Research is being performed with David A. Quinn and F. Landis Markley at NASA-Goddard Space Flight to develop a new sensor approach for attitude determination using Global Positioning System signals. The concept involves the use of multiple GPS antenna elements arrayed on a single sensor head to provide maximum GPS space vehicle availability. A number of sensor element configurations are being considered. In addition to the navigation function, the array is used to find which GPS space vehicles are within the field-of-view of each antenna element. Attitude determination is performed by considering the sightline vectors of the found GPS space vehicles together with the fixed boresight vectors of the individual antenna elements. The advantages of new GPS attitude sensor include:
Differential carrier-phase measurements are not required
Attitude errors from multipath can be reduced or even eliminated
Integer ambiguities do not need to be resolved
Line biases do not need to be determined
Results from research can be obtained from:
[1] Crassidis, J.L., Quinn, D.A., Markley, F.L., and McCullough, J.D., “A Novel Sensor for Attitude Determination Using Global Positioning System Signals,” Proceedings of the AIAA Guidance, Navigation, and Control Conference, Boston, MA, Aug. 1998, AIAA Paper #98-4228, pp. 708-717.
The goal for the solution of Kepler’s equation is to determine the eccentric anomaly accurately, given the mean anomaly and eccentricity.
M = E – e sin(E)
This study presents a new approach to solve this very well-documented problem. We focus on demonstrating the procedure for both the elliptical and hyperbolic cases. It is found that by means of a series approximation, an angle identity, the application of Sturm’s theorem and an iterative correction method, the need to evaluate transcendental functions or store tables is eliminated. A 15th-order polynomial is developed through a series approximation of Kepler’s equation. Sturm’s theorem is used to prove that only one real roots exists for this polynomial for the given range of mean anomaly and eccentricity. An initial approximation for this root is found using a 3rd-order polynomial. Then a one time generalized Newton-Raphson correction is applied to obtain accuracies to the level of around 10-15 rad for the elliptical case and 10-13 rad for the hyperbolic case, which is near machine precision.
Research is being performed to develop a new approach for robust adaptive control. This approach, called Model-Error Control Synthesis (MECS), uses an optimal real-time nonlinear estimator to determine model-error corrections to the control input. The estimator determines the model error using a one time-step ahead approach. Control compensation is achieved by using the estimated model-error as a signal synthesis adaptive correction to the nominal control input so that maximum performance is achieved in the face of extreme model uncertainty and disturbance inputs. The MECS approach has many significant advances, including:
The determined model is a natural by-product of the state estimator
Model parameters need not be updated in order to achieve robust performance
It can easily handle both time-varying parameter changes in the model and unmodeled disturbance inputs
This work is sponsored by National Science Foundation. Results from research can be obtained from:
[1] Kim, J.-R., and Crassidis, J.L., “Spacecraft Attitude Control Using Approximate Receding-Horizon Model-Error Control Synthesis,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 5, Sept.-Oct. 2006, pp. 1023-1031.
[2] Alsuwaidan, B., and Crassidis, J.L., “Robust Aircraft Longitudinal Control Using Model-Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, Keystone, CO, Aug. 2006, AIAA Paper #2006-6050.
[3] Kim, J.-R., and Crassidis, J.L., “Spacecraft Attitude Control Using Approximate Receding-Horizon Model-Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, Aug. 2005, AIAA Paper #2005-6178.
[4] Kim, J.-R., and Crassidis, J.L., “Fundamental Relation of Approximate Receding-Horizon Optimization to the Simple Mass-Spring-Damper System,” AIAA Guidance, Navigation, and Control Conference, Austin, TX, Aug. 2003, AIAA Paper #2003-5563.
[5] Kim, J.-R., and Crassidis, J.L., “Limit-Cycle Oscillation Control of Aeroelastic System Using Model-Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, Austin, TX, Aug. 2003, AIAA Paper #2003-5506.
[6] Kim, J.-R., and Crassidis, J.L., “Robust Spacecraft Attitude Control Using Model-Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, Monterey, CA, Aug. 2002, AIAA Paper #02-4576.
[7] Kim, J.-R., and Crassidis, J.L., “Model-Error Control Synthesis Using Approximate Receding-Horizon Control Laws,” AIAA Guidance, Navigation, and Control Conference, Montreal, CA, Aug. 2001, AIAA Paper #01-4220.
[8] Kim, J.-R., and Crassidis, J.L., “Linear Stability Analysis of Model Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, Denver, CO, Aug. 2000, AIAA Paper #00-3963.
[9] Crassidis, J.L., “Robust Control of Nonlinear Systems Using Model Error Control Synthesis,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 22, No. 4, July-Aug. 1999, pp. 595-601.
Systems comprised of a number of computing nodes all supporting a common mission. All nodes can be given the same task or asked to support the mission through a subset of tasks. Decentalized systems offer several advantages over their centralized counterparts including:
Each node does not require intrinsic knowledge of the system topology
Topology is variable. Nodes can be added or subtracted without significantly impacting the overall system
Less vulnerable to single-point failures
Computational load can be spread amongst nodes for efficiency
Decentralized systems also suffer from some disadvantages:
All nodes may not have access to all information contained within the system
Multiple nodes have access to the same information
Examples of decentralized systems include robotic swarms, cooperative UAVs, formation flying spacecraft and formation of synthetic apertures using multiple smaller sensors.
Decentralized Estimation
Decentralized Attitude Estimation
Decentralized estimation representes an important aspect of decentralized systems. Because various nodes within the system may not have access to all measurements within the system, the individual estimates will be suboptimal. In a perfect world there would exist a means to combine the estimates from all of the nodes into a single estimate which makes use of all system measurements and is optimal. Difficulty arises because some measurements may be used by more than one node leading the estimates from those nodes to be correlated. An example of such a system is the spacecraft attitude estimator shown. Because each extended Kalman filter (EKF) makes use of a common gyro measurement the two estimates will be correlated. The problem to be solved is how can we efficiently and consistently fuse the individual estimates from each EKF to obtain the best possible estimate?
Covariance Intersection
Covariance Intersection
An elegant solution for the fusion of estimates with unknown correlations is the Covariance Intersection (CI) algorithm [Julier and Uhlmann, 1997]. As the name suggests, the CI algorithm is routed in the fiundamentals of Gaussian intersection. Appreciation for the CI algorithm is gained by considering the fusion of two estimates in 2D. In 2D the covariance of a Gaussian random variable can be interpreted as an ellipse. If multiple estimates of the same 2D state vector are available, their covariance ellipses will intersect as shown. The CI algorithm expresses the covariance of the fused estimate as the smallest covariance ellipse which contains all of the intersection of the two individual covariances. Depending on the confidence in each estimate or a desired final statistic, each individual covariance can be weighted by a scalar value which leads the CI algorithm to include a family of solutions as shown.
Another elegant property of the CI algorithm is that, while being derived from a geometric viewpoint, it can also be derived from a matrix- and scalar-weighted optimization problem. This property allows the CI algorithm to be extended to the fusion of higher dimensional state vectors and an arbitrary number of estimates.
Covariance Intersection for Attitude Estimation
While the CI algorithm provides a meaningful and elegant solution for the problem of fusion under unknown correlations, the fusion of attitude states is not trivial. The main difficulty with fusing attitude estimates is the choice of attitude parametrization. The traditional attitude parametrization of choice for space applications, the quaternion, must satisfy a unit norm constraint. This leads the CI fused estimate to be the solution of a constrained optimization problem. For state vectors including only a single quaternion there are several solutions to the resulting optimization problem. For fusion of state vectors containing more than a single quaternion iterative solution methods are required which also seek to mitigate the increasing numeric instability of the problem statement.
References
Julier, S. J., and Uhlmann, J., K., “A Non-divergent Estimation Algorithm in the Presence of Unknown Correlations,” American Control Conference, Albuquerque, NM, IEEE Publications, Piscataway, NJ, June 1997, pp. 2369 – 2373.
Julier, S. J., and Uhlmann, J., K., General Decentralized Data Fusion with Covariance Intersection (CI) in Handbook of Multisensor Data Fusion. CRC Press. Boca Raton, FL., 2001, Chap. 12.
Shuster, M. D., “A Survey of Attitude Representations,” Journal of the Astronautical Sciences, Vol. 41, No. 4, Oct.-Dec. 1993, pp. 439-517.
Cheng, Y., Banas, W.D., and Crassidis, J.L., “Quaternion Data Fusion,” Itzhack Y. Bar-Itzhack Memorial Symposium on Estimation, Navigation, and Spacecraft Control, Haifa, Israel, Oct. 2012, Paper MoA1 .3.
A new generalized approach for multiple-model adaptive estimation (MMAE) is being developed, which can be used for time-varying and nonlinear systems. This approach is based on using the autocorrelation of the measurement-minus-estimate residual. Initial results indicate that the new generalized MMAE approach can provide better convergence properties than the standard approach. MMAE schemes are widely used on a number applications, such as fault detection, robust tracking of vehicles, network centric warfare applications, information technology applications and extreme events. The new generalized MMAE approach has the potential to revolutionize these areas.
A new method is discussed, based on an unsupervised learning state variable method that uses a multiple-model adaptive estimation approach to determine the most probable shape and other intrinsic features of a space object in orbit among a number of candidate models while simultaneously recovering the observed resident space object’s inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters to provide multiple space object state estimates, where each filter is purposefully dependent on a mutually unique resident space object model. Estimates on the conditional probability of each model given the available measurements are provided from the multiple-model adaptive estimation approach. Each filter employs the Unscented (or Sigma-Point) estimation approach, reducing passively-collected electro-optical data to infer the unknown state vector comprised of the space object inertial-to-body orientation, position and their respective temporal rates. Each hypothesized model results in a different observed optical cross-sectional area. The effect of solar radiation pressure may be recovered from accurate angles-data alone, if the collected measurements span a sufficiently long period of time so as to make the non-conservative mismodeling effects noticeable. However, for relatively short data arcs, this effect is weak and thus the temporal brightness of the resident space object can be used in concert with the angles data to exploit the fused sensitivity to both space object characteristics and associated trajectory, the very same ones which drive the non-conservative dynamic effects. Recovering these characteristics and trajectories with sufficient accuracy is shown in this proposal, where the characteristics are inherent in unique space object models.
Objectives
Figure 1 MMAE Process
Figure 2 MMAE with Five RSO Models
The objectives of this work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. This work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.
Research
Shape estimation is an important issue in the observation of RSOs, because the shape influences the dynamics of the object and may provide valuable information on the object’s origin or intent. There exists a number of methods for estimating the shape of an object. These methods vary in the sensor type used, technique used to resolve shape, and effective ranges for proper shape resolution. Radar-based methods have been extensively used for shape estimation, which include radar cross-sectioning approaches and range Doppler interferometry. These techniques were first developed in the field of planetary radar astronomy to estimate the shape of natural satellites, but then were later applied to the imaging of artificial Earth orbiting satellites. These methods are limited by the RSO size and distance. RSOs can be imaged in low-Earth orbits that are much larger in the dimension than the wavelength of the radar signal. To image RSOs smaller and farther than these ranges requires very powerful radar devices, making these economically unattractive.
Laser radar-based (LADAR) methods have also been used to estimate the shape of RSOs. LADAR provides a three-dimensional scan of the object, which can resolve shape geometry at ranges of 1 km, returning a cloud of points of the measured relative position of an object. DiMatteo [1] used LADAR scans to perform a least squares fit of the LADAR returns to previously assembled point cloud models to estimate the shape of an RSO. Licther [2] developed a filter approach to simultaneously estimate dynamic states, geometric shape, and mass model parameters of a satellite using multiple observations with LADAR sensors. In Ref. [2] a probabilistic map of the RSO is constructed using a sensor uncertainty model and the dynamics experienced by the RSO to estimate the shape of the same. Using well modeled dynamical relationships of the RSO provides enhancements to be implemented within a filter architecture in this shape estimate approach.
Resolved images have been used to estimate the size and shape of satellites as well. These methods work either directly with the pixels of the images or are used to identify features of the RSO. Features, such as corners, edges and markers, are located and tracked temporally to estimate higher level motion and the structure of the ridged body. The feature-based methods rely on continuously identifying and tracking higher level traits of the RSO by using a Kalman filter to estimate feature location and motion parameters. Although these methods estimate the motion of features they do not by themselves provide a detailed estimate of the shape of the object and only give a sparse set of feature points of the object. Pixel-based methods rely on pixel-level information, and use the shading, texture and optical flow of the images to estimate the shape of an object at each time step using a monocular camera. Since these methods rely on pixel-level computations they typically involve very high-dimensional states and therefore are very computationally expensive. These methods are also very sensitive to pixel-level detail and are easily corrupted by unpredictable light intensities, reflective material and wrinkled surfaces. They require high resolution of the object to resolve meaningful shape estimates, and therefore are only effective for space-based sensors and or high resolution ground-based telescopes.
Some powerful ground-based telescopes, like the Air Force Maui Optical and Supercomputing (AMOS) site Advance Electro-Optical System (AEOS), can resolve RSOs such as Hubble Space Telescope and the International Space Station to very high detail, but most objects are too small and or too distant (making them dim) to lend themselves to ground-based resolved imaging. For example operational RSOs in geosynchronous orbits and “micro” and “nano” satellites are too small to be resolved using ground-based optical observations. Angular measurements of these smaller objects are still made to provide their coordinates as they traverse the sky. Although the amount of light collected from these objects is small, information can still be extracted from these data which can be used to resolve their shapes.
Light curves (the RSO temporal brightness) have also been used to estimate the shape for an object. Light curve approaches have been studied to estimate the shape and state of asteroids. Reference [3] used light curves and thermal emissions to recover the three-dimensional shape of an object assuming its orientation with respect to the observer is known. The benefits of using light curve data is that use of this approach is not limited to larger objects in lower orbits but can be applied to small and dim objects in higher orbits, such as geostationary. Here light curve data is considered for shape estimation as well as other intrinsic parameters such as material properties. Light curve data is useful because it provides a mechanism to estimate both position and attitude, as well as the respective rates.
There are several aspects of using light curve data (temporal photometry) that make it particularly advantageous for object detection, identification and tracking. Light curve data are the time-varying sensor wavelength-dependent apparent magnitude of energy (e.g. photons) scattered (reflected) off of an object along the line-of-sight to an observer. Because the apparent magnitude of the RSO is a function of its size, orientation, and surface material properties, one or more of these characteristics should be recoverable from the photometric data. This can aid in the detection and identification of an RSO after a catalog of spacecraft data with material properties is developed, and may also prove to be powerful for never-seen-before objects. Determining the material properties of an object can also give insight into its surface instrumentation and equipment, i.e. solar panels or painted aluminum.
There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.
Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.
Preliminary results for shape estimation of the approach are shown in Ref. [5]. For the development of the measured light curve data a six-faceted RSO is used. Five shapes are tested in a multiple hypothesis approach to assess the performance of the method. Results from the MMAE solution are shown in Figure 2. The solution shows that the approach is viable by identifying the correct shape. This provides a basis for optimism but much more work needs to be done. This includes: 1) using more complex shape models in the shape model bank, 2) incorporating a generalized MMAE [6] approach to obtain faster convergence rates, 3) using multiband data to improve performance, and 4) extend the work to assess the observability of estimating other intrinsic properties, such as the spacecraft material properties.
References
[1] DiMatteo, J., Florakis, D., Weichbrod, A., and Milam, M., “Proximity Operations Testing with a Rotating and Translating Resident Space Object,” AIAA Guidance, Navigation and Control Conference, Aug. 2009, AIAA-2009-6293.
[2] Lichter, M. D. and Dubowsky, S., “State, Shape, and Parameter Estimation of Space Objects from Range Images,” Proceedings of Robotics: Science and Systems, June 2005.
[3] Calef, B., Africano, J., Birge, B., Hall, D., and Kervin, P., “Photometric Signature Inversion,” Proceedings of the International Society for Optical Engineering, Vol. 6307, Aug. 2006, Paper 11.
[4] Jah, M. and Madler, R., “Satellite Characterization: Angles and Light Curve Data Fusion for Spacecraft State and Parameter Estimation,” Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, Vol. 49, Wailea, Maui, HI, Sept. 2007.
[5] Linares, R., Crassidis, J.L., Jah, M.K., and Kim, H., “Astrometric and Photometric Data Fusion for Resident Space Object Orbit, Attitude, and Shape Determination Via Multiple-Model Adaptive Estimation,” AIAA Guidance, Navigation, and Control Conference, Toronto, CA, Aug. 2010, AIAA Paper #2010-8341.
[6] Alsuwaidan, B.N., Crassidis, J.L., and Cheng, Y., “Generalized Multiple-Model Adaptive Estimation Using an Autocorrelation Approach” IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, No. 3, July 2011, pp. 2138-2152.
Geometric integration employs a numerical method that preserves geometric or group properties of the exact differential equation solution trajectory.
Motivation
Space Object Cloud
One prevailing field in which this research is very pertinent is Space Situational Awareness (SSA). The U.S. Air Force is collecting data in order to catalogue Earth orbiting satellites, objects and debris. Accurate tracking of all Earth-orbiting objects is important since their presence can be extremely hazardous to current space missions as well as disruptive for any future mission. This danger can either be passive in the case of debris or active intentional threats. However, the data necessary to estimate the attitude of such objects is sparse as a result of the number of sensors available and the large number of objects in orbit. In particular, for objects in low-Earth orbit (LEO), observation windows may last only a few minutes and opportunities to obtain data are infrequent. As a result, an object’s attitude may often need to be propagated very accurately over long time intervals before an update is possible.
Truncation and Roundoff Error Tradeoff
In summary, the problem is that
there are an increasing number of space objects to track
sensor time per object is limited
many objects yield infrequent pass opportunities
Advanced estimation techniques require accurate integration during extended propagation intervals when limited observation data is available.
Objective: Employ a Lie group method developed by Crouch and Grossman for the numerical integration of a quaternion parameterized attitude. Its inherent ability to integrate along the unit hypersphere helps to minimize truncation errors while maintaining the quaternion unit norm constraint.
Findings
For small time-steps (< 1s) the CG geometric approach did not perform as well as classical Runge-Kutta (RK) methods. Geometric approaches require more calculations and in this step-size regime, roundoff error and machine precision dominate.
Significant improvement is observed using a fourth-order CG algorithm with larger time-steps (~> 1s). The quaternion norm constraint is maintained essentially to within machine precision and attitude errors are reduced by approximately two orders of magnitude.
Applications
High Fidelity Orbit Simulation
The results are particularly important for high fidelity attitude dynamics. Most perturbing forces, such as drag, solar radiation pressure, magnetic forces and gravity gradients, are a direct function of attitude. Attitude dynamics are much faster than orbital dynamics and therefore dictate the integration time-step in any simulator. Improvements made using a geometric integration method significantly increased accuracy at larger time-steps. The great computational cost of high fidelity models and long-term propagation intervals (days, weeks or months) is therefore reduced.
In applications involving satellite attribute estimation, the size, shape, surface materials and attitude may be unknown. Accurate attitude estimate propagation between measurement updates is essential. Falling well within the domain of SSA, satellite attribute estimation suffers from the same challenges: limited sensor time due to over-tasking, infrequent pass opportunities and longer propagation intervals. While sparse data must be used most effectively, attitude propagation between measurement updates must be as accurate as possible.
References
Andrle, M.S., and Crassidis, J.L., “Geometric Integration of Quaternions,” AIAA/AAS Astrodynamics Specialist Conference, Minneapolis, MN, Aug. 2012, AIAA Paper #2012-4421.
Research is being performed for vision-based attitude and position determination for formation flying applications using a newly-developed sensor by Dr. John L. Junkins employing Position Sensing Diodes to determine line-of-sight vectors to optical beacons.
The vision-based navigation (VISNAV) system comprises of an optical sensor of a new kind combined with specific light sources (beacons) in order to achieve a selective or “intelligent” vision. The sensor is made up of a Position Sensing Diode (PSD) placed in the focal plane of a wide angle lens. When the rectangular silicon area of the PSD is illuminated by energy from a beacon focused by the lens, it generates electrical currents in four directions that can be processed with appropriate electronic equipment. While the individual currents depend on the intensity of the light, their imbalances are weakly dependent on the intensity and are almost linearly proportional to the location of the centroid of the light beam in the PSD.
Spacecraft formation flying is an evolving technology with many possible applications, such as long baseline interferometry, stereographic imaging, synthetic apertures, and distinguishing spatial from temporal magnetospheric variations. A significant advantage of distributed spacecraft platforms over a single multifunctional spacecraft is that single point failures can be rectified through replacement of cheaper and smaller spacecraft to maintain mission capability, thus providing a more reliable and robust system. Many missions (in particular interferometry missions) rely on precise relative position and attitude knowledge in order to maintain mission requirements. To date, most research studies into determining relative positions and attitudes between vehicles have involved using the Global Positioning System (GPS), which restricts the spacecraft formation to near-Earth applications. An application of GPS-like technology to a deep space mission has been proposed, but this requires extensive hardware development and is subject to the generic GPS performance-limiting effects, including multipath, geometric dilution of precision, integer ambiguity resolution, and cycle slip. The main objective of the proposed research is to provide a novel, reliable, and autonomous relative navigation and attitude determination system, employing relatively simple electronic circuits with modest digital signal processing (DSP) requirements, and being fully independent of any external systems.
This work is sponsored by NASA-Goddard Space Flight Center. Results from research can be obtained from:
[1] Andrle, M.S., Hyun, B., Crassidis, J.L., and Linares, R., “Deterministic Relative Attitude Determination of Formation Flying Spacecraft,” AIAA/AAS Astrodynamics Specialist Conference, Honolulu, HI, Aug. 2008, AIAA Paper #2008-6934.
[2] Kim, S.-G., Crassidis, J.L., Cheng, Y., Fosbury, A.M., and Junkins, J.L., “Kalman Filtering for Relative Spacecraft Attitude and Position Estimation,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, Jan.-Feb. 2007, pp. 133-143.
[3] Banas, W.D., and Crassidis, J.L., “Micro-Arcsecond Line-of-Sight Filtered Performance for Spacecraft Formation Flying Paper Number,” AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO, Aug. 2006, AIAA Paper #2006-6530.
[4] Kim, S.-G., Crassidis, J.L., Cheng, Y., Fosbury, A.M., and Junkins, J.L., “Kalman Filtering for Relative Spacecraft Attitude and Position Estimation,” AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, Aug. 2005, AIAA Paper #2005-6087.
[5] Kappagantula, K., and Crassidis, J.L., “Linearizing Assumptions and Control Design for Spacecraft Formation Flying Maneuvers,” 18th International Symposium on Space Flight Dynamics, Munich, Germany, Oct. 2004, ESA SP-548.
[6] Yim, J.R., Crassidis, J.L., and Junkins, J.L., “Autonomous Orbit Navigation of Two Spacecraft System Using Relative Line of Sight Vector Measurements,” AAS Space Flight Mechanics Meeting, Maui, HI, Feb. 2004, AAS Paper #04-257.
[7] Sun, D., and Crassidis, J.L., “Observability Analysis of Six Degree of Freedom State Determination Using Vector Observations,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 25, No. 6, Nov.-Dec. 2002, pp. 1149-1157.
[8] Alonso, R., Du, J.-Y., Hughes, D., Junkins, J.L., and Crassidis, J.L., “Relative Navigation for Formation Flying of Spacecraft,” Proceedings of the Flight Mechanics Symposium, NASA-Goddard Space Flight Center, Greenbelt, MD, June 2001, pp. 115-129.
[9] Crassidis, J.L., Alonso, R., and Junkins, J.L., “Optimal Attitude and Position Determination from Line-of-Sight Measurements,” The Journal of the Astronautical Sciences, Vol. 48, Nos. 2-3, April-Sept. 2000, pp. 391-408.
[10] Yim, J.R., Crassidis, J.L., and Junkins, J.L., “Autonomous Orbit Navigation of Interplanetary Spacecraft,” AIAA Guidance, Navigation, and Control Conference, Denver, CO, Aug. 2000, AIAA Paper #00-3936.
[11] Alonso, R., Crassidis, J.L., and Junkins, J.L., “Vision-Based Relative Navigation for Formation Flying of Spacecraft,” AIAA Guidance, Navigation, and Control Conference, Denver, CO, Aug. 2000, AIAA Paper #00-4439.
Research is being performed to develop improved spacecraft attitude determination and control algorithms. In particular, robust algorithms are being sought that provide attitude information with a minimal complement of attitude sensors. Also, research is being performed to improve the accuracy of existing hardware sensors through software modifications. Some current and past projects include:
This work is sponsored by NASA-Goddard Space Flight Center. Results from research can be obtained from:
[1] Crassidis, J.L., Cheng, Y., and Nebelecky, C.K., “Decentralized Attitude Estimation Using a Quaternion Covariance Intersection Approach,” AAS F. Landis Markley Astronautics Symposium, Cambridge, MD, June-July 2008, AAS Paper #2008-284.
[2] Markley, F.L., Cheng, Y., Crassidis, J.L., and Oshman, Y., “Averaging Quaternions,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, July-Aug. 2007, pp. 1193-1196.
[3] Crassidis, J.L., Markley, F.L., and Cheng, Y., “A Survey of Nonlinear Attitude Estimation Methods,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, Jan.-Feb. 2007, pp. 12-28.
[4] Kumar, A., and Crassidis, J.L., “Colored-Noise Kalman Filter for Vibration Mitigation of Position/Attitude Estimation Systems,” AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, Aug. 2007, AIAA Paper #2007-6516.
[5] Lam, Q., and Crassidis, J.L., “Evaluation of a Multiple Model Adaptive Estimation for Space Vehicle’s Enhanced Navigation Solution,” AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, Aug. 2007, AIAA Paper #2007-6816.
[6] Cole, C.L., and Crassidis, J.L., “Fast Star Pattern Recognition Using Spherical Triangles,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 1, Jan.-Feb. 2006, pp. 64-71.
[7] Cheng, Y., Crassidis, J.L., and Markley, F.L., “Attitude Estimation for Large Field-of-View Sensors,” The Journal of the Astronautical Sciences, Vol. 54, Nos. 3-4, July-Dec. 2006, pp. 433-448.
[8] Crassidis, J.L., Lai, K.-L., and Harman, R.R. “Real-Time Attitude-Independent Three-Axis Magnetometer Calibration,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, Jan.-Feb. 2005, pp. 115-120.
[9] Crassidis, J.L., and Cole, C.L., “Fast Star Pattern Recognition using Spherical Triangles,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Providence, RI, Aug. 2004, AIAA Paper #2004-5389.
[10] Cheng, Y., and Crassidis, J.L., “Particle Filtering for Sequential Spacecraft Attitude Estimation,” AIAA Guidance, Navigation, and Control Conference, Providence, RI, Aug. 2004, AIAA Paper #2004-5337.
[11] Crassidis, J.L., and Markley, F.L., “Unscented Filtering for Spacecraft Attitude Estimation,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4, July-Aug. 2003, pp. 536-542.
[12] Crassidis, J.L., Lai, K.-L., and Harman, R.R., “Real-Time Attitude-Independent Three-Axis Magnetometer Calibration,” Flight Mechanics Symposium, NASA-Goddard Space Flight Center, Greenbelt, MD, Oct. 2003, NASA CP-2003-212246.
[13] Lai, K.-L., Crassidis, J.L., and Harman, R.R., “In-Space Spacecraft Alignment Calibration Using the Unscented Filter,” AIAA Guidance, Navigation, and Control Conference, Austin, TX, Aug. 2003, AIAA Paper #2003-5563.
[14] Singla, P., Crassidis, J.L., and Junkins, J.L., “Spacecraft Angular Rate Estimation Algorithms for Star Tracker-Based Attitude Determination,” 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico, Feb. 2003, AAS Paper # 03-191.
[15] Sun, D., and Crassidis, J.L., “Observability Analysis of Six Degree of Freedom State Determination Using Vector Observations,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 25, No. 6, Nov.-Dec. 2002, pp. 1149-1157.
[16] Crassidis, J.L., “Angular Velocity Determination Directly from Star Tracker Measurements,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 25, No. 6, Nov.-Dec. 2002, pp. 1165-1168.
[17] Kim, J.-R., and Crassidis, J.L., “Robust Spacecraft Attitude Control Using Model-Error Control Synthesis,” AIAA Guidance, Navigation, and Control Conference, Monterey, CA, Aug. 2002, AIAA Paper #02-4576.
[18] Singla, P., Griffith, D.T., Crassidis, J.L., and Junkins, J.L., “Attitude Determination and Autonomous On-Orbit Calibration of Star Tracker for GIFTS Mission,” AAS/AIAA Space Flight Mechanics Meeting, San Antonio, TX, Jan. 2002, AAS Paper #02-101.
[19] Crassidis, J.L., Alonso, R., and Junkins, J.L., “Optimal Attitude and Position Determination from Line-of-Sight Measurements,” The Journal of the Astronautical Sciences, Vol. 48, Nos. 2-3, April-Sept. 2000, pp. 391-408.
[20] Crassidis, J.L., Vadali, S.R., and Markley, F.L., “Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers,” AIAA Journal of Guidance, Control and Dynamics, Vol. 23, No. 3, May-June 2000, pp. 564-566.
[21] Yim, J.R., Crassidis, J.L., and Junkins, J.L., “Autonomous Orbit Navigation of Interplanetary Spacecraft,” AIAA Guidance, Navigation, and Control Conference, Denver, CO, Aug. 2000, AIAA Paper #00-3936.
[22] Crassidis, J.L., and Markley, F.L., “Nonlinear Predictive Control of Spacecraft,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 20, No. 6, Nov.-Dec. 1997, pp. 1096-1103.
[23] Crassidis, J.L., and Markley, F.L., “A Minimum Model Error Approach for Attitude Estimation,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 20, No. 6, Nov.-Dec. 1997, pp. 1241-1247.
[24] Crassidis, J.L., and Markley, F.L., “Predictive Filtering for Attitude Estimation Without Rate Sensors,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 20, No. 3, May-June 1997, pp. 522-527.
[25] Crassidis, J.L., and Markley, F.L., “A Predictive Attitude Determination Algorithm,” Proceedings of the Flight Mechanics/Estimation Theory Symposium, NASA-Goddard Space Flight Center, Greenbelt, MD, May 1997, pp. 249-263.
[25] Crassidis, J.L., Markley, F.L., Kyle, A.M., and Blackman, K., “Attitude Determination Designs for the GOES Spacecraft,” Proceedings of the SPIE International Symposium on Optical Science, Engineering, and Instrumentation, Denver, CO, Vol. 2812, Aug. 1996, Paper #74.
[27] Crassidis, J.L., and Markley, F.L., “Attitude Estimation Using Modified Rodrigues Parameters,” Proceedings of the Flight Mechanics/Estimation Theory Symposium, NASA-Goddard Space Flight Center, Greenbelt, MD, May 1996, pp. 71-83.
[28] Crassidis, J.L., Andrews, S.F., Markley, F.L., and Ha, K., “Contingency Designs for Attitude Determination of TRMM,” Proceedings of the Flight Mechanics/Estimation Theory Symposium, NASA-Goddard Space Flight Center, Greenbelt, MD, May 1995, pp. 419-433.
Determining the extent and location of leaks on the International Space Station (ISS) is vital to maintain the operational status and safety of the station. The first indication of a leak on the ISS will likely be a drop in internal pressure. However, the gas leaving the station will likely cause a reaction force. Research is being performed with Dr. Srinivas R. Vadali to develop tools to determine approximate locations and sizes of ISS leaks based on measurements from the attitude determination system. The research has two specific goals:
Determine force and torque inputs from ISS attitude measurements
Quantify size and location of leaks from the determined forces and torques
The second item may have multiple solutions. Therefore additional information, such as hatch closures, will be incorporated into the overall system tool in order to help reject spurious solutions.
This work was sponsored by United Space Alliance. Results from research can be obtained from:
[1] Kim, J.-W., Crassidis, J.L., Vadali, S.R., and Dershowitz, A.L., “International Space Station Leak Localization Using Attitude Response Data ,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 5, Sept.-Oct. 2006, pp. 1041-1050.
[2] Kim, J.-W., Crassidis, J.L., Vadali, S.R., and Dershowitz, A.L., “International Space Station Leak Localization Using Vent Torque Estimation,” 55th International Astronautical Conference, Vancouver, BC, Oct. 2004, IAC-04-A.4.10.
[3] Kim, J.-W., Crassidis, J.L., Vadali, S.R., and Dershowitz, A.L., “International Space Station Leak Localization Using Attitude Disturbance Estimation,” IEEE Aerospace Conference, Big Sky, MT CA, March 2003, IEEEAC Paper #1391.
[4] Kim, J.-W., Crassidis, J.L., Vadali, S.R., and Dershowitz, A.L., “ISS Leak Localization Using Attitude Response,” AIAA Guidance, Navigation, and Control Conference, Montreal, CA, Aug. 2001, AIAA Paper #01-4272.
