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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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This paper describes the derivation of a continuous matrix differential equation for the SIRF filter, and the development of a computer algorithm to implement this filter.
Four mathematical models of linear first and second order high pass washout filters were analyzed. These models were Euler's Integration, Zero-Order Hold, Bilinear Transformation, and Second-Order Adams-Bashforth Integration. Bode responses for each model at various sample rates were compared to the continuous filter response. Higher sample rates produced Bode responses approaching the continuous response and the Bilinear Transformation model produced the best responses over the frequency spectrum and sample rates. Pole location analysis of each model in the z-plane showed the Bilinear Transformation and Zero-Order Hold models gave stable poles regardless of time step size, whereas the other models did not display stable poles. A near constant gain error over the entire frequency spectrum was discovered in the Zero-Order Hold cases and a correction gain was calculated for the first-order high-pass filter case.
A method is presented for the signature analysis of pulses by reconstructing in the time domain the shape of the pulse prior to its passing through the measurement system. This deconvolution technique is first evaluated using an idealized system and analytical pulse models and is shown to provide improved results. An experimental situation is then treated; system-component models are developed for the digitizer, tape recorder, filter, transducer and mechanical structure. To accommodate both calibration results and manufacturer's data, and to provide stable mathematical models entails considerable effort: some 30 parameters must be identified to model this system - which is still a substantial approximation - albeit of very high order. Experimental pulses generated by a ball drop, spark discharge and a tearing crack are then deconvoluted 'back through' the system as modeled, using this technique. These results are compared and indicate (a) that consistent shapes may be expected from a given type of source and (b) that some sources can be identified with greater clarity using the deconvolution approach.
The GRACE (Gravity Recovery And Climate Experiment) mission is designed to make global, highly accurate measurements of the Earth's gravity field with high spatial resolution. Ancillary GPS occultation measurements are also to be carried out for atmospheric monitoring. In the dual-1-way biased ranging of this mission, the range between two satellites separated by 100 to 200 km in nearly polar, coplanar, circular orbits, is measured to very high precision, to within an additive constant, through the exchange of K- and Ka-band sinusoidal signals. Such biased ranging data, along with GPS L-band range and phase data, can be processed and fit over successive multiday intervals to obtain accurate estimates of the Earth's gravity field. This report approximately models and analyzes this process, from the generation of the RF signals at the two satellites through the extraction of the geopotential. The steps include generation of the transmitted signals, processing the received signals to extract high-rate baseband phase, carrying out a dual-1-way combination of baseband phase to extract high-rate biased range for each band, combining K- and Ka-band ranges to correct for the ionosphere effect, and processing the resulting high-rate biased range values to extract three types of reduced-rate observables: biased range, range rate and range acceleration. The version of dual-1-way biased ranging developed by this report improves upon previous versions in a number of ways: highly accurate satellite-timetag corrections derived from concurrent GPS data, better baseband phase extraction using highly digital processing, highly accurate USO-rate calibration derived from concurrent GPS data, an improved method for extracting high-rate biased range from baseband phase, improved filtering for extracting reduced- rate observables from high-rate biased range, and parallel extraction of three observable types.
Optimum filter for aircraft inertial navigator and radio position fix data mixing using mathematical model of error propagation
The theoretical aspects of an orbit determination filter that incorporates ground-system error sources as model parameters for use in interplanetary navigation are presented in this article. This filter, which is derived from sequential filtering theory, allows a systematic treatment of errors in calibrations of transmission media, station locations, and earth orientation models associated with ground-based radio metric data, in addition to the modeling of the spacecraft dynamics. The discussion includes a mathematical description of the filter and an analytical comparison of its characteristics with more traditional filtering techniques used in this application. The analysis in this article shows that this filter has the potential to generate navigation products of substantially greater accuracy than more traditional filtering procedures.
A computer program estimates the relative positions and orientations of two space structures from data on the angular positions and distances of fiducial objects on one structure as measured by a target tracking electronic camera and laser range finders on another structure. The program is written specifically for determining the relative alignments of two antennas, connected by a long truss, deployed in outer space from a space shuttle. The program is based partly on transformations among the various coordinate systems involved in the measurements and on a nonlinear mathematical model of vibrations of the truss. The program implements a Kalman filter that blends the measurement data with data from the model. Using time series of measurement data from the tracking camera and range finders, the program generates time series of data on the relative position and orientation of the antennas. A similar program described in a prior NASA Tech Briefs article was used onboard for monitoring the structures during flight. The present program is more precise and designed for use on Earth in post-flight processing of the measurement data to enable correction, for antenna motions, of scientific data acquired by use of the antennas.
On August 5th 2012, The Mars Science Laboratory entry vehicle successfully entered Mars atmosphere and landed the Curiosity rover on its surface. A Kalman filter approach has been implemented to reconstruct the entry, descent, and landing trajectory based on all available data. The data sources considered in the Kalman filtering approach include the inertial measurement unit accelerations and angular rates, the terrain descent sensor, the measured landing site, orbit determination solutions for the initial conditions, and a new set of instrumentation for planetary entry reconstruction consisting of forebody pressure sensors, known as the Mars Entry Atmospheric Data System. These pressure measurements are unique for planetary entry, descent, and landing reconstruction as they enable a reconstruction of the freestream atmospheric conditions without any prior assumptions being made on the vehicle aerodynamics. Moreover, the processing of these pressure measurements in the Kalman filter approach enables the identification of atmospheric winds, which has not been accomplished in past planetary entry reconstructions. This separation of atmosphere and aerodynamics allows for aerodynamic model reconciliation and uncertainty quantification, which directly impacts future missions. This paper describes the mathematical formulation of the Kalman filtering approach, a summary of data sources and preprocessing activities, and results of the reconstruction.
The paper describes a simulation of a filtering analysis which yields radiation distributions, measured by a wide-field-of-view radiometer on board an earth satellite, on a scale smaller than the field of view of the instrument. Mathematical models are developed to represent an orbiting wide-field-of-view radiometer to provide simulated measurement data. The simulated measurements are analyzed by a data inversion technique to obtain estimates of the radiation heat fluxes at the top of the atmosphere. By comparing the estimated field to a real radiation field, the effects of directional model errors and sampling strategies are revealed.
In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.
A discrete gust model has been designed which includes an expression for the number of times per unit time thy wind exceeds a specific value. This expression, based on Rice's (1944, 1945) number-of-crossings model, assumes that the yearly mean wind speed is averaged over a period of 10 minutes to 1 (one) hour. Vertical and lateral coherence functions are the basis for a mathematical filter which isolates atmospheric disturbances of a characteristic size (e. g., those which would completely engulf a rotor). Predictions are calculated usising the given definition of cut-off frequency, then they are compared with actual data, showing that the model is reliable. The expression is provided in a format such that it may be used for engineering design calculations.
An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.
ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.
Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.
A key drawback to estimating geodetic and geodynamic parameters over time based on satellite laser ranging (SLR) observations is the inability to accurately model all the forces acting on the satellite. Errors associated with the observations and the measurement model can detract from the estimates as well. These 'model errors' corrupt the solutions obtained from the satellite orbit determination process. Dynamical models for satellite motion utilize known geophysical parameters to mathematically detail the forces acting on the satellite. However, these parameters, while estimated as constants, vary over time. These temporal variations must be accounted for in some fashion to maintain meaningful solutions. The primary goal of this study is to analyze the feasibility of using a sequential process noise filter for estimating geodynamic parameters over time from the Laser Geodynamics Satellite (LAGEOS) SLR data. This evaluation is achieved by first simulating a sequence of realistic LAGEOS laser ranging observations. These observations are generated using models with known temporal variations in several geodynamic parameters (along track drag and the J(sub 2), J(sub 3), J(sub 4), and J(sub 5) geopotential coefficients). A standard (non-stochastic) filter and a stochastic process noise filter are then utilized to estimate the model parameters from the simulated observations. The standard non-stochastic filter estimates these parameters as constants over consecutive fixed time intervals. Thus, the resulting solutions contain constant estimates of parameters that vary in time which limits the temporal resolution and accuracy of the solution. The stochastic process noise filter estimates these parameters as correlated process noise variables. As a result, the stochastic process noise filter has the potential to estimate the temporal variations more accurately since the constraint of estimating the parameters as constants is eliminated. A comparison of the temporal resolution of solutions obtained from standard sequential filtering methods and process noise sequential filtering methods shows that the accuracy is significantly improved using process noise. The results show that the positional accuracy of the orbit is improved as well. The temporal resolution of the resulting solutions are detailed, and conclusions drawn about the results. Benefits and drawbacks of using process noise filtering in this type of scenario are also identified.
Beginning with the mathematical prediction of planetary orbits in the early seventeenth century up through the most recent developments in sensor fusion methods, many techniques have emerged that can be employed on the problem of endo and exoatmospheric trajectory estimation. Although early methods were ad hoc, the twentieth century saw the emergence of many systematic approaches to estimation theory that produced a wealth of useful techniques. The broad genesis of estimation theory has resulted in an equally broad array of mathematical principles, methods and vocabulary. Among the fundamental ideas and methods that are briefly touched on are batch and sequential processing, smoothing, estimation, and prediction, sensor fusion, sensor fusion architectures, data association, Bayesian and non Bayesian filtering, the family of Kalman filters, models of the dynamics of the phases of a rocket's flight, and asynchronous, delayed, and asequent data. Along the way, a few trajectory estimation issues are addressed and much of the vocabulary is defined.
Advanced method of acoustic pulse reflectivity testing developed for use in determining sizes and locations of failures within structures. Used to detect breaks in electrical transmission lines, detect faults in optical fibers, and determine mechanical properties of materials. In method, structure vibrationally excited with acoustic pulse (a "ping") at one location and acoustic response measured at same or different location. Measured acoustic response digitized, then processed by finite-impulse-response (FIR) filtering algorithm unique to method and based on acoustic-wave-propagation and -reflection properties of structure. Offers several advantages: does not require training, does not require prior knowledge of mathematical model of acoustic response of structure, enables detection and localization of multiple failures, and yields data on extent of damage at each location.
The purpose of this document is to demonstrate the use of the Extended Kalman Filter as a tool for battery state estimation and the estimation of battery state of charge. The mathematical details based on the equivalent circuit model are presented followed by an electrochemical engineering model. A simplified first-order model is used to demonstrate the procedure followed by second and third-order models. Next a simplified electrochemistry model is presented along with observer development. State observability is calculated for the simpler equivalent circuit models and the simplified electrochemistry model. An outline of the battery model parameter identification method is presented, and model performance based on experimental and flight data is demonstrated.