MER entry, descent, and landing reconstruction using an unscented Kalman filter
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MER EDL reconstruction unscented Kalman filter↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Cooperative Navigation within UAV Swarms via Centralized-Unscented Kalman Filtering to Reduce C-SWAP Requirements
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Jaramillo, Eryn↗
Cooperative Navigation within UAV Swarms via Centralized-Unscented Kalman Filtering to Reduce C-SWAP Requirements
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Jaramillo, Eryn↗
Comparison of Nonlinear Filtering Techniques for Lunar Surface Roving Navigation
Leading up to the Apollo missions the Extended Kalman Filter, a modified version of the Kalman Filter, was developed to estimate the state of a nonlinear system. Throughout the Apollo missions, Potter's Square Root Filter was used for lunar navigation. Now that NASA is returning to the Moon, the filters used during the Apollo missions must be compared to the filters that have been developed since that time, the Bierman-Thornton Filter (UD) and the Unscented Kalman Filter (UKF). The UD Filter involves factoring the covariance matrix into UDUT and has similar accuracy to the Square Root Filter; however it requires less computation time. Conversely, the UKF, which uses sigma points, is much more computationally intensive than any of the filters; however it produces the most accurate results. The Extended Kalman Filter, Potter's Square Root Filter, the Bierman-Thornton UD Filter, and the Unscented Kalman Filter each prove to be the most accurate filter depending on the specific conditions of the navigation system.
Kimber, Lemon↗
Comparison of EKF and UKF for Robotic Missions to Mars
The batched Kalman lter works well for a wide variety of orbit determination scenarios but requires linearized approximations to the underlying dynamical system. Furthermore, implementation depends on the computation of partial derivatives for all measurements and parameters used in the lter, a non-trivial task even when analytical derivations are possible. To address these limitations, many extensions and modi - cations to the linear Kalman lter have been proposed over the years since Kalman's initial publication. Our investigation examines two popular variants of the Kalman lter, namely the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), within the context of spacecraft missions to Mars. The EKF relies on the same mathematical basis as the classic version of the lter, however it sequentially updates the linearization as the ltering process is conducted. In contrast, the UKF is built upon the unscented transform which samples the nearby solution space and numerically propagates perturbed trajectories as part of the update / estimation process. We assess the performance of the ltering algorithms under a variety of mission scenarios with the goal of establishing decision criteria for which implementation to use under di ering circumstances.
Ely, Todd↗
Exploration of an Adaptive Routine for Battery Modeling
The purpose of this document is to explore the use of adaptive routines in battery modeling. The adaptive routines consist of real-time state estimators combined with battery parameter model components that are adjusted in real-time as battery data becomes available. Several aspects are explored. It is shown that model parameter identification is possible for simple battery models using available input/output data measurements. The online system identification used is recursive least squares. Model identification may be combined with a state observer such as the extended Kalman filter or the unscented Kalman filter to form an adaptive model combined with state estimation. However, such a combination is found to be problematic due to uncertainty, observability and stability issues. This paper is organized as follows. Section 1 introduces adaptive routines and possible roles they play in battery modeling. In Section 2 real-time parameter identification is described with results based on battery data. Section 3 reviews various state estimators and results using a simple battery model. In Section 4 parameter identification and state estimation are combined to form an adaptive routine. Finally, in Section 5 conclusions are drawn and future work is suggested.
Adaptive↗
Iterated Sigma-Point Kalman Filtering for Trajectory Reconstruction
Two second-order Kalman filtering methods are added to the New Statistical Trajec-tory Estimation Program (NewSTEP). The two filters are of the class of Sigma-Point Kalman Filters, namely the Unscented Kalman Filter and the Divided Difference Filter. Both filters are implemented with an iterative measurement update step. Results from simulation test case and a flight data test case are provided to show the filter performance. The results indicate that the new second-order filters pro-duce trajectory estimates with reduced uncertainties when compared to the existing first-order filtering method.
Sophia Vedvik↗
A Comparison of Filter-based Approaches for Model-based Prognostics
Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the stateparameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.
prognostics↗
Filtering in Hybrid Dynamic Bayesian Networks
We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the 2 - T i e Slice DBN (2T-DBN) from [Koller & Lerner, 20001 to model fault detection in a watertank system. In [Koller & Lerner, 20001 a generic Particle Filter (PF) is used for inference. We extend the experiment and perform approximate inference using The Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). Furthermore, we combine these techniques in a 'non-strict' Rao-Blackwellisation framework and apply it to the watertank system. We show that UKF and UKF in a PF framework outperfom the generic PF, EKF and EKF in a PF framework with respect to accuracy and robustness in terms of estimation RMSE. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. We also show that the choice of network structure is very important for the performance of the generic PF and the EKF algorithms, but not for the UKF algorithms. Furthermore, we investigate the influence of data noise in the water[ank simulation. Theory and implementation is based on the theory presented.
Andersen, Morten Nonboe↗
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.↗
Adaptable Iterative and Recursive Kalman Filter Schemes
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
Zanetti, Renato↗
Mars Aerobraking Spacecraft State Estimation by Processing Inertial Measurement Unit Data
Aerobraking is an efficient technique for orbit adjustment of planetary spacecraft, such as Magellan (Venus), Mars Global Surveyor, and Mars Odyssey. Determination of the vehicle state during the aerobraking phase has conventionally been performed using only radiometric tracking data prior to and following the atmospheric drag pass. This approach is sufficiently accurate and timely to meet current mission operational requirements; however, it is expensive in terms of ground support and leads to delayed results because ofthe need for post-drag pass data. This research presents a new approach to estimation of the vehicle state during the atmospheric pass that sequentially incorporates observations from an Inertial Measurement Unit (IMU) and models of the vehicle and environment. The approach, called Inertial Measurements for Aerobraking Navigation (IMAN), is shown to perform at a level comparable to the conventional methods in terms of navigation accuracy and superior to them in terms of availability of the results immediately after completion ofthe pass. Furthermore, the research shows that IMAN can be used to reliably predict subsequent periapsis times and locations over all aerobraking regimes. IMAN also yields accurate peak dynamic pressure and heating rates, critical for a successful corridor control strategy, comparable to navigation team reconstructed values. This research also provides the first instance of the utilization of the Unscented Kalman Filter for the purpose of estimating an actual spacecraft trajectory arc about another planet.
Unscented Kalman Filter↗
Improving SGP4 Orbit Determination with New State Estimation Algorithm
The Simplified General Perturbations 4 Model (SGP4) is a well-known tool for performing satellite orbit determination. However, uncertainties and inaccuracies in the initial state inputs (required by SGP4) degrade the performance of the propagator. We present a new state estimation algorithm that allows for independent computation of these initial inputs using Unscented Kalman Filtering and GPS data from a satellite. The algorithm is tested on real flight data and demonstrates a notable performance improvement over the standard method of orbit determination using SGP4.
97 MATHEMATICS AND COMPUTING↗
Nonlinear consider covariance analysis using a sigma-point filter formulation
The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.
covariance↗
Filtering in Hybrid Dynamic Bayesian Networks
We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).
Andersen, Morten Nonboe↗
Design of a supervisory control system for autonomous operation of advanced reactors
Advanced reactors to be deployed in the coming decades will face deregulated energy markets, and may adopt flexible operation to boost profitability. To aid in the transition from baseload to flexible operation paradigm, autonomous operation is sought. This work focuses on the control aspect of autonomous operation. Specifically, a hierarchical control system is designed to support constraint enforcement during routine operational transients. Within the system, data-driven modeling, physics-based state observation, and classical control algorithms are integrated to provide an adaptable and robust solution. A 320 MW Fluoride-cooled High-temperature Pebble-bed Reactor is the design basis for demonstrating the proposed control system. The hierarchical control system consists of a supervisory layer and low-level layer. The supervisory layer receives requests to change the system's operating conditions (e.g., the current reactor power to meet a load -follow), and accepts or rejects them based on constraints that have been assigned. Constraints are issued to keep the plant within an optimal operating region. The low-level layer interfaces with the actuators of the system to fulfill requested changes, while maintaining tracking and regulation duties. Further, to accept requests at the supervisory layer, the Reference Governor algorithm was adopted. To model the dynamics of the reactor, a system identification algorithm, Dynamic Mode Decomposition, was utilized. To estimate the evolution of process variables that cannot be directly measured (e.g., the propagation of delayed neutron precursors), the Unscented Kalman Filter, incorporating a nonlinear model of nuclear dynamics, was adopted. The composition of these algorithms led to a numerical demonstration of constraint enforcement during a 40% power drop transient (at a rate of 5 %/min). Uncontrolled secondary-side temperatures were successfully constrained. Adaptability of the proposed system was demonstrated by modifying the constraint values, and enforcing them during the transient. Robustness was also demonstrated by enforcing constraints under noisy environments.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Minimum entropy filtering for a single output non-Gaussian stochastic system using state transformation
This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.
42 ENGINEERING↗
Economic Analysis of Condition-Monitoring-Based Predictive Maintenance in Power Plants under Market Elasticity
Condition-monitoring-based predictive maintenance can increase the power plant availability by preventing forced outages. However, the actual on-stream time depends on market elasticity and dynamics, which are affected by cost and penetration of other power generation technologies. This paper develops a systematic approach for the economic analysis of investment in condition monitoring technologies with due consideration of market elasticity. Focus is on corrosion monitoring in coal-fired power plants (CFFPs) since corrosion in high-temperature coal-fired boilers is a leading cause of equipment failure. Investment in sensor networks for measuring corrosion and operating conditions like metal temperature and concentrations of O 2 and SO 2 is investigated. The unscented Kalman filter is used to estimate corrosion in the waterwall section of the boiler under multiple sensor networks. Electricity produced by CFPPs in the future in the U.S. due to changes in availability under market elasticity is studied. Sensitivity of the incremental net present value to factors like the number, type, and cost of sensors is analyzed.
Electrochemistry↗