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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Real time estimation of ship motions using Kalman filtering techniques

The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering techniques, for application in VTOL aircraft landing. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.

Triantafyllou, M. S.↗
NASA NTRS1991

An extended Kalman filter for spinning spacecraft attitude estimation

An extended Kalman filter for real-time ground attitude estimation of a gyro-less spinning spacecraft was developed and tested. The filter state vector includes the angular momentum direction, phase angle, inertial nutation angle, and inertial and body nutation rates. The filter solves for the nutating three-axis attitude and accounts for effects due to principle axes offset from the body axes. The attitude is propagated using the kinematics of a rigid body symmetric about the principle spin axis; disturbance torques are assumed to be small. Filter updates consist only of the measured angles between celestial objects (Sun, Earth, etc.) and the nominal spin axis, and the times these angles were measured. Both simulated data and real data from the Dynamics Explorer -A (DE-A) spacecraft were used to test the filter; the results are presented. Convergence was achieved rapidly from a wide range of a priori state estimates, and sub-degree accuracy was attained. Systematic errors affecting the solution accuracy are discussed, as are the results of an attempt to solve for sensor measurement angle biases in the state vector.

Baker, David F.↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Kalman filter estimation of human pilot-model parameters

The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters.

Schiess, J. R.↗
NASA NTRS1980

UDU/T/ covariance factorization for Kalman filtering

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Thornton, C. L.↗
NASA NTRS1977

Numerical comparison of Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗
NASA NTRS1976

Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗
DOE OSTI2021

Decentralized Data-Driven Estimation of Generator Rotor Speed and Inertia Constant Based on Adaptive Unscented Kalman Filter

This paper proposes an online decentralized and data-driven method for synchronous generator rotor speed and inertia estimation. First, an analytical relationship between the generator terminal voltage/current phasors and its internal rotor speed is derived using the Thevenin equivalent. The parameters of the latter are obtained via a recursive estimator, which allows us to estimate the generator's internal rotor speed from voltage/current phasors without the need for any generator information. Second, we reformulate the equivalent swing equation into the Kalman filter form, which enables us to use a priori-estimated internal rotor speed along with measured real and reactive power injections to obtain an estimate of the inertia for each online synchronous generator. This is achieved through an adaptive unscented Kalman filter. We demonstrate that the use of terminal bus frequency to approximate the rotor speed for inertia estimation by existing methods leads to large estimation biases/errors. Numerical simulations carried out on the IEEE 39-bus and Texas 2000-bus systems reveal that our proposed method is consistently more accurate than existing methods. Moreover, our proposed method is insensitive to both the type and location of system disturbances, and it is robust to different levels of measurement noise.

bus frequency↗
NASA NTRS2002

Attitude Error Representations for Kalman Filtering

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

Markley, F. Landis↗
NASA NTRS1998

A Low Cost Approach to Simultaneous Orbit, Attitude, and Rate Estimation Using an Extended Kalman Filter

An innovative approach to autonomous attitude and trajectory estimation is available using only magnetic field data and rate data. The estimation is performed simultaneously using an Extended Kalman Filter, a well known algorithm used extensively in onboard applications. The magnetic field is measured on a satellite by a magnetometer, an inexpensive and reliable sensor flown on virtually all satellites in low earth orbit. Rate data is provided by a gyro, which can be costly. This system has been developed and successfully tested in a post-processing mode using magnetometer and gyro data from 4 satellites supported by the Flight Dynamics Division at Goddard. In order for this system to be truly low cost, an alternative source for rate data must be utilized. An independent system which estimate spacecraft rate has been successfully developed and tested using only magnetometer data or a combination of magnetometer data and sun sensor data, which is less costly than a gyro. This system also uses an Extended Kalman Filter. Merging the two systems will provide an extremely low cost, autonomous approach to attitude and trajectory estimation. In this work we provide the theoretical background of the combined system. The measurement matrix is developed by combining the measurement matrix of the orbit and attitude estimation EKF with the measurement matrix of the rate estimation EKF, which is composed of a pseudo-measurement which makes the effective measurement a function of the angular velocity. Associated with this is the development of the noise covariance matrix associated with the original measurement combined with the new pseudo-measurement. In addition, the combination of the dynamics from the two systems is presented along with preliminary test results.

Deutschmann, Julie↗
NASA NTRS1988

Recursive least squares estimation and Kalman filtering by systolic arrays

One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).

Chen, M. J.↗
NASA NTRS1994

An improved conscan algorithm based on a Kalman filter

Conscan is commonly used by DSN antennas to allow adaptive tracking of a target whose position is not precisely known. This article describes an algorithm that is based on a Kalman filter and is proposed to replace the existing fast Fourier transform based (FFT-based) algorithm for conscan. Advantages of this algorithm include better pointing accuracy, continuous update information, and accommodation of missing data. Additionally, a strategy for adaptive selection of the conscan radius is proposed. The performance of the algorithm is illustrated through computer simulations and compared to the FFT algorithm. The results show that the Kalman filter algorithm is consistently superior.

Eldred, D. B.↗
DOE OSTI2020

Speeding up particle track reconstruction using a parallel Kalman filter algorithm

One of the most computationally difficult problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material effects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filter-based methods for highly parallel, many-core SIMD architectures that are now prevalent in high-performance hardware. In this paper, we discuss the design and performance of the improved tracking algorithm, referred to as mkFit. A key piece of the algorithm is the Matriplex library, containing dedicated code to optimally vectorize operations on small matrices. The physics performance of the mkFit algorithm is comparable to the nominal CMS tracking algorithm when reconstructing tracks from simulated proton-proton collisions within the CMS detector. We study the scaling of the algorithm as a function of the parallel resources utilized and find large speedups both from vectorization and multi-threading. mkFit achieves a speedup of a factor of 6 compared to the nominal algorithm when run in a single-threaded application within the CMS software framework.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1999

A Self-Tuning Kalman Filter for Autonomous Navigation using the Global Positioning System (GPS)

Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.

Truong, S. H.↗
NASA NTRS1999

A Self-Tuning Kalman Filter for Autonomous Navigation Using the Global Positioning System (GPS)

Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS (Global Positioning Systems) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.

Truong, Son H.↗
NASA NTRS1984

State estimation Kalman filter using optical processings Noise statistics known

Reference is made to a study by Casasent et al. (1983), which gave a description of a frequency-multiplexed acoustooptic processor and showed how it was capable of performing all the individual operations required in Kalman filtering. The data flow and organization of all required operations however, were not detailed in that study. Consideration is given here to a simpler Kalman filter state estimation problem. Equally spaced time-sampled intervals (k times T sub s, with k the iterative time index) are assumed. It is further assumed that the system noise vector w and the measurement noise vector v are uncorrelated and Gaussian distributed and that the noise statistics (Q and R) and the system model (Phi, Gamma, H) are known. The error covariance matrix P and the extrapolated error covariance matrix M can thus be precomputed and the Kalman gain matrix K sub k can be precomputed and stored for each input time sample.

Jackson, J.↗