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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Distribution System State Estimation Using a Multiple Iteration Extended Kalman Filter Approach

To support the operation of modern distribution systems, operators require real-time visibility into system states. Due to a lack of measurements and unbalanced operation, the state estimation in distribution systems is challenging as compared to transmission systems. This paper proposes the utilization of a Multiple Iteration - Extended Kalman Filter based approach for the distribution system state estimation. This modified version of the baseline extended Kalman filter iterates over the update step multiple times thereby reducing the estimation error. The proposed algorithm along with the auxiliary algorithms such as bad data detection is integrated into a co-simulation environment. Case studies show that the proposed state estimation method can result in a lesser estimation error as compared to the baseline approach.

Bhatti, Bilal Ahmad↗
NASA NTRS1993

Kalman filter estimation of attitude and gyro bias with the QUEST observation model

The loss function for the Wahba attitude estimation problem employs unit vector observations with scalar weights. It is usually associated with the QUEST observation model, where the actual sensor noise is assumed the same for all components of the observed vector, regardless of the position in the field of view. The QUEST model has the great advantage of being sensor-independent except for the scalar parameter that characterizes the sensor errors. Although efficient algorithms for solving the Wahba problem exist, extending these algorithms to estimate gyro biases or sensor alignments has had mixed success. However, it is straightforward to estimate bias and alignment parameters with a Kalman filter. This paper investigates the use of an extended Kalman filter for the attitude and gyro bias that incorporates the QUEST observation model, to be referred to as the Unit Vector Filter (UVF). The UVF results are compared with those from a more conventional filter, the Real-Time Sequential Filter (RTSF), for which the residual is the two-dimensional projection of the unit vector onto the plane perpendicular to the sensor boresight. The RTSF is similar in design to that used by Multimission Modular Spacecraft for onboard attitude determination. An apparent obstacle to the use of unit vectors as measurements is their singular noise covariance matrix. Shuster has shown that this problem should not affect filter performance. The UVF and RTSF are tested using actual flight data from the Extreme Ultraviolet Explorer (EUVE). It is found that these filters generate nearly identical attitude and gyro bias estimates, thus validating the use of unit vectors and the QUEST noise model.

Sedlak, J.↗
NASA NTRS1991

Fusion techniques using distributed Kalman filtering for detecting changes in systems

A comparison is made of the performances of two detection strategies that are based on different data fusion techniques. The strategies detect changes in a linear system. One detection strategy involves combining the estimates and error covariance matrices of distributed Kalman filters, generating a residual from the used estimates, comparing this residual to a threshold, and making a decision. The other detection strategy involves a distributed decision process in which estimates from distributed Kalman filters are used to generate distributed residuals which are compared locally to a threshold. Local decisions are made and these decisions are then fused into a global decision. The performances of each of these detection schemes are compared, and it is concluded that better performance is achieved when local decisions are made and then fused into a global decision.

Belcastro, Celeste M.↗
NASA NTRS1990

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Park, K. C.↗
NASA NTRS2001

Attitude Representations for Kalman Filtering

The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.

Markley, F. Landis↗
NASA NTRS2007

Tracking and Data Relay Satellite (TDRS) Orbit Estimation Using an Extended Kalman Filter

Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.

Ward, Douglas T.↗
NASA NTRS2002

A Wavelet Based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.

Auger, Ludovic↗
NASA NTRS2003

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

Tangborn, Andrew↗
NASA NTRS2007

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis↗
NASA NTRS2008

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis↗
NASA NTRS2002

Recent Flight Results of the TRMM Kalman Filter

The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls the roll and pitch attitude based on the Earth Sensor Assembly (ESA) output. TRMM's nominal orbit altitude was 350 km, until raised to 402 km to prolong mission life. During the boost, the ESA experienced a decreasing signal to noise ratio, until sun interference at 393 km altitude made the ESA data unreliable for attitude determination. At that point, the backup attitude determination algorithm, an extended Kalman filter, was enabled. After the boost finished, TRMM reacquired its nadir-pointing attitude, and continued its mission. This paper will briefly discuss the boost and the decision to turn on the backup attitude determination algorithm. A description of the extended Kalman filter algorithm will be given. In addition, flight results from analyzing attitude data and the results of software changes made onboard TRMM will be discussed. Some lessons learned are presented.

Andrews, Stephen F.↗
NASA NTRS2015

Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter

Orbit determination (OD) analysis results are presented for the Lunar Reconnaissance Orbiter (LRO) using a commercially available Extended Kalman Filter, Analytical Graphics' Orbit Determination Tool Kit (ODTK). Process noise models for lunar gravity and solar radiation pressure (SRP) are described and OD results employing the models are presented. Definitive accuracy using ODTK meets mission requirements and is better than that achieved using the operational LRO OD tool, the Goddard Trajectory Determination System (GTDS). Results demonstrate that a Vasicek stochastic model produces better estimates of the coefficient of solar radiation pressure than a Gauss-Markov model, and prediction accuracy using a Vasicek model meets mission requirements over the analysis span. Modeling the effect of antenna motion on range-rate tracking considerably improves residuals and filter-smoother consistency. Inclusion of off-axis SRP process noise and generalized process noise improves filter performance for both definitive and predicted accuracy. Definitive accuracy from the smoother is better than achieved using GTDS and is close to that achieved by precision OD methods used to generate definitive science orbits. Use of a multi-plate dynamic spacecraft area model with ODTK's force model plugin capability provides additional improvements in predicted accuracy.

Orbit Determination↗
NASA NTRS2005

An Extension to the Kalman Filter for an Improved Detection of Unknown Behavior

The use of Kalman filter (KF) interferes with fault detection algorithms based on the residual between estimated and measured variables, since the measured values are used to update the estimates. This feedback results in the estimates being pulled closer to the measured values, influencing the residuals in the process. Here we present a fault detection scheme for systems that are being tracked by a KF. Our approach combines an open-loop prediction over an adaptive window and an information-based measure of the deviation of the Kalman estimate from the prediction to improve fault detection.

Benazera, Emmanuel↗
NASA NTRS1991

A simulation study of turbofan engine deterioration estimation using Kalman filtering techniques

Deterioration of engine components may cause off-normal engine operation. The result is an unecessary loss of performance, because the fixed schedules are designed to accommodate a wide range of engine health. These fixed control schedules may not be optimal for a deteriorated engine. This problem may be solved by including a measure of deterioration in determining the control variables. These engine deterioration parameters usually cannot be measured directly but can be estimated. A Kalman filter design is presented for estimating two performance parameters that account for engine deterioration: high and low pressure turbine delta efficiencies. The delta efficiency parameters model variations of the high and low pressure turbine efficiencies from nominal values. The filter has a design condition of Mach 0.90, 30,000 ft altitude, and 47 deg power level angle (PLA). It was evaluated using a nonlinear simulation of the F100 engine model derivative (EMD) engine, at the design Mach number and altitude over a PLA range of 43 to 55 deg. It was found that known high pressure turbine delta efficiencies of -2.5 percent and low pressure turbine delta efficiencies of -1.0 percent can be estimated with an accuracy of + or - 0.25 percent efficiency with a Kalman filter. If both the high and low pressure turbine are deteriorated, the delta efficiencies of -2.5 percent to both turbines can be estimated with the same accuracy.

Lambert, Heather H.↗
NASA NTRS2006

Flexible Generation of Kalman Filter Code

Domain-specific program synthesis can automatically generate high quality code in complex domains from succinct specifications, but the range of programs which can be generated by a given synthesis system is typically narrow. Obtaining code which falls outside this narrow scope necessitates either 1) extension of the code generator, which is usually very expensive, or 2) manual modification of the generated code, which is often difficult and which must be redone whenever changes are made to the program specification. In this paper, we describe adaptations and extensions of the AUTOFILTER Kalman filter synthesis system which greatly extend the range of programs which can be generated. Users augment the input specification with a specification of code fragments and how those fragments should interleave with or replace parts of the synthesized filter. This allows users to generate a much wider range of programs without their needing to modify the synthesis system or edit generated code. We demonstrate the usefulness of the approach by applying it to the synthesis of a complex state estimator which combines code from several Kalman filters with user-specified code. The work described in this paper allows the complex design decisions necessary for real-world applications to be reflected in the synthesized code. When executed on simulated input data, the generated state estimator was found to produce comparable estimates to those produced by a handcoded estimator

Richardson, Julian↗