationship. Then the particular problem of quaternion estimation is analyzed. It is shown that the discrepancy stems from the fact that the functional relationship exists between the elements of the quaternion but not between its estimate elements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2001

In-Space Calibration of a Gyro Quadruplet

This work presents a new approach to gyro calibration where, in addition to being used for computing attitude that is needed in the calibration process, the gyro outputs are also used as measurements in a Kalman filter. This work also presents an algorithm for calibrating a quadruplet rather than the customary triad gyro set. In particular, a new misalignment error model is derived for this case. The new calibration algorithm is applied to the EOS-AQUA satellite gyros. The effectiveness of the new algorithm is demonstrated through simulations.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2001

State-Dependent Pseudo-Linear Filter for Spacecraft Attitude and Rate Estimation

This paper presents the development and performance of a special algorithm for estimating the attitude and angular rate of a spacecraft. The algorithm is a pseudo-linear Kalman filter, which is an ordinary linear Kalman filter that operates on a linear model whose matrices are current state estimate dependent. The nonlinear rotational dynamics equation of the spacecraft is presented in the state space as a state-dependent linear system. Two types of measurements are considered. One type is a measurement of the quaternion of rotation, which is obtained from a newly introduced star tracker based apparatus. The other type of measurement is that of vectors, which permits the use of a variety of vector measuring sensors like sun sensors and magnetometers. While quaternion measurements are related linearly to the state vector, vector measurements constitute a nonlinear function of the state vector. Therefore, in this paper, a state-dependent linear measurement equation is developed for the vector measurement case. The state-dependent pseudo linear filter is applied to simulated spacecraft rotations and adequate estimates of the spacecraft attitude and rate are obtained for the case of quaternion measurements as well as of vector measurements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2000

A LEO Satellite Navigation Algorithm Based on GPS and Magnetometer Data

The Global Position System (GPS) has become a standard method for low cost onboard satellite orbit determination. The use of GPS as an attitude and rate sensor has also been developed in the recent past. Additionally, focus has been given to attitude and orbit estimation using the magnetometer, a low cost, reliable sensor. Combining measurements from both GPS and a magnetometer can provide a robust navigation system which takes advantage of the estimation qualities of both measurements. Ultimately a low cost, accurate navigation system can result, potentially eliminating the need for more costly sensors, including gyroscopes. This work presents the development and preliminary testing of a unified navigation algorithm which produces estimates of attitude, angular rate, position, and velocity for a low earth orbit (LEO) spacecraft. The system relies on GPS phase, range, and range rate data as well as magnetometer data. The algorithm used is an extended Kalman filter (EKF) developed to provide LEO attitude, orbit, and rate estimates using magnetometer and sun sensor data. Incorporating sun sensor data into the EKF improved the attitude and rate estimates. For many LEO spacecraft the sun data is available during only a portion of the orbit. However, GPS data is available continuously throughout the orbit. GPS can produce accurate orbit estimates and combining GPS and magnetometer data improves the attitude and rate estimates. The magnetometer based EKF can converge from large initial errors in position, velocity, and 3 attitude . Combining the magnetometer and GPS data into a single EKF will provide a more robust and accurate system. The EKF is based on an existing EKF. The GPS measurement models for phase, range, and range rate are incorporated into the existing structure of the filter. The original EKF produced the orbit estimates in terms of Keplerian elements. Due to the nature of the GPS measurements and ease of computation, the orbit estimates are converted to the Cartesian position and velocity. The measurement model for the magnetometer is adjusted for this change in the state and the measurements. Preliminary test results based on simulated GPS and magnetometer data are included.

Deutschmann, Julie↗

NASA NTRS2000

Comprehensive Evaluation of Attitude and Orbit Estimation Using Actual Earth Magnetic Field Data

A single, augmented Extended Kalman Filter (EKF), which simultaneously and autonomously estimates spacecraft attitude and orbit has been developed and successfully tested with real magnetometer and gyro data only. Because the earth magnetic field is a function of time and position, and because 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 orbit and attitude errors. Thus, conceivably these differences could be used to estimate both orbit and attitude; an observability study validated this assumption. The results of testing the EKF with actual magnetometer and gyro data, from four satellites supported by the NASA Goddard Space Flight Center (GSFC) Guidance, Navigation, and Control Center, are presented and evaluated. They confirm the assumption that a single EKF can estimate both attitude and orbit when using gyros and magnetometers only.

Deutschmann, Julie K.↗

NASA NTRS1999

Angular-Rate Estimation using Star Tracker Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quaternion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Azor, R.↗