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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 NTRS1991

A spatial disorientation predictor device to enhance pilot situational awareness regarding aircraft attitude

An effort was initiated at the Armstrong Aerospace Medical Research Laboratory (AAMRL) to investigate the improvement of the situational awareness of a pilot with respect to his aircraft's spatial orientation. The end product of this study is a device to alert a pilot to potentially disorienting situations. Much like a ground collision avoidance system (GCAS) is used in fighter aircraft to alert the pilot to 'pull up' when dangerous flight paths are predicted, this device warns the pilot to put a higher priority on attention to the orientation instrument. A Kalman filter was developed which estimates the pilot's perceived position and orientation. The input to the Kalman filter consists of two classes of data. The first class of data consists of noise parameters (indicating parameter uncertainty), conflict signals (e.g. vestibular and kinesthetic signal disagreement), and some nonlinear effects. The Kalman filter's perceived estimates are now the sum of both Class 1 data (good information) and Class 2 data (distorted information). When the estimated perceived position or orientation is significantly different from the actual position or orientation, the pilot is alerted.

Chelette, T. L.↗

DOE OSTI2020

Distributed PV generation estimation using multi‐rate and event‐driven Kalman kriging filter

Not Available

14 SOLAR ENERGY↗

NASA NTRS1974

A self-reorganizing digital flight control system for aircraft

This paper presents a design method for digital self-reorganizing control systems which is optimally tolerant of failures in aircraft sensors. The functions of this system are accomplished with software instead of the popular and costly technique of hardware duplication. The theoretical development, based on M-ary hypothesis testing, results in a bank of M Kalman filters operating in parallel in the failure detection logic. A moving window of the innovations of each Kalman filter drives the detection logic to decide the failure state of the system. The detection logic also selects the optimal state estimate (for control logic) from the bank of Kalman filters. The design process is applied to the design of a self-reorganizing control system for a current configuration of the space shuttle orbiter at Mach 5 and 120,000 feet. The failure detection capabilities of the system are demonstrated using a real-time simulation of the system with noisy sensors.

Montgomery, R. C.↗

DOE OSTI2020

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows, but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data and the trained model can be retrained effectively due to power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging AI-friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

42 ENGINEERING↗

NASA NTRS1973

Filtering theory applied to orbit determination

Modifications to the extended Kalman filter and the Jazwinski filter are made and compared with the classical extended Kalman filter in applications to orbit determination using real data. The results show that with the kind of data available today, the application of filtering theories in this field presents many problems.

Torroglosa, V.↗

NASA NTRS2011

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

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

Calhoun, Philip C.↗

NASA NTRS1987

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.

Vathsal, S.↗

NASA NTRS2002

Observer-Based Magnetic Bearing Controller Developed for Aerospace Flywheels

A prototype of a versatile, observer-based magnetic bearing controller for aerospace flywheels was successfully developed and demonstrated on a magnetic bearing test rig (see the photograph) and an actual flywheel module. The objective of this development included a fast, yet low risk, control development process, and a robust, high-performance controller for a large variety of flywheels. This required a good system model, an efficient development procedure, and a model-based controller that addressed the key problems associated with flywheel and bearing imbalance, sensor error, and vibration. The model used in this control development and tuning procedure included the flexible rotor dynamics and motor-induced vibrations. Such a model was essential for low-risk scheduling of speed-dependent control parameters and for reliable evaluation of novel control strategies. The successfully tested control prototype utilized an extended Kalman filter to estimate the true rotor principal-axis motion from the raw sensor position feedback. For control refinement, the extended Kalman filter also estimated and eliminated the combined effects of mass-imbalance and sensor runouts from the input data. A key advantage of the design based on the extended Kalman filter is its ability to accurately estimate both the rotor's principal-axis position and gyroscopic rates with the least amount of phase lag. This is important for control parameter scheduling to dampen the gyroscopic motions. Because of large uncertainties in the magnetic bearing and imbalance characteristics, this state-estimation scheme alone is insufficient for containing the rotor motion within the desired 1-mil excursion radius. A nonlinear gain adjustment based on an estimation of the principal-axis orbit size was needed to provide a coarse (nonoptimal), but robust, control of the orbit growth. Control current minimization was achieved with a (steepest gradient) search of synchronous errors in the principal-axis position input data. Actual flywheel tests of this observer-based controller (developed entirely in-house) at the NASA Glenn Research Center showed that the model correctly predicted the rotor orbit growth as a function of rotational speed, and it demonstrated the capability of gain adjustments to arrest this growth. Data from these tests on an actual flywheel module spun to 26,000 rpm proved that the controller was able to contain the shaft motion to within much less than 0.5 mils of radial excursion with axis currents less than 300 mA in root-mean-square estimate. The test speed range was limited because of thermal expansion concerns for this particular flywheel unit, not because of any deficiency in the controller. Simulations for this unit indicated that the controller should be robust up to its top operating speed of 60,000 rpm. Aside from these important achievements, and most significantly, it took less than 1 week to adapt this controller from the simple test rig to the actual flywheel and to demonstrate full five-axis levitation and control. This demonstration showed that both the controller and the model-based development and tuning framework are easily adaptable to a wide range of rotors and bearing configurations and, hence, are capable of reducing design risks and costs for many future flywheel technology developments.

Le, Dzu K.↗

NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗

NASA NTRS2001

GPS/Magnetometer Based Satellite Navigation and Attitude Determination

In recent years algorithms were developed for orbit, attitude and angular-rate determination of Low Earth Orbiting (LEO) satellites. Those algorithms rely on measurements of magnetometers, which are standard, relatively inexpensive, sensors that are normally installed on every LEO satellite. Although magnetometers alone are sufficient for obtaining the desired information, the convergence of the algorithms to the correct values of the satellite orbital parameters, position, attitude and angular velocity is very slow. The addition of sun sensors reduces the convergence time considerably. However, for many LEO satellites the sun data is not available during portions of the orbit when the spacecraft (SC) is in the earth shadow. It is here where the GPS space vehicles (SV) can provide valuable support. This is clearly demonstrated in the present paper. Although GPS measurements alone can be used to obtain SC position, velocity, attitude and angular-rate, the use of magnetometers improve the results due to the synergistic effect of sensor fusion. Moreover, it is possible to obtain these results with less than three SVs. In this paper we introduce an estimation algorithm, which is a combination of an Extended Kalman Filter (EKF) and a Pseudo Linear Kalman Filter (PSELIKA).

Deutschmann, Julie↗

NASA NTRS2006

An Empirical Comparison between Two Recursive Filters for Attitude and Rate Estimation of Spinning Spacecraft

The advantages of inducing a constant spin rate on a spacecraft are well known. A variety of science missions have used this technique as a relatively low cost method for conducting science. Starting in the late 1970s, NASA focused on building spacecraft using 3-axis control as opposed to the single-axis control mentioned above. Considerable effort was expended toward sensor and control system development, as well as the development of ground systems to independently process the data. As a result, spinning spacecraft development and their resulting ground system development stagnated. In the 1990s, shrinking budgets made spinning spacecraft an attractive option for science. The attitude requirements for recent spinning spacecraft are more stringent and the ground systems must be enhanced in order to provide the necessary attitude estimation accuracy. Since spinning spacecraft (SC) typically have no gyroscopes for measuring attitude rate, any new estimator would need to rely on the spacecraft dynamics equations. One estimation technique that utilized the SC dynamics and has been used successfully in 3-axis gyro-less spacecraft ground systems is the pseudo-linear Kalman filter algorithm. Consequently, a pseudo-linear Kalman filter has been developed which directly estimates the spacecraft attitude quaternion and rate for a spinning SC. Recently, a filter using Markley variables was developed specifically for spinning spacecraft. The pseudo-linear Kalman filter has the advantage of being easier to implement but estimates the quaternion which, due to the relatively high spinning rate, changes rapidly for a spinning spacecraft. The Markley variable filter is more complicated to implement but, being based on the SC angular momentum, estimates parameters which vary slowly. This paper presents a comparison of the performance of these two filters. Monte-Carlo simulation runs will be presented which demonstrate the advantages and disadvantages of both filters.

Harman, Richard R.↗

NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗

NASA NTRS2001

Kalman plus weights: a time scale algorithm

KPW is a time scale algorithm that combines Kalman filtering with the basic time scale equation (BTSE). A single Kalman filter that estimates all clocks simultaneously is used to generate the BTSE frequency estimates, while the BTSE weights are inversely proportional to the white FM variances of the clocks. Results from simulated clock ensembles are compared to previous simulation results from other algorithms.

time time scales stability Kalman filtering↗

NASA NTRS1975

Fixed memory least squares filtering

Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.

Bierman, G. J.↗

NASA NTRS2006

On the Extraction of Angular Velocity from Attitude Measurements

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping.

Bar-Itzhack, I. Y.↗

NASA NTRS2006

Rigid Body Rate Inference from Attitude Variation

Bar-Itzhack, I. Y.↗

NASA NTRS2001

State Estimation for K9

The goal of 'Estimate' is to take advantage of attitude information to produce better pose while staying flexible and robust. Currently there are several instruments that are used for attitude: gyros, inclinometers, and compasses. However, precise and useful attitude information cannot come from one instrument. Integration of rotational rates, from gyro data for example, would result in drift. Therefore, although gyros are accurate in the short-term, accuracy in the long term is unlikely. Using absolute instruments such as compasses and inclinometers can result in an accurate measurement of attitude in the long term. However, in the short term, the physical nature of compasses and inclinometers, and the dynamic nature of a mobile platform result in highly volatile and therefore useless data. The solution then is to use both absolute and relative data. Kalman Filtering is known to be able to combine gyro and compass/inclinometer data to produce stable and accurate attitude information. Since the model of motion is linear and the data comes in as discrete samples, a Discrete Kalman Filter was selected as the core of the new estimator. Therefore, 'Estimate' can be divided into two parts: the Discrete Kalman Filter and the code framework.

Xu, Ru-Gang↗