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At least 325 records · Page 18

Identification of linear stochastic systems through projection filters

A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite-difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model.

Chen, Chung-Wen↗

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗

Motion estimation of objects in KC-135 microgravity

The simulated microgravity environment aboard a KC-135 aircraft flying along a parabolic trajectory was used to study the ability of an autonomous space robot to grasp a freely translating and rotating object. Since the KC-135 cabin environment and the instrumentation for the Extravehicular Activity Helper/Retriever (EVAHR) do not provide a practical intertial reference frame, estimators based on the extended Kalman filter algorithm were used to model the relative translational dynamics of the KC-135 and the EVAHR. The estimator algorithms require intensive mathematical computation and therefore, i860 real-time. Estimator design, implementation concerns, and issues specific to the KC-135 environment are discussed and the architecture of the KC-135 translational state estimator is depicted.

Hewgill, Lisa↗

On optimal filtering of GPS dual frequency observations without using orbit information

The concept of optimal filtering of observations collected with a dual frequency GPS P-code receiver is investigated in comparison to an approach for C/A-code units. The filter presented here uses only data gathered between one receiver and one satellite. The estimated state vector consists of a one-way pseudorange, ionospheric influence, and ambiguity biases. Neither orbit information nor station information is required. The independently estimated biases are used to form double differences where, in case of a P-code receiver, the wide lane integer ambiguities are usually recovered successfully except when elevation angles are very small. An elevation dependent uncertainty for pseudorange measurements was discovered for different receiver types. An exponential model for the pseudorange uncertainty was used with success in the filter gain computations.

Eueler, Hans-Juergen↗

Spline-based distributed system identification with application to large space antennas

A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.

Banks, H. T.↗

Venus gravity west of Beta Regio

Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography, on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km, if the surface material has a density of 2.6 g/cu cm. However, this is not a unique interpretation.

Goldberg, Z. M.↗

Algorithms for Autonomous GPS Orbit Determination and Formation Flying: Investigation of Initialization Approaches and Orbit Determination for HEO

This report summarizes the efforts to date in processing GPS measurements in High Earth Orbit (HEO) applications by the Colorado Center for Astrodynamics Research (CCAR). Two specific projects were conducted; initialization of the orbit propagation software, GEODE, using nominal orbital elements for the IMEX orbit, and processing of actual and simulated GPS data from the AMSAT satellite using a Doppler-only batch filter. CCAR has investigated a number of approaches for initialization of the GEODE orbit estimator with little a priori information. This document describes a batch solution approach that uses pseudorange or Doppler measurements collected over an orbital arc to compute an epoch state estimate. The algorithm is based on limited orbital element knowledge from which a coarse estimate of satellite position and velocity can be determined and used to initialize GEODE. This algorithm assumes knowledge of nominal orbital elements, (a, e, i, omega, omega) and uses a search on time of perigee passage (tau(sub p)) to estimate the host satellite position within the orbit and the approximate receiver clock bias. Results of the method are shown for a simulation including large orbital uncertainties and measurement errors. In addition, CCAR has attempted to process GPS data from the AMSAT satellite to obtain an initial estimation of the orbit. Limited GPS data have been received to date, with few satellites tracked and no computed point solutions. Unknown variables in the received data have made computations of a precise orbit using the recovered pseudorange difficult. This document describes the Doppler-only batch approach used to compute the AMSAT orbit. Both actual flight data from AMSAT, and simulated data generated using the Satellite Tool Kit and Goddard Space Flight Center's Flight Simulator, were processed. Results for each case and conclusion are presented.

Axelrad, Penina↗

Active Flutter Suppression Using Reduced-Order Modeling for Transonic Aeroservoelastic Control Law Development

In this paper, several aerodynamic reduced-order models (ROMs) are generated and coupled with structural models to form aeroelastic ROMs. The aerodynamic ROMs generated here include the effects of control surface motion and are appropriate for use in aeroservoelastic applications. Simple observer-based full-state feedback controllers were designed from these aeroelastic ROMs. Additionally, observer gain matrices were designed from and coupled to the aeroelastic ROMs. Each (linear) observer was then used to estimate the dynamics of a (nonlinear) stand-alone computational fluid-structure dynamics simulation. Then, using the estimated states and the full-state feedback controller, control surface commands were fed back into the computational fluid-structure dynamics simulation to successfully achieve active flutter suppression. The process, as well as some results, are presented in this paper.

Waite, Josiah M.↗

On attitude estimation schemes for fine-pointing control

This paper studies single-axis equations of motion that are applicable to a spacecraft or to a space experiment pointing assembly whose motion has been perfectly isolated from the carrier vehicle. It considers four state estimators for implementation in the control loop for a stellar observation experiment. The first three estimators are very general and do not make use of input torque in their prediction models, while the proposed fourth estimator utilizes this information. It is shown via closed-loop covariance analysis that the best achievable pointing performance with the best of the first three estimators is limited to about 0.125 arc-sec (rms) with the given rate-gyro and star-tracker inaccuracies. It is also shown that the fourth estimator has the capability of achieving a pointing performance far superior to the performance achievable using the first three estimators. The fourth estimator relies on the ability to accurately generate the desired control torque (i.e., low input noise).

Joshi, S. M.↗

A Battery Health Monitoring Framework for Planetary Rovers

Batteries have seen an increased use in electric ground and air vehicles for commercial, military, and space applications as the primary energy source. An important aspect of using batteries in such contexts is battery health monitoring. Batteries must be carefully monitored such that the battery health can be determined, and end of discharge and end of usable life events may be accurately predicted. For planetary rovers, battery health estimation and prediction is critical to mission planning and decision-making. We develop a model-based approach utilizing computaitonally efficient and accurate electrochemistry models of batteries. An unscented Kalman filter yields state estimates, which are then used to predict the future behavior of the batteries and, specifically, end of discharge. The prediction algorithm accounts for possible future power demands on the rover batteries in order to provide meaningful results and an accurate representation of prediction uncertainty. The framework is demonstrated on a set of lithium-ion batteries powering a rover at NASA.

prediction↗

Towards Autonomous Lunar Resource Excavation via Reinforcement Learning

To continue on a sustainable and flexible path, NASA needs to address the challenge of collecting and moving large amounts of regolith at the destination. NASA’s Regolith Advanced Surface Systems Operations Robot (RASSOR) is principally designed to mine and deliver regolith for In-Situ Resource Utilization (ISRU) processing. RASSOR’s design enables it to efficiently collect and deposit regolith, return collected material for processing, and myriad related ISRU activities. To reliably perform these operations on the lunar surface, RASSOR software and sensory systems need to be robust and maximize the information extracted from a reduced sensor payload. Herein, we present preliminary findings from the Intelligent Capabilities Enhanced RASSOR project. We created reduced-order simulation environments to develop autonomous trenching controllers via reinforcement learning and prototype state estimation architectures. The goal of reinforcement learning is for an agent to learn a policy (task strategy) through interactions with an environment. When the agent performs an action, a change occurs in environment state and a numerical reward is received which informs the agent whether the action performed was good or not. Since reinforcement learning algorithms learn through trial-and-error, a simulation is a desirable first environment for development and learning. We developed two simulations, the first is a 2D excavation simulation developed to facilitate parameter selection, and a 3D simulation developed using a game physics engine, to simulate simplified soil interactions and increase the fidelity of the dynamic models of the robotic agents. The development of this 3D simulation has enabled the training of additional sensing capabilities and research both at the granular mechanics and operations levels. We experimented with various virtual sensor payloads to identify a combination that enabled efficient excavation operation and learning. Our reward function is based on how much material is excavated per step. A penalty is also received for leaving the dig site and to smooth the acceleration of the drum arms. We implemented pseudo time-of-flight sensors to report distance from each drum to ground and the height above ground which was found to be more efficient than existing solutions. Our findings suggest that reinforcement learning for autonomous operations has learned viable trenching strategies within 3000 training episodes in our simplified 2D environment and helped identify desirable sensing capabilities, arrangements, and considerations such as the positioning of time-of-flight sensors. Future work includes expanding our simulation to more complex environments and scenarios, and transfer learning from simulation to RASSOR 2.0 hardware for deployment in the Regolith Test Bin at NASA's Kennedy Space Center.

rassor↗

Estimation in satellite control.

The use of estimators or observers is discussed as applied to satellite attitude control and the control of drag-free satellites. The practical problems of implementation are discussed, and the relative advantages of full and reduced state estimators are compared, particularly in terms of their effectiveness and bandwidth as filters. Three applications are used to illustrate the principles. They are: (1) a reaction wheel control system, (2) a spinning attitude control system, and (3) a drag-free satellite translational control system. Fixed estimator gains are shown to be adequate for these (and many other) applications. Our experience in the hardware realization of estimators has led to categorize the error sources in terms of those that improve with increased estimator gains and those that get worse with increased estimator gains.

Debra, D. B.↗

Starling Formation-Flying Optical Experiment: Initial Operations and Flight Results

This paper presents initial flight results for angles-only navigation of a swarm of small spacecraft, conducted during the Starling Formation-Flying Optical Experiment (StarFOX). StarFOX is one of four experiments aboard the NASA Starling mission, which consists of four CubeSats launched in July 2023. Angles-only methods apply inter-satellite bearing angles obtained by on-board cameras for navigation, increasing satellite autonomy and enabling new mission concepts. Nevertheless, prior flight demonstrations have only featured one observer and target and have relied upon a-priori target orbit knowledge for initialization, translational maneuvers to resolve target range, and external absolute orbit updates to maintain convergence. StarFOX overcomes these limitations by applying the angles-only Absolute and Relative Trajectory Measurement System (ARTMS), which integrates three novel algorithms. Image Processing detects and tracks multiple targets in images, using multi-hypothesis methods and domain-specific kinematic modeling, and computes target bearing angles. Batch Orbit Determination computes initial swarm orbit estimates from bearing angle batches, via iterative batch least squares and sampling of the weakly observable target range. Sequential Orbit Determination leverages an adaptive, efficient unscented Kalman filter with nonlinear models to refine swarm state estimates over time. Multi-observer measurements shared over an intersatellite link are seamlessly fused to enable robust absolute and relative orbit determination. Initial StarFOX experiments are the first demonstrations of autonomous angles-only navigation for a satellite swarm, including multi-target and multi-observer relative navigation; autonomous initialization of navigation for unknown targets; and simultaneous absolute and relative orbit determination. Relative navigation accuracy of 1% (single observer) and 0.2% (multi-observer) of the inter-satellite range is achieved under challenging measurement conditions. Results demonstrate promising performance with regards to ongoing StarFOX campaigns and the application of angles-only navigation to future distributed missions.

Relative Navigation↗

Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.

Hutsell, Steven T.↗

Parameter identification of linear discrete stochastic systems with time delays

An identification algorithm that uses the maximum likelihood technique to identify the unknown time delays, plant parameters, and noise covariances of linear discrete stochastic systems is presented. Cases of additive white noise and colored measurement noises are considered. The likelihood function is evaluated using either a minimum-variance (Kalman) filter or a minimal-order observer. The Kalman filter is used in the identification algorithm to provide minimum-variance estimates. The minimal-order observer is a lower-dimensional and computationally simpler filter, and is advantageous especially for systems with long delays. It provides a less optimal solution to the minimum-mean-square state estimation problem. The colored-noise observer algorithm has the disadvantage of having to compute an extra error covariance matrix of lower order.

Wong, E. C.↗

ICE-RASSOR: Intelligent Capabilities Enhanced Regolith Advanced Surface Systems Operations Robot

NASA’s Regolith Advanced Surface Systems Operations Robot (RASSOR) is principally designed to mine and deliver regolith for In-Situ Resource Utilization (ISRU)processing. RASSOR’s design enables it to efficiently collect and deposit regolith, return collected material for processing, and myriad related ISRU activities. To reliably perform these operations on the lunar surface, RASSOR software and sensory systems need to be robust and maximize the information extracted from a reduced sensor payload. Herein, we present preliminary findings from the Intelligent Capabilities Enhanced RASSOR project. We apply supervised learning using real data to estimate the soil mass collected without the need for mass flow rate monitors or other explicate sensing techniques. We also create a reduced-order simulation environment to develop autonomous trenching controllers via reinforcement learning and prototype state estimation architectures. Our initial results suggest that excavated regolith mass can be inferred within 2.9% RMS error of full scale, and reinforcement learning for autonomous operations has learned viable trenching strategies and helped identify desirable sensing capabilities, arrangements, and considerations. Future work includes regolith mass estimation during dynamic operation, expanding our simulation to more complex environments, and transfer learning from simulation to hardware.

machine learning↗