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NASA NTRS2005

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.↗

NASA NTRS2005

NASA Tech Briefs, May 2005

Topics covered include: Fastener Starter; Multifunctional Deployment Hinges Rigidified by Ultraviolet; Temperature-Controlled Clamping and Releasing Mechanism; Long-Range Emergency Preemption of Traffic Lights; High-Efficiency Microwave Power Amplifier; Improvements of ModalMax High-Fidelity Piezoelectric Audio Device; Alumina or Semiconductor Ribbon Waveguides at 30 to 1,000 GHz; HEMT Frequency Doubler with Output at 300 GHz; Single-Chip FPGA Azimuth Pre-Filter for SAR; Autonomous Navigation by a Mobile Robot; Software Would Largely Automate Design of Kalman Filter; Predicting Flows of Rarefied Gases; Centralized Planning for Multiple Exploratory Robots; Electronic Router; Piezo-Operated Shutter Mechanism Moves 1.5 cm; Two SMA-Actuated Miniature Mechanisms; Vortobots; Ultrasonic/Sonic Jackhammer; Removing Pathogens Using Nano-Ceramic-Fiber Filters; Satellite-Derived Management Zones; Digital Equivalent Data System for XRF Labeling of Objects; Identifying Objects via Encased X-Ray-Fluorescent Materials - the Bar Code Inside; Vacuum Attachment for XRF Scanner; Simultaneous Conoscopic Holography and Raman Spectroscopy; Adding GaAs Monolayers to InAs Quantum-Dot Lasers on (001) InP; Vibrating Optical Fibers to Make Laser Speckle Disappear; Adaptive Filtering Using Recurrent Neural Networks; and Applying Standard Interfaces to a Process-Control Language.

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NASA NTRS2015

Cauchy Drag Estimation For Low Earth Orbiters

Recent work on minimum variances estimators based on Cauchy distributions appear relevant to orbital drag estimation. Samples form Cauchy distributions which are part of a class of heavy-tailed distributions, are characterized by long stretches of fairly small variation, punctuated by large variations that are many times larger than could be expected from a Gaussian. Such behavior can occur when solar storms perturb the atmosphere. In this context, the present work describes an embedding of the scalar Idan-Speyer Cauchy Estimator to estimate density corrections, within an Extended Kalman Filter that estimates the state of a low Earth orbiter. In contrast to the baseline Kalman approach, the larger formal errors of the present approach fully and conservatively bound the predictive error distribution, even in the face of unanticipated density disturbances of hundreds of percent.

Low Earth↗

NASA NTRS2021

Sequential Wald Test Employing a Constrained Filter Bank: Application to Spacecraft Conjunctions

A binary Wald sequential probability ratio test that uses the residuals of norm-inequality-constrained Kalman filters for its likelihood ratio may be employed for a class of compound hypothesis tests on non-stationary systems. The hypotheses concern an inequality constraint on the norm of some elements of the system state. Each of two filters minimizes the summed-squares of its estimation errors subject to one or the other direction of the inequality constraint. This solution is motivated by the problem of satellite conjunction assessment, wherein the constraint concerns the close approach distance between two space objects. The outcome of the test can inform decisions concerning risk mitigation maneuvers.

J. Russell Carpenter↗

NASA NTRS1984

Proceedings of the Sixteenth Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting

The effects of ionospheric and tropospheric propagation on time and frequency transfer, advances in the generation of precise time and frequency, time transfer techniques and filtering and modeling were among the topics emphasized. Rubidium and cesium frequency standard, crystal oscillators, masers, Kalman filters, and atomic clocks were discussed.

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NASA NTRS1997

Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗

NASA NTRS2012

Functional Near Infrared Spectroscopy: Watching the Brain in Flight

Functional Near Infrared Spectroscopy (fNIRS) is an emerging neurological sensing technique applicable to optimizing human performance in transportation operations, such as commercial aviation. Cognitive state can be determined via pattern classification of functional activations measured with fNIRS. Operational application calls for further development of algorithms and filters for dynamic artifact removal. The concept of using the frequency domain phase shift signal to tune a Kalman filter is introduced to improve the quality of fNIRS signals in realtime. Hemoglobin concentration and phase shift traces were simulated for four different types of motion artifact to demonstrate the filter. Unwanted signal was reduced by at least 43%, and the contrast of the filtered oxygenated hemoglobin signal was increased by more than 100% overall. This filtering method is a good candidate for qualifying fNIRS signals in real time without auxiliary sensors

Harrivel, Angela↗

NASA NTRS2012

Functional Near Infrared Spectroscopy: Watching the Brain in Flight

Functional Near Infrared Spectroscopy (fNIRS) is an emerging neurological sensing technique applicable to optimizing human performance in transportation operations, such as commercial aviation. Cognitive state can be determined via pattern classification of functional activations measured with fNIRS. Operational application calls for further development of algorithms and filters for dynamic artifact removal. The concept of using the frequency domain phase shift signal to tune a Kalman filter is introduced to improve the quality of fNIRS signals in real-time. Hemoglobin concentration and phase shift traces were simulated for four different types of motion artifact to demonstrate the filter. Unwanted signal was reduced by at least 43%, and the contrast of the filtered oxygenated hemoglobin signal was increased by more than 100% overall. This filtering method is a good candidate for qualifying fNIRS signals in real time without auxiliary sensors.

Harrivel, Angela↗

NASA NTRS1983

Simulation and analysis of differential global positioning system for civil helicopter operations

A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.

Denaro, R. P.↗

NASA NTRS1987

Simplified solution for a class of fading memory filters

A fading memory filter is a least squares estimator (LSE) that applies an exponentially decaying weight to past measurements. When compared with a standard Kalman filter, its key advantages are asymptotic stability and reduced sensitivity to modeling errors. This paper derives a simple solution for a class of fading memory filters, resulting in a reduction in computational complexity. Steady state filter solutions are obtained for second- and third-order filters used in a global positioning system (GPS) receiver for high dynamic vehicles.

Statman, Joseph I.↗

NASA NTRS1972

Application of advanced filtering methods to the determination of the interplanetary orbit of Mariner '71.

This paper presents the results of the applications of advanced filtering methods to the determination of the interplanetary orbit of the Mariner '71 spacecraft. The advanced techniques are specific extensions of the Kalman filter. The special problems associated with applying these techniques are discussed and the particular algorithmic implementations are outlined. The advanced methods are compared against the weighted least squares filters of conventional application. The results reveal that relatively simple advanced filter configurations yield solutions superior to those of the conventional methods when applied to the Mariner '71 radio measurements.

Rourke, K. H.↗

NASA NTRS1988

Nonlinear modeling and estimation of slew induced structural deformations

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformation are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, T. A. W., III↗

NASA NTRS1991

Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, Thomas A. W., III↗

NASA NTRS1972

Nonlinear and adaptive estimation techniques in reentry

The development and testing of nonlinear and adaptive estimators for reentry (e.g. space shuttle) navigation and model parameter estimation or identification are reported. Of particular interest is the identifcation of vehicle lift and drag characteristics in real time. Several nonlinear filters were developed and simulated. Adaptive filters for the real time identification of vehicle lift and drag characteristics, and unmodelable acceleration, were also developed and tested by simulation. The simulations feature an uncertain system environment with rather arbitrary model errors, thus providing a definitive test of estimator performance. It was found that nonlinear effects are indeed significant in reentry trajectory estimation and a nonlinear filter is demonstrated which successfully tracks through nonlinearities without degrading the information content of the data. Under the same conditions the usual extended Kalman filter diverges and is useless. The J-adaptive filter is shown to successfully track errors in the modeled vehicle lift and drag characteristics. The same filter concept is also shown to track successfully through rather arbitrary model errors, including lift and drag errors, vehicle mass errors, atmospheric density errors, and wind gust errors.

Jazwinski, A. H.↗

NASA NTRS1972

Control system estimation and design for aerospace vehicles with time delay

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Allgaier, G. R.↗

NASA NTRS1987

Range filtering for sequential GPS receivers with external sensor augmentation

The filtering of the satellite range and range-rate measurements from single channel sequential Global Positioning System receivers is usually done with an extended Kalman filter which has state variables defined in terms of an orthogonal navigation reference frame. An attractive suboptimal alternative is range-domain filtering, in which the individual satellite measurements are filtered separately before they are combined for the navigation solution. The main advantages of range-domain filtering are decreased processing and storage requirements and simplified tuning. Several range filter mechanization alternatives are presented, along with an innovative approach for combining the filtered range-domain quantities to determine the navigation state estimate. In addition, a method is outlined for incorporating measurements from auxiliary sensors such as altimeters into the navigation state estimation scheme similarly to the satellite measurements. A method is also described for incorporating inertial measurements into the navigation state estimator as a process driver.

Paielli, Russell↗

NASA NTRS1987

Range filtering for sequential GPS receivers

Paielli, Russell↗

NASA NTRS1983

Hardware verification of distributed/adaptive control

Adaptive control techniques are studied for their future application to the control of large space structures, where uncertain or changing parameters may destabilize standard control system designs. The approach used is to examine an extended Kalman filter estimator, in which the state vector is augmented with the unknown parameters. The associated Riccatti equation is linearized about the case of exact knowledge of the parameters. By assuming that parameter variations occur slowly, the filter complexity is reduced further yet. Simulations on a two degree-of-freedom oscillator demonstrate the parameter-tracking capability of the filter, and an implementation on the JPL Flexible Beam Facility using an incorrect model shows the adaptive filter/optimal control to be stable where a standard Kalman filter/optimal control design is unstable.

Eldred, D. B.↗