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Kalman filter estimation of attitude and gyro bias with the QUEST observation model
The loss function for the Wahba attitude estimation problem employs unit vector observations with scalar weights. It is usually associated with the QUEST observation model, where the actual sensor noise is assumed the same for all components of the observed vector, regardless of the position in the field of view. The QUEST model has the great advantage of being sensor-independent except for the scalar parameter that characterizes the sensor errors. Although efficient algorithms for solving the Wahba problem exist, extending these algorithms to estimate gyro biases or sensor alignments has had mixed success. However, it is straightforward to estimate bias and alignment parameters with a Kalman filter. This paper investigates the use of an extended Kalman filter for the attitude and gyro bias that incorporates the QUEST observation model, to be referred to as the Unit Vector Filter (UVF). The UVF results are compared with those from a more conventional filter, the Real-Time Sequential Filter (RTSF), for which the residual is the two-dimensional projection of the unit vector onto the plane perpendicular to the sensor boresight. The RTSF is similar in design to that used by Multimission Modular Spacecraft for onboard attitude determination. An apparent obstacle to the use of unit vectors as measurements is their singular noise covariance matrix. Shuster has shown that this problem should not affect filter performance. The UVF and RTSF are tested using actual flight data from the Extreme Ultraviolet Explorer (EUVE). It is found that these filters generate nearly identical attitude and gyro bias estimates, thus validating the use of unit vectors and the QUEST noise model.
Analytic Spacecraft Attitude and Rate Estimation Performance During Attitude Sensor Outages
Analytic expressions for spacecraft attitude and rate estimation performance of an attitude estimation filter in terms of sensor specifications are useful tools for spacecraft design. Farrenkopf (1978) famously found analytic expressions for steady-state pre-update and post-update attitude and gyro bias estimate error variances for an attitude estimation filter for a single-axis spacecraft with a Rate Output Gyro (ROG). Markley and Reynolds (2000) extended the analysis for a Rate-Integrating Gyro (RIG) with angle white noise. These expressions allow for the rapid evaluation of system performance during preliminary mission design phases. One contribution of this paper is the analytic calculation of the steady-state pre-update and post-update angular rate estimate uncertainty for both the ROG and RIG cases. The primary contribution of this paper is the extension of the results for both the ROG and the RIG cases to the situation of an attitude sensor outage. This situation arises frequently in practice; for example when a star sensor’s field of view is occluded, when a star sensor’s readings are unreliable during a thruster burn that vibrates the spacecraft, or during star sensor outages due to radiation upsets. Analytic expressions for the attitude estimate uncertainty, gyro bias estimate uncertainty, and angular rate estimate uncertainty are given in terms of the attitude sensor outage interval, the star tracker measurement noise, and gyro noise parameters. Validity of the analytic results is demonstrated via Monte Carlo simulation.
Analytic Spacecraft Attitude and Rate Estimation Performance During Attitude Sensor Outages
Analytic expressions for spacecraft attitude and rate estimation performance of an attitude estimation filter in terms of sensor specifications are useful tools for spacecraft design. Farrenkopf (1978) famously found analytic expressions for steady-state pre-update and post-update attitude and gyro bias estimate error variances for an attitude estimation filter for a single-axis spacecraft with a Rate Output Gyro (ROG). Markley and Reynolds (2000) extended the analysis for a Rate-Integrating Gyro (RIG) with angle white noise. These expressions allow for the rapid evaluation of system performance during preliminary mission design phases. One contribution of this paper is the analytic calculation of the steady-state pre-update and post-update angular rate estimate uncertainty for both the ROG and RIG cases. The primary contribution of this paper is the extension of the results for both the ROG and the RIG cases to the situation of an attitude sensor outage. This situation arises frequently in practice; for example when a star sensor’s field of view is occluded, when a star sensor’s readings are unreliable during a thruster burn that vibrates the spacecraft, or during star sensor outages due to radiation upsets. Analytic expressions for the attitude estimate uncertainty, gyro bias estimate uncertainty, and angular rate estimate uncertainty are given in terms of the attitude sensor outage interval, the star tracker measurement noise, and gyro noise parameters. Validity of the analytic results is demonstrated via Monte Carlo simulation.
Solar Cruiser Technology Maturation Plans
The NASA Marshall Space Flight Center (MSFC) developed the Solar Cruiser mission concept to mature solar sail technology for use in future Heliophysics missions, as well as missions of interest across a broad user community (e.g., space weather and Earth polar observatories). Solar Cruiser will serve as a pathfinder for missions that observe the solar environment from unique vantage points such as a high inclination solar mission opening a fundamentally new range of observational capabilities for the Heliophysics Program and for space weather monitoring. Sustained observations away from the Sun-Earth line (SEL) present unique opportunities for answering the outstanding science questions of Heliophysics, improving space-weather monitoring and prediction, and revealing new information about our Sun and solar system. Propellantless solar sails can be used to create artificial equilibria and maintain indefinite station-keeping at locations sunward of L1 along the SEL, or at any desired offset from the SEL leading or trailing the Earth in its orbit. They can change the heliocentric inclination of a spacecraft from the ecliptic to as high as solar polar, stopping and remaining at any intermediate inclination orbit in between. Sails can be used to hover over the Earth’s poles, using solar photon pressure to offset the Earth’s gravitational attraction, creating functional equivalents of geostationary earth orbits. The Solar Cruiser mission would fly a small spacecraft with a large (>1,600 square meter) solar sail containing embedded reflectivity control devices (RCDs) and photovoltaic cells. The mission concept includes successful deployment of the solar sail, validation of all sail subsystems, controlled station-keeping inside of the Sun-Earth L1 point, attitude control of the sail with the RCDs (including spinning and de-spinning), demonstration of pointing performance for science imaging, and an increase in heliocentric inclination (out of the ecliptic). To demonstrate the requisite sail technology, the Solar Cruiser project will design, fabricate, deploy, and fly the Solar Sail Propulsion Element (SSPE). The SSPE incorporates the following three systems: • The Solar Sail System (SSS) provides the large propulsive surface required for acceleration and smaller reflectivity-changing surfaces for roll control. • The Active Mass Translator System (AMT) provides SSPE motion with respect to the sailcraft bus for pitch and yaw control. • The Solar Sail Attitude Determination and Control System (SSADCS) consists of embedded software to 1) provide autonomous sailcraft attitude estimation, attitude pointing control, and reaction wheel momentum management following sail deployment and 2) execute the uplinked inertial attitude pointing commands to maintain the desired sailcraft trajectory. The plans for maturing each of these technology systems to TRL 5 and beyond are described herein.
Estimation of attitude sensor timetag biases
This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.
Use of nonlinear identification in robust attitude and attitude rate estimation for SAMPEX
A method is described for obtaining optimal attitude estimation/identification algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. The absence of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. In addition, attitude data is occasionally unavailable (for example, during sun occultation). As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is an increased need for accurate models of the rotational dynamics. The Minimum Model Error(MME)/Least Square Correlation(LSC) algorithm accurately identifies an improved model for SAMPEX to be used during periods of complete data loss or extreme noise. The model correction is determined by estimating only one orbit(the identification pass) just prior to the assumed data loss(the prediction pass). The MME estimator correctly predicted the states during the identification phase, but more importantly determines the necessary model correction trajectory, d(t). The LSC algorithm is then used to find this trajectory's functional form, H(x(t)). The results show significant improvement of the new corrected model's attitude estimates as compared to the original uncorrected model's estimates. The possible functional form of the correction term is limited at this point in the study to functions strictly of the estimated states. The results, however, strongly suggest that functions based on the relative position of the satellite may also be possible candidates for future consideration.
A Short Tutorial on Inertial Navigation System and Global Positioning System Integration
The purpose of this document is to describe a simple method of integrating Inertial Navigation System (INS) information with Global Positioning System (GPS) information for an improved estimate of vehicle attitude and position. A simple two dimensional (2D) case is considered. The attitude estimates are derived from sensor data and used in the estimation of vehicle position and velocity through dead reckoning within the INS. The INS estimates are updated with GPS estimates using a Kalman filter. This tutorial is intended for the novice user with a focus on bringing the reader from raw sensor measurements to an integrated position and attitude estimate. An application is given using a remotely controlled ground vehicle operating in assumed 2D environment. The theory is developed first followed by an illustrative example.
Measuring attitude with a gradiometer
Static attitude estimation and dynamic attitude estimation are used to describe a gradiometer composed of a number of accelerometers that are used to measure a combination of the local gravity gradient and instrument rotation effects. After a series of measures to isolate the gradient, a global mesh of measurements can be obtained that determine the planetary external gravity potential. Orbital and spacecraft models are developed to determine if, when the gravity potential is known, the same measurements, unsupported by any other information can be used to infer the spacecraft attitude.
Colored noise effects on batch attitude accuracy estimates
The effects of colored noise on the accuracy of batch least squares parameter estimates with applications to attitude determination cases are investigated. The standard approaches used for estimating the accuracy of a computed attitude commonly assume uncorrelated (white) measurement noise, while in actual flight experience measurement noise often contains significant time correlations and thus is colored. For example, horizon scanner measurements from low Earth orbit were observed to show correlations over many minutes in response to large scale atmospheric phenomena. A general approach to the analysis of the effects of colored noise is investigated, and interpretation of the resulting equations provides insight into the effects of any particular noise color and the worst case noise coloring for any particular parameter estimate. It is shown that for certain cases, the effects of relatively short term correlations can be accommodated by a simple correction factor. The errors in the predicted accuracy assuming white noise and the reduced accuracy due to the suboptimal nature of estimators that do not take into account the noise color characteristics are discussed. The appearance of a variety of sample noise color characteristics are demonstrated through simulation, and their effects are discussed for sample estimation cases. Based on the analysis, options for dealing with the effects of colored noise are discussed.
Improved Modeling in a Matlab-Based Navigation System
An innovative approach to autonomous navigation is available for low earth orbit satellites. The system is developed in Matlab and utilizes an Extended Kalman Filter (EKF) to estimate the attitude and trajectory based on spacecraft magnetometer and gyro data. Preliminary tests of the system with real spacecraft data from the Rossi X-Ray Timing Explorer Satellite (RXTE) indicate the existence of unmodeled errors in the magnetometer data. Incorporating into the EKF a statistical model that describes the colored component of the effective measurement of the magnetic field vector could improve the accuracy of the trajectory and attitude estimates and also improve the convergence time. This model is identified as a first order Markov process. With the addition of the model, the EKF attempts to identify the non-white components of the noise allowing for more accurate estimation of the original state vector, i.e. the orbital elements and the attitude. Working in Matlab allows for easy incorporation of new models into the EKF and the resulting navigation system is generic and can easily be applied to future missions resulting in an alternative in onboard or ground-based navigation.
Spacecraft attitude determination using a second-order nonlinear filter
The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.
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.
Automating Surface Attitude Positioning and Pointing Operations for Mars 2020
The Surface Attitude Positioning and Pointing (SAPP) subsystem of the Mars Perseverance rover keeps track of the rover’s position and attitude on the surface of Mars. The SAPP Downlink Engineering Operations team members receive data from the rover on a daily basis. They must interpret the data to make sure the rover is staying safe and to support uplink planning. The SAPP team keeps track of the error growth in the rover’s attitude estimate due to noise in the Rover Inertial Measurement Unit’s (RIMU) gyroscopes used to propagate that attitude estimate whenever the rover is moving. Whenever this error grows to a particular threshold, SAPP is responsible for updating the onboard attitude knowledge using the RIMU’s accelerometers to estimate rover roll and pitch and sun imaging to estimate rover yaw, thereby reducing this attitude estimation error. Accurate attitude estimation is required so that the rover can successfully point its High Gain Antenna (HGA) to receive information from Earth and as a backup to the Mars orbiters used for sending data from the rover to Earth, point instruments on its Remote Sensing Mast (RSM), and support safe movement and placement of instruments by the rover’s ARM relative to the Martian surface. The Mars 2020 Engineering Operations team has been working to increase the operational efficiency of the mission and eventually move to a five-hour timeline for daily operations. In pursuit of this goal, the SAPP Engineering Operations team has automated their downlink process by developing a centralized Jupyter notebook to analyze the data received daily from the rover. The SAPP downlink Jupyter notebook automatically collects the data relevant to the SAPP subsystem and visualizes this information in plots and tables that can be easily read by downlink operators to aid them in assessing the status of the subsystem. Various Application Programming Interfaces (APIs) have been incorporated into the downlink daily notebook to automate the collection and posting of data, such as gathering and posting data products to the cloud. The SAPP team has also developed a SAPP downlink software library that includes functions to aid the notebook in processing data. In addition to assessing the SAPP subsystem on a daily basis, operators need to assess the long-term trending behavior of the subsystem over time. An automated trending process has been developed to collect information from the daily notebooks in order to plot and analyze that data in a centralized place. These daily and trending processes have expedited the SAPP downlink assessment and laid the groundwork to completely automate the SAPP downlink process so that SAPP operators are unnecessary unless something unexpected occurs. This paper will provide an overview of the functions that the SAPP subsystem carries out on a daily basis, and will then dive into the automations that have been developed for daily and trending downlink assessment. An assessment of the downlink efficiency will be provided, along with a summary of lessons learned and work to go. Finally, the authors will discuss how these types of automated spacecraft health assessments could be more broadly used within mission operations.
Functional evaluation of the Galileo attitude and articulation control subsystem using FUNSIM
The functional performance of the Galileo spacecraft's attitude and articulation control subsystem is evaluated. The tests are performed utilizing the simulation program developed on an IBM 370 system known as the Functional Simulation (FUNSIM). FUNSIM is an entirely software-based simulation which uses the actual flight software in HAL/S and simulated spacecraft dynamics in FORTRAN language. A description of how the test cases were selected to verify that the algorithms perform functionally correctly, and a summary of the problems encountered are included in the paper. The benefits of having an alternative test bed such as FUNSIM to the real-time simulation test beds which utilize the spacecraft hardware components in discovering the problems are described. A sample test case which shows that the desired tasks were performed functionally correctly is included in the paper. The commands in this test are selected to start the dual-spin spacecraft initially in launch mode and lead it all the way to inertial mode. Major attitude control algorithms such as rotor and platform attitude estimators, clock and core platform attitude estimators, clock and core platform controllers, and the command turn and burn are examined.
Comprehensive evaluation of attitude and orbit estimation using real earth magnetic field data
A single, augmented extended Kalman filter (EKF) which simultaneously and autonomously estimates spacecraft attitude and orbit was developed and tested with simulated and real magnetometer and rate data. Since the earth's magnetic field is a function of time and position, and since time is accurately known, the differences between the computed and measured magnetic field components, as measured by the magnetometers throughout the entire spacecraft's orbit, are a function of orbit and attitude errors. These differences can be used to estimate the orbit and attitude. The test results of the EKF with magnetometer and gyro data from three NASA satellites are presented and evaluated.
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.
Optimal estimation and attitude control of a solar electric propulsion spacecraft
Established procedures of linear, quadratic, Gaussian optimal estimation and control are developed and interpreted for their application to the problem of attitude control of spacecraft with dynamically significant elastic appendages. Results are presented both in general terms and for specific application to a solar electric spacecraft. Comparisons are made between alternative coordinate systems, and a realistic range of design parameters is considered. For single axis control, system evaluation is accomplished by simulation of a fifteenth-order spacecraft plant with alternative second-order, fourth-order, and sixth-order constant gain estimators. Results point out the importance of modeling errors.