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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Biased estimation for dynamic systems.

Optimization and regulation of static and dynamic systems require good estimates of the states of the system model and the parameters of the model in the presence of input and measurement noise. A biased estimator is proposed as an alternative to the familiar best linear unbiased estimator. Depending on the value of a constant, this biased estimator can be made unbiased and is then identical to the best linear unbiased estimator, thus permitting additional freedom of choice in design and application. The sum of squared errors of this bs tmator can be less than the best linear unbiased case. An existence theorem is established and various properties are discussed.

Chang, J. W.↗
NASA NTRS2022

GEDI Launches a New Era of Biomass Inference from Space

Accurate estimation of aboveground forest biomass stocks is required to assess the impacts of land use changes such as deforestation and subsequent regrowth on concentrations of atmospheric CO 2 . The Global Ecosystem Dynamics Investigation (GEDI) is a lidar mission launched by NASA to the International Space Station in 2018. GEDI was specifically designed to retrieve vegetation structure within a novel, theoretical sampling design that explicitly quantifies biomass and its uncertainty across a variety of spatial scales. In this paper we provide the estimates of pan-tropical and temperate biomass derived from two years of GEDI observations. We present estimates of mean biomass densities at 1 km resolution, as well as estimates aggregated to the national level for every country GEDI observes, and at the sub-national level for the United States. For all estimates we provide the standard error of the mean biomass. These data serve as a baseline for current biomass stocks and their future changes, and the mission’s integrated use of formal statistical inference points the way towards the possibility of a new generation of powerful monitoring tools from space.

Ralph Dubayah↗
NASA NTRS1977

Failure detection and correction for turbofan engines

In this paper, a failure detection and correction strategy for turbofan engines is discussed. This strategy allows continuing control of the engines in the event of a sensor failure. An extended Kalman filter is used to provide the best estimate of the state of the engine based on currently available sensor outputs. Should a sensor failure occur the control is based on the best estimate rather than the sensor output. The extended Kalman filter consists of essentially two parts, a nonlinear model of the engine and up-date logic which causes the model to track the actual engine. Details on the model and up-date logic are presented. To allow implementation, approximations are made to the feedback gain matrix which result in a single feedback matrix which is suitable for use over the entire flight envelope. The effect of these approximations on stability and response is discussed. Results from a detailed nonlinear simulation indicate that good control can be maintained even under multiple failures.

Corley, R. C.↗
NASA NTRS1984

Liquidlike state of dense hydrogen

Some difficulties associated with estimates of the ground-state energy difference between liquid and solid metallic hydrogen based on many-body perturbation theory are pointed out. Arguments based on liquid-state perturbation theory which indicate that the energy difference may be much smaller than was found in a previous calculation are presented.

Carlsson, A. E.↗
NASA NTRS1988

Estimation of the reaction rate for the formation of CH3O from H + H2CO - Implications for chemistry in the solar system

Troe's (1977) approximate theory is presently used in conjunction with transition state theory to estimate the rate coefficient of the reaction by which CO is reduced to CH4; attention is given to the role that may be played in the reduction process by the formation of the CH3O radical from H + H2CO. Attention is given to the implications of such a reaction (1) for the CO chemistry on Jupiter and within the solar nebula, (2) for the interpretation of such experimental results as those of Bar-Nun and Shaviv (1975) and Bar-Nun and Chang (1983), and (3) for organic synthesis in the prebiotic terrestrial atmosphere.

Yung, Yuk L.↗
NASA NTRS2011

Model Adaptation for Prognostics in a Particle Filtering Framework

One of the key motivating factors for using particle filters for prognostics is the ability to include model parameters as part of the state vector to be estimated. This performs model adaptation in conjunction with state tracking, and thus, produces a tuned model that can used for long term predictions. This feature of particle filters works in most part due to the fact that they are not subject to the "curse of dimensionality", i.e. the exponential growth of computational complexity with state dimension. However, in practice, this property holds for "well-designed" particle filters only as dimensionality increases. This paper explores the notion of wellness of design in the context of predicting remaining useful life for individual discharge cycles of Li-ion batteries. Prognostic metrics are used to analyze the tradeoff between different model designs and prediction performance. Results demonstrate how sensitivity analysis may be used to arrive at a well-designed prognostic model that can take advantage of the model adaptation properties of a particle filter.

Saha, Bhaskar↗
NASA NTRS1983

Classification and area estimation of land covers in Kansas using ground-gathered and LANDSAT digital data

Ground-gathered data and LANDSAT multispectral scanner (MSS) digital data from 1981 were analyzed to produce a classification of Kansas land areas into specific types called land covers. The land covers included rangeland, forest, residential, commercial/industrial, and various types of water. The analysis produced two outputs: acreage estimates with measures of precision, and map-type or photo products of the classification which can be overlaid on maps at specific scales. State-level acreage estimates were obtained and substate-level land cover classification overlays and estimates were generated for selected geographical areas. These products were found to be of potential use in managing land and water resources.

May, G. A.↗
NASA NTRS1971

Applications of generalized inverses to estimation in dynamic systems.

Generalized matrix inverses are used to obtain an estimation procedure for estimation of the state vector of a dynamic system. This sequential procedure is studied analytically with respect to the choice of an arbitrary vector. The covariance matrix of the estimator is determined and compared to the optimal Kalman type procedure. A numerical example illustrates the procedure and compares it to the optimal one.

Prochaska, B. J.↗
NASA NTRS2017

Dual Extended Kalman Filter for the Identification of Time-Varying Human Manual Control Behavior

A Dual Extended Kalman Filter was implemented for the identification of time-varying human manual control behavior. Two filters that run concurrently were used, a state filter that estimates the equalization dynamics, and a parameter filter that estimates the neuromuscular parameters and time delay. Time-varying parameters were modeled as a random walk. The filter successfully estimated time-varying human control behavior in both simulated and experimental data. Simple guidelines are proposed for the tuning of the process and measurement covariance matrices and the initial parameter estimates. The tuning was performed on simulation data, and when applied on experimental data, only an increase in measurement process noise power was required in order for the filter to converge and estimate all parameters. A sensitivity analysis to initial parameter estimates showed that the filter is more sensitive to poor initial choices of neuromuscular parameters than equalization parameters, and bad choices for initial parameters can result in divergence, slow convergence, or parameter estimates that do not have a real physical interpretation. The promising results when applied to experimental data, together with its simple tuning and low dimension of the state-space, make the use of the Dual Extended Kalman Filter a viable option for identifying time-varying human control parameters in manual tracking tasks, which could be used in real-time human state monitoring and adaptive human-vehicle haptic interfaces.

manual control↗
NASA NTRS1975

Experience gained from computer processing of physical experimental data during the restoration of measured values

The processing stage in which the restored values of the physical parameters are received is described. The following main steps are discussed: estimation of the state of the telemetry data, processing of the calibration data, and determination of the errors in the data; data decommutation and analysis of the structure of measurement cycles for each instrument; decoding, estimates of the reliability of the restored data, and their agreement with the models adopted for the measurement process; and analysis of errors due to deterministic and random factors. A block diagram of the method is presented.

Mamotko, Z. N.↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS1979

Concerning an application of the method of least squares with a variable weight matrix

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

Sukhanov, A. A.↗
NASA NTRS2012

Isotopic Ratios in Titan's Methane: Measurements and Modeling

The existence of methane in Titan's atmosphere (approx. 6% level at the surface) presents a unique enigma, as photochemical models predict that the current inventory will be entirely depleted by photochemistry in a timescale of approx 20 Myr. In this paper, we examine the clues available from isotopic ratios (C-12/C-13 and D/H) in Titan's methane as to the past atmosphere history of this species. We first analyze recent infrared spectra of CH4 collected by the Cassini Composite Infrared Spectrometer, measuring simultaneously for the first time the abundances of all three detected minor isotopologues: (13)CH4, (12)CH3D, and (13)CH3D. From these we compute estimates of C-12/C-13 = 86.5 +/- 8.2 and D/H = (1.59 +/- 0.33) x 10(exp -4) , in agreement with recent results from the Huygens GCMS and Cassini INMS instruments. We also use the transition state theory to estimate the fractionation that occurs in carbon and hydrogen during a critical reaction that plays a key role in the chemical depletion of Titan's methane: CH4 + C2H yields CH3 + C2H2. Using these new measurements and predictions we proceed to model the time evolution of C-12/C-13 and D/H in Titan's methane under several prototypical replenishment scenarios. In our Model 1 (no resupply of CH4), we find that the present-day C-12/C-13 implies that the CH4 entered the atmosphere 60-1600 Myr ago if methane is depleted by chemistry and photolysis alone, but much more recently-most likely less than 10 Myr ago-if hydrodynamic escape is also occurring. On the other hand, if methane has been continuously supplied at the replenishment rate then the isotopic ratios provide no constraints, and likewise for the case where atmospheric methane is increasing, We conclude by discussing how these findings may be combined with other evidence to constrain the overall history of the atmospheric methane.

Nixon, C. A.↗
NASA NTRS2006

On the Quality of the Nimbus 7 LIMS Version 6 Ozone for Studies of the Middle Atmosphere

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) radiance profile dataset of 1978/79 was reconditioned and reprocessed to Version 6 (V6) profiles of temperature and species that are improved significantly over those from Version 5 (V5). The LIMS V6 dataset was archived for public use in 2002. Improvements for its ozone include: (1) a more accurate accounting for instrument and spacecraft motion effects in the radiances, (2) the use of better spectroscopic line parameters for its ozone forward model, (3) retrievals of all its scans, (4) more accurate and compatible temperature versus pressure profiles (or T(p)), which are needed for the registration of the ozone radiances and for the removal of temperature effects from them, and (5) a better accounting for interfering species in the lower stratosphere. The retrieved V6 ozone profiles extend from near cloud top altitudes to about 80 km and from 64S to 84N latitude with better sampling along the orbit than for the V5 dataset. Calculated estimates of the single-profile precision and accuracy are provided for the V6 ozone from this study. Precision estimates based on the data themselves are of order 3% or better from 1 to 30 hPa. Estimates of total systematic error for a single profile are hard to generalize because the separate sources of error may not all be of the same sign and they depend somewhat on the atmospheric state. It is estimated that the V6 zonal mean ozone distributions are accurate to within 9% to 7% from 50 hPa to 3 hPa, respectively. Effects of a temperature bias can be significant and may be present at 1 to 2 hPa though. There may be ozone biases of order 10% at those levels due to possible biases of up to +2 K, but there is no indication of a similar problem elsewhere in the stratosphere. Simulation studies show that the LIMS retrievals are also underestimating slightly the small amplitudes of the atmospheric temperature tides, which affect its retrieved day/night ozone differences. There are small biases in the middle to lower stratosphere for the ascending versus descending node LIMS ozone, due principally to not accounting for the asymmetric weighting of its radiances across the tangent layer. The estimates of total accuracy were assessed by comparing the daily zonal mean LIMS ozone distributions against those from the Nimbus 7 SBUV Version 8 (V8) dataset for the same period. Generally, the LIMS V6 ozone agrees well with SBUV, except perhaps in the tropical lower stratosphere where the LIMS ozone is less. Still, the accuracy for LIMS V6 ozone in the lower stratosphere is improved over that found for LIMS V5, as indicated by several LIMS comparisons with ECC ozonesonde profiles. The LIMS V6 ozone is considered especially suitable for detailed studies of large-scale stratospheric processes above the 100-hPa level. Comparison of diurnal, photochemical model calculations with the monthly-averaged, upper stratospheric ozone observed from LIMS V6 indicates only a slight ozone deficit for the model at about 2 hPa. However, that deficit exhibits little to no seasonal variation and is in good agreement with similar model comparisons for a seasonal time series of ozone obtained with ground-based microwave instruments. Because the LIMS V6 ozone in the lower stratosphere has improved accuracy and sampling versus that of V5, it should now be possible to conduct quantitative studies of ozone transport and chemistry for the northern hemisphere, polar stratospheric winter of 1978/79 a time period when the catalytic loss of ozone due to reactive chlorine should not have been a major factor for the Arctic region.

Remsberg, Ellis↗
NASA NTRSDate not supplied

Estimation of Permanent Magnet Synchronous Motor Parameters using a Linear Unknown Input Interval Observer

This paper develops and evaluate a technique to estimate the speed and unknown load torque of a permanent magnet synchronous motor (PMSM). An interval unknown input observer (UIO) for linear time-invariant (LTI) systems is designed and utilized to estimate the PMSM parameters. Interval UIOs are advantageous as they allow for the estimation of both states and unknown inputs, while accounting for varying uncertainty sources, such as model and measurement uncertainties inherent in dynamic systems and processes. First, the nonlinear PMSM model is linearized to transform it to a suitable form for application of the linear interval UIO. Then, the interval UIO is applied to jointly estimate the motor speed and the unknown load torque disturbance. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state (motor speed) and then for the unknown input (load torque). The proposed approach and its limitations are demonstrated for the nonlinear PMSM model derived from its equivalent electrical circuit.

Elinirina I Robinson↗
NASA NTRS1989

A tesselated probabilistic representation for spatial robot perception and navigation

The ability to recover robust spatial descriptions from sensory information and to efficiently utilize these descriptions in appropriate planning and problem-solving activities are crucial requirements for the development of more powerful robotic systems. Traditional approaches to sensor interpretation, with their emphasis on geometric models, are of limited use for autonomous mobile robots operating in and exploring unknown and unstructured environments. Here, researchers present a new approach to robot perception that addresses such scenarios using a probabilistic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field that maintains stochastic estimates of the occupancy state of each cell in the grid. The cell estimates are obtained by interpreting incoming range readings using probabilistic models that capture the uncertainty in the spatial information provided by the sensor. A Bayesian estimation procedure allows the incremental updating of the map using readings taken from several sensors over multiple points of view. An overview of the Occupancy Grid framework is given, and its application to a number of problems in mobile robot mapping and navigation are illustrated. It is argued that a number of robotic problem-solving activities can be performed directly on the Occupancy Grid representation. Some parallels are drawn between operations on Occupancy Grids and related image processing operations.

Elfes, Alberto↗
NASA NTRS1993

Hybrid state-space self-tuning control of uncertain linear systems

The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.

Shieh, L. S.↗
NASA NTRS2011

Historic Emissions from Deforestation and Forest Degradation in Mato Grosso, Brazil: 1. Source Data Uncertainties

Historic carbon emissions are an important foundation for proposed efforts to Reduce Emissions from Deforestation and forest Degradation and enhance forest carbon stocks through conservation and sustainable forest management (REDD+). The level of uncertainty in historic carbon emissions estimates is also critical for REDD+, since high uncertainties could limit climate benefits from mitigation actions. Here, we analyzed source data uncertainties based on the range of available deforestation, forest degradation, and forest carbon stock estimates for the Brazilian state of Mato Grosso during 1990-2008. Results: Deforestation estimates showed good agreement for multi-year trends of increasing and decreasing deforestation during the study period. However, annual deforestation rates differed by >20% in more than half of the years between 1997-2008, even for products based on similar input data. Tier 2 estimates of average forest carbon stocks varied between 99-192 Mg C/ha, with greatest differences in northwest Mato Grosso. Carbon stocks in deforested areas increased over the study period, yet this increasing trend in deforested biomass was smaller than the difference among carbon stock datasets for these areas. Conclusions: Patterns of spatial and temporal disagreement among available data products provide a roadmap for future efforts to reduce source data uncertainties for estimates of historic forest carbon emissions. Specifically, regions with large discrepancies in available estimates of both deforestation and forest carbon stocks are priority areas for evaluating and improving existing estimates. Full carbon accounting for REDD+ will also require filling data gaps, including forest degradation and secondary forest, with annual data on all forest transitions.

Morton, Douglas C.↗