Accurate Estimates in Less Than a Minute: Conceptual Estimating in Excel Using Historical Data
No abstract available
Butts, Glenn↗
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Grid2: A Program for Rapid Estimation of the Jovian Radiation Environment: A Numeric Implementation of the GIRE2 Jovian Radiation Model for Estimating Trapped Radiation for Mission Concept Studies
Grid2 is a program that utilizes the Galileo Interim Radiation Electron model 2 (GIRE2) Jovian radiation model to compute fluences and doses for Jupiter missions. (Note: The iterations of these two softwares have been GIRE and GIRE2; likewise Grid and Grid2.) While GIRE2 is an important improvement over the original GIRE radiation model, the GIRE2 model can take as long as a day or more to compute these quantities for a complete mission. Grid2 fits the results of the detailed GIRE2 code with a set of grids in local time and position thereby greatly speeding up the execution of the model--minutes as opposed to days. The Grid2 model covers the time period from 1971 to 2050and distances of 1.03 to 30 Jovian diameters (Rj). It is available as a direct-access database through a FORTRAN interface program. The new database is only slightly larger than the original grid version: 1.5 gigabytes (GB) versus 1.2 GB.
Europa↗
NASA Project Cost Estimating Capability: New Analyses for Spacecraft Estimating
No abstract available
Alford, Brian↗
Observational estimates of the aerosol direct radiative effect: improving CALIPSO-based estimates and the role of lidar observations
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Tyler Thorsen↗
Improved Estimation of Backscattering Differential Phase in Rain and Its Utilization in Rainfall Estimation
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54 ENVIRONMENTAL SCIENCES↗
A Generic Framework to Design Perturbation Signals for Parameter Estimation of Dynamic Systems: A Test Case for Inertia Estimation
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Bhujel, Niranjan [Sandia National Laboratories (SN↗
Performance Comparison of Circular and Spherical Error Probable Estimators
This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.
97 MATHEMATICS AND COMPUTING↗
Comparison of Precision of Biomass Estimates in Regional Field Sample Surveys and Airborne LiDAR-Assisted Surveys in Hedmark County, Norway
Airborne scanning LiDAR (Light Detection and Ranging) has emerged as a promising tool to provide auxiliary data for sample surveys aiming at estimation of above-ground tree biomass (AGB), with potential applications in REDD forest monitoring. For larger geographical regions such as counties, states or nations, it is not feasible to collect airborne LiDAR data continuously ("wall-to-wall") over the entire area of interest. Two-stage cluster survey designs have therefore been demonstrated by which LiDAR data are collected along selected individual flight-lines treated as clusters and with ground plots sampled along these LiDAR swaths. Recently, analytical AGB estimators and associated variance estimators that quantify the sampling variability have been proposed. Empirical studies employing these estimators have shown a seemingly equal or even larger uncertainty of the AGB estimates obtained with extensive use of LiDAR data to support the estimation as compared to pure field-based estimates employing estimators appropriate under simple random sampling (SRS). However, comparison of uncertainty estimates under SRS and sophisticated two-stage designs is complicated by large differences in the designs and assumptions. In this study, probability-based principles to estimation and inference were followed. We assumed designs of a field sample and a LiDAR-assisted survey of Hedmark County (HC) (27,390 km2), Norway, considered to be more comparable than those assumed in previous studies. The field sample consisted of 659 systematically distributed National Forest Inventory (NFI) plots and the airborne scanning LiDAR data were collected along 53 parallel flight-lines flown over the NFI plots. We compared AGB estimates based on the field survey only assuming SRS against corresponding estimates assuming two-phase (double) sampling with LiDAR and employing model-assisted estimators. We also compared AGB estimates based on the field survey only assuming two-stage sampling (the NFI plots being grouped in clusters) against corresponding estimates assuming two-stage sampling with the LiDAR and employing model-assisted estimators. For each of the two comparisons, the standard errors of the AGB estimates were consistently lower for the LiDAR-assisted designs. The overall reduction of the standard errors in the LiDAR-assisted estimation was around 40-60% compared to the pure field survey. We conclude that the previously proposed two-stage model-assisted estimators are inappropriate for surveys with unequal lengths of the LiDAR flight-lines and new estimators are needed. Some options for design of LiDAR-assisted sample surveys under REDD are also discussed, which capitalize on the flexibility offered when the field survey is designed as an integrated part of the overall survey design as opposed to previous LiDAR-assisted sample surveys in the boreal and temperate zones which have been restricted by the current design of an existing NFI.
Comparison↗
Performance of mean-frequency estimators for Doppler radar and lidar
The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Phi, the ratio of the average signal energy per estimate to the spectral noise level; and Omega, which is proportional to the number of independent samples per estimate. For fixed Phi and Omega, the Cramer-Rao bound (CRB) (theoretical best performance) for unbiased estimators of mean frequency (normalized by the spectral width of the signal), signal power, and spectral width are essentially independent of the number of data samples M. For large Phi, the estimators of mean frequency are unbiased and the performance is independent of M. The spectral domain estimators and covariance based estimators are bounded by the approximate period of M. The spectral domain estimators and covariance based estimators are bounded by the approximate periodogram CRB. The standard deviation of the maximum-likelihood estimator approaches the exact CRB, which can be more than a factor of 2 better than the performance of the spectral domain estimators or covariance-based estimators for typical Omega. For small Phi, the estimators are biased due to the effects of the uncorrelated noise (white noise), which results in uniformly distributed 'bad' estimates. The fraction of bad estimates is a function of Phi and M with weak dependence on the parameter Omega. Simple empirical models describe the standard deviation of the good estimates and the fraction of bad estimates. For Doppler lidar and for large Phi, better performance is obtained by using many low-energy pulses instead of one pulse with the same total energy. For small Phi, the converse is true.
Frehlich, R. G.↗
Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)
A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.
Global Precipitation Climatology Project (GPCP)↗
Lidar-Based Estimates of Above-Ground Biomass in the Continental US and Mexico Using Ground, Airborne, and Satellite Observations
Existing national forest inventory plots, an airborne lidar scanning (ALS) system, and a space profiling lidar system (ICESat-GLAS) are used to generate circa 2005 estimates of total aboveground dry biomass (AGB) in forest strata, by state, in the continental United States (CONUS) and Mexico. The airborne lidar is used to link ground observations of AGB to space lidar measurements. Two sets of models are generated, the first relating ground estimates of AGB to airborne laser scanning (ALS) measurements and the second set relating ALS estimates of AGB (generated using the first model set) to GLAS measurements. GLAS then, is used as a sampling tool within a hybrid estimation framework to generate stratum-, state-, and national-level AGB estimates. A two-phase variance estimator is employed to quantify GLAS sampling variability and, additively, ALS-GLAS model variability in this current, three-phase (ground-ALS-space lidar) study. The model variance component characterizes the variability of the regression coefficients used to predict ALS-based estimates of biomass as a function of GLAS measurements. Three different types of predictive models are considered in CONUS to determine which produced biomass totals closest to ground-based national forest inventory estimates - (1) linear (LIN), (2) linear-no-intercept (LNI), and (3) log-linear. For CONUS at the national level, the GLAS LNI model estimate (23.95 +/- 0.45 Gt AGB), agreed most closely with the US national forest inventory ground estimate, 24.17 +/- 0.06 Gt, i.e., within 1%. The national biomass total based on linear ground-ALS and ALS-GLAS models (25.87 +/- 0.49 Gt) overestimated the national ground-based estimate by 7.5%. The comparable log-linear model result (63.29 +/-1.36 Gt) overestimated ground results by 261%. All three national biomass GLAS estimates, LIN, LNI, and log-linear, are based on 241,718 pulses collected on 230 orbits. The US national forest inventory (ground) estimates are based on 119,414 ground plots. At the US state level, the average absolute value of the deviation of LNI GLAS estimates from the comparable ground estimate of total biomass was 18.8% (range: Oregon,−40.8% to North Dakota, 128.6%). Log-linear models produced gross overestimates in the continental US, i.e., N2.6x, and the use of this model to predict regional biomass using GLAS data in temperate, western hemisphere forests is not appropriate. The best model form, LNI, is used to produce biomass estimates in Mexico. The average biomass density in Mexican forests is 53.10 +/- 0.88 t/ha, and the total biomass for the country, given a total forest area of 688,096 sq km, is 3.65 +/- 0.06 Gt. In Mexico, our GLAS biomass total underestimated a 2005 FAO estimate (4.152 Gt) by 12% and overestimated a 2007/8 radar study's figure (3.06 Gt) by 19%.
Hybrid 3-Phase sampling↗
A Systematic Approach for Model-Based Aircraft Engine Performance Estimation
A requirement for effective aircraft engine performance estimation is the ability to account for engine degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. This paper presents a linear point design methodology for minimizing the degradation-induced error in model-based aircraft engine performance estimation applications. The technique specifically focuses on the underdetermined estimation problem, where there are more unknown health parameters than available sensor measurements. A condition for Kalman filter-based estimation is that the number of health parameters estimated cannot exceed the number of sensed measurements. In this paper, the estimated health parameter vector will be replaced by a reduced order tuner vector whose dimension is equivalent to the sensed measurement vector. The reduced order tuner vector is systematically selected to minimize the theoretical mean squared estimation error of a maximum a posteriori estimator formulation. This paper derives theoretical estimation errors at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the estimation accuracy achieved through conventional maximum a posteriori and Kalman filter estimation approaches. Maximum a posteriori estimation results demonstrate that reduced order tuning parameter vectors can be found that approximate the accuracy of estimating all health parameters directly. Kalman filter estimation results based on the same reduced order tuning parameter vectors demonstrate that significantly improved estimation accuracy can be achieved over the conventional approach of selecting a subset of health parameters to serve as the tuner vector. However, additional development is necessary to fully extend the methodology to Kalman filter-based estimation applications.
Simon, Donald L.↗
Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation
An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.
Simon, Donald L.↗
Sampling Size Optimization for Bioburden Density Estimation in Planetary Protection
Planetary protection (PP) is a discipline that focuses on minimizing the biological contamination of spacecraft to ensure compliance with international policy. Precise estimation of bioburden - the total number of microbes in or on spacecraft hardware – and the bioburden density are of utmost importance for PP. Such estimation is the way concordance with requirements is demonstrated, and it is critical for quantifying the potential risk of inadvertently contaminating other planetary bodies. Although a suite of molecular techniques have been used to thoroughly characterize and profile the microbiome of various cleanroom environments and spacecraft, the gold standard remains the physical enumeration of microbes via culturing of samples directly taken from spacecraft and associated surfaces. However, due to technical, budgetary, and programmatic constraints, only a manageable portion (around 10%) of the entire spacecraft surface is directly sampled with cotton swabs or wipes. To generate the bioburden current best estimate (CBE) for components not directly verifiable, the accepted approach is to apply a NASA-defined bioburden estimate based on the components’ manufacturing or assembly environment. This approach utilizes a prespecified bioburden density estimation that applies a maximum value across the total surface area of the specified component. For hardware components that underwent similar assembly processes, an implied bioburden is adopted for all components, based on a direct verification of a representative component within the same lot. Once all components have a CBE, the bioburden estimates are generated. In previous publication [ 1], we have shown that statistical risks quantifying the accuracy of the estimates for sampled, prespecified, and implied components can be derived and ranked. For mean squared error (MSE) function, the risks are available analytically and hence a cost function can be obtained to optimize the risks with respect to the sampling area and sampling cost. Since the sampling area and sampling cost are two complimentary variables, their sum will have a well-defined minimum. This paper presents the multivariate optimization of the integrated risk of an empirical Bayes estimator to determine the optimal sampling schedule for a given number of components. It is assumed that given a number of components, N, the bioburden density for each component can either be sampled, implied, or prespecified. The multivariate optimization searches through different options to sample, imply or prespecify the bioburden density for a component, and account for the component’s surface area and cost of sampling. The idea of the optimization is based on the observation that the statistical risk of using an estimator is a monotonically decreasing function of the sampled area. The larger the sampled area, the lower the risk of using the estimator as the estimator becomes more and more accurate as the sampling area increases. On the other hand, the cost of sampling is monotonically increasing as the sampled surface grows. This makes the risk and total cost of sampling complimentary variables which can be counterbalanced to achieve an optimal overall value with respect to the sampled surface. In this paper, the integrated risk has been used to quantify the accuracy of the estimator. This risk has been selected because it depends on neither the true value of the parameter nor on the collected data. The cost of each sample was also available to obtain the total cost of sampling of N components. The paper will present the results based on computer-simulated data as well as the data collected during the InSight mission. The computer-simulated data have N components with randomly generated total areas and each component assigned to one of the three categories according to the method of estimating of bioburden density: sampled, implied, or prespecified. The cost of sampling is also available. The cost of sampling is estimated based on a cost model provided by the planetary protection group at JPL. For this paper, the overall cost was assumed to be a linear function of exposure. The optimization process finds the allocation of the components to the three categories that minimizes the tradeoff between integrated risk and total cost. For the InSight data, a set of components is selected representing all three categories, and optimization is performed to determine if the performed allocation was optimal or if a better allocation could have been obtained. To the best of our knowledge, this work is the first attempt not only perform an accurate estimation of bioburden density but also do it in an optimal way.
97 - MATHEMATICS AND COMPUTING↗
A model for the cost of doing a cost estimate
A model for estimating the cost required to do a cost estimate for Deep Space Network (DSN) projects that range from $0.1 to $100 million is presented. The cost of the cost estimate in thousands of dollars, C(sub E), is found to be approximately given by C(sub E) = K((C(sub p))(sup 0.35)) where C(sub p) is the cost of the project being estimated in millions of dollars and K is a constant depending on the accuracy of the estimate. For an order-of-magnitude estimate, K = 24; for a budget estimate, K = 60; and for a definitive estimate, K = 115. That is, for a specific project, the cost of doing a budget estimate is about 2.5 times as much as that for an order-of-magnitude estimate, and a definitive estimate costs about twice as much as a budget estimate. Use of this model should help provide the level of resources required for doing cost estimates and, as a result, provide insights towards more accurate estimates with less potential for cost overruns.
Remer, D. S.↗
The cost of doing a cost estimate
A model for estimating the cost required to do a cost estimate for Deep Space Network (DSN) projects that range from $0.1 to $100 million is presented. The cost of the cost estimate in thousands of dollars, C(sub E), is found to be approximately given by C(sub E) = K(/C(sub p)/(sup 0.35)) where C(sub p) is the cost of the project being estimated in millions of dollars and K is a constant depending on the accuracy of the estimate. For an order-of-magnitude estimate, K = 24; for a budget estimate, K = 60; and for a definitive estimate, K = 115. That is, for a specific project, the cost of doing a budget estimate is about 2.5 times as much as that for an order-of-magnitude estimate, and a definitive estimate costs about twice as much as a budget estimate. Use of this model should help provide the level of resources required for doing cost estimates and, as a result, provide insights towards more accurate estimates with less potential for cost overruns.
Remer, Donald S.↗
A novel multistage estimation of the signal parameters of a possibly data-modulated sinusoid under very high dynamics
A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first stage algorithm is selected to be a modified least squares algorithm operating upon the differential signal model and referred to as differential least squares. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.
Kumar, Rajendra↗