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NASA NTRS2016

A Survey of Cost Estimating Methodologies for Distributed Spacecraft Missions

Satellite constellations present unique capabilities and opportunities to Earth orbiting and near-Earth scientific and communications missions, but also present new challenges to cost estimators. An effective and adaptive cost model is essential to successful mission design and implementation, and as Distributed Spacecraft Missions (DSM) become more common, cost estimating tools must become more representative of these types of designs. Existing cost models often focus on a single spacecraft and require extensive design knowledge to produce high fidelity estimates. Previous research has examined the limitations of existing cost practices as they pertain to the early stages of mission formulation, for both individual satellites and small satellite constellations. Recommendations have been made for how to improve the cost models for individual satellites one-at-a-time, but much of the complexity in constellation and DSM cost modeling arises from constellation systems level considerations that have not yet been examined. This paper constitutes a survey of the current state-of-theart in cost estimating techniques with recommendations for improvements to increase the fidelity of future constellation cost estimates. To enable our investigation, we have developed a cost estimating tool for constellation missions. The development of this tool has revealed three high-priority shortcomings within existing parametric cost estimating capabilities as they pertain to DSM architectures: design iteration, integration and test, and mission operations. Within this paper we offer illustrative examples of these discrepancies and make preliminary recommendations for addressing them. DSM and satellite constellation missions are shifting the paradigm of space-based remote sensing, showing promise in the realms of Earth science, planetary observation, and various heliophysical applications. To fully reap the benefits of DSM technology, accurate and relevant cost estimating capabilities must exist; this paper offers insights critical to the future development and implementation of DSM cost estimating tools.

Foreman, Veronica L.↗
NASA NTRS2018

Satellite Remote Sensing Estimation of River Discharge: Application to the Yukon River Alaska

A methodology based on general hydraulic relations for rivers has been developed to estimate the discharge (flow rate) of rivers using satellite remote sensing observations. The estimates of discharge, flow depth, and flow velocity are derived from remotely observed water surface area, water surface slope, and water surface height, and demonstrated for two reaches of the Yukon River in Alaska, at Eagle (reach length 34.7 km) and near Stevens Village (reach length 38.3 km). The method is based on fundamental equations of hydraulic flow resistance in rivers, including the Manning equation and the Prandtl-von Karman universal velocity distribution equation. The method employs some new hydraulic relations to help define flow resistance and height of the zero flow boundary in the channel. Estimates are made both with and without calibration. The water surface area of the river reach is measured by using a provisional version of the U.S. Geological Survey (USGS) Landsat based product named Dynamic Surface Water Extent (DSWE). The water surface height and slope measurements require a self-consistent datum, and are derived from observations from the Jason-2 satellite altimeter mission. At both reach locations, the Jason-2 radar altimeter non-winter heights consistently tracked the stage recorded at USGS streamgages with a standard deviation of differences (error) during the non-winter periods of less than 7%. Part of the error may be due to differences in the gage and altimeter crossing locations with respect to the range of stage change and the response to changes in discharge at the upstream and downstream locations. For the non-winter periods, the radar derived slope estimates (mean = 0.0003) were constant over the mission lifetime, and in agreement with previously measured USGS water surface slopes and slopes determined from USGS topographic maps. The accuracy of the mean of the uncalibrated daily estimates of discharge varied between reaches, ranging from 13% near Stevens Village (N = 90) to −21% at Eagle (N = 246) based on the absolute error, and 5% to −6% based on the error of the log of the estimates. Calibrating to the mean of USGS daily discharge estimates from the streamflow rating for the same period of record at each streamgage resulted in mean absolute errors ranging from 1% to 2%, and log errors ranging from 1% or less. The error pattern of the estimates shows that without calibration, even though the mean is well simulated, the high and low end values over the range of estimates may have significant bias.

Bjerklie, David M.↗
NASA NTRSDate not supplied

Satellite Based Precipitation Estimation in Orographic Regions within the Southwestern United States

Predicting precipitation-induced landslides requires accurate estimation of orographic precipitation. Many research studies have been done to estimate orographic precipitation using measurement/estimation methods that include rain gauges, ground-based radar, satellite-based estimates, and modeling. Each method has strengths and weaknesses, but none have been able to fully resolve orographic precipitation. The Integrated Multi-satellitE Retrievals for Global Precipitation Measurement Mission (IMERG) early run product provides precipitation estimates at a 0.1° spatial resolution, at half-hour time scales, with only a 4-hour latency. This product is currently used for the global landslide hazard assessment, but there are known issues in mountainous terrain that the IMERG algorithm has not been able to fully resolve; and the sparse gauge density in these regions makes it even more difficult. In this study, precipitation events were identified using high temporal resolution (5-15 minute) precipitation observations from rain gauges in mountainous terrain in the southwestern United States. The brightness temperature from several infrared (IR) bands from the Geostationary Operational Environmental Satellite (GOES) 16 satellite were used to estimate precipitation with a k-nearest neighbor machine learning model. Compared to IMERG, the IR estimates from GOES-16 performed better at predicting gauge-identified precipitation events. Additionally, the IR-only based estimates were able to estimate precipitation when IMERG failed to detect precipitation, false negative events. While additional analysis is needed, results indicate the need for better integration of IR observations for more accurate precipitation estimation in mountainous regions.

Jessica Sutton↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS1976

Maximum likelihood estimates of lift and drag characteristics obtained from dynamic aircraft maneuvers

A maximum likelihood estimation method for obtaining lift and drag characteristics from dynamic flight maneuvers was investigated. This paper describes the method and compares the estimates of lift and drag obtained by using the method with estimates obtained from wind-tunnel tests and from established methods for obtaining estimates from flight data. In general, the lift and drag coefficients extracted from dynamic flight maneuvers by the maximum likelihood estimation technique are in good agreement with the estimates obtained from the wind-tunnel tests and the other methods. When maneuvers that met the requirements of both flight methods were analyzed, the results of each method were nearly the same. The maximum likelihood estimation technique showed promise in terms of estimating lift and drag characteristics from dynamic flight maneuvers. Further studies should be made to assess the best mathematical model and the most desirable type of dynamic maneuver to get the highest quality results from this technique.

Iliff, K. W.↗
NASA NTRS1977

Two phase sampling for wheat acreage estimation

A two-phase Landsat-based sample allocation and wheat proportion estimation method was developed. The technique employs manual, Landsat full frame-based wheat or cultivated land proportion estimates from a large number of segments comprising a first sample phase to optimally allocate a small phase-two sample of computer or manually processed segments. Proportion estimates from each phase are then linked by regression or probability proportional to estimated size estimators to provide wheat proportion estimates and standard errors by reporting unit. Application to the Kansas Southwest CRD (Crop Reporting District) for 1974 produced a wheat acreage estimate for that CRD within 2.42% of the USDA SRS-based estimate using a lower CRD inventory budget than for a simulated reference LACIE (Large Area Crop Inventory Experiment) system.

Thomas, R. W.↗
NASA NTRS1982

In-flight estimation of spacecraft attitude sensor accuracies and alignments

A simple estimator is developed for determining in flight the accuracies of vector attitude sensors. The estimator is unbiased and independent of the configuration of the sensors. In addition, the estimator requires neither an a priori estimate of sensor accuracies nor an estimate of the spacecraft attitude. A covariance analysis of the estimator is given. Data from the Magsat mission is analyzed as a example. A simple algorithm for estimating attitude sensor misalignments, which is independent of any knowledge of the spacecraft attitude, is also presented. This misalignment estimator is applied to in-flight data from the Solar Maximum Mission.

Schuster, M. D.↗
NASA NTRS1983

A sampling system for estimating the cultivation of wheat (Triticum aestivum L) from LANDSAT data

Using digitally processed MSS/LANDSAT data as auxiliary variable, a methodology to estimate wheat (Triticum aestivum L) area by means of sampling techniques was developed. To perform this research, aerial photographs covering 720 sq km in Cruz Alta test site at the NW of Rio Grande do Sul State, were visually analyzed. LANDSAT digital data were analyzed using non-supervised and supervised classification algorithms; as post-processing the classification was submitted to spatial filtering. To estimate wheat area, the regression estimation method was applied and different sample sizes and various sampling units (10, 20, 30, 40 and 60 sq km) were tested. Based on the four decision criteria established for this research, it was concluded that: (1) as the size of sampling units decreased the percentage of sampled area required to obtain similar estimation performance also decreased; (2) the lowest percentage of the area sampled for wheat estimation with relatively high precision and accuracy through regression estimation was 90% using 10 sq km s the sampling unit; and (3) wheat area estimation by direct expansion (using only aerial photographs) was less precise and accurate when compared to those obtained by means of regression estimation.

Parada, N. D. J.↗
NASA NTRS1985

More than you want to know about maximum likelihood estimation

The maximum likelihood estimator has been used to extract stability and control derivatives from flight data for many years. Most of the literature on aircraft estimation concentrates on new developments and applications, assuming familiarity with basic estimation concepts. Some of these basic concepts are presented. The maximum likelihood estimator is briefly discussed and the aircraft equations of motion that the estimator uses. The basic concepts of minimization and estimation are examined for a simple computed aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to help illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the computed example are also developed for the analysis of flight data.

Iliff, K. W.↗
NASA NTRS1984

Exploring the use of structural models to improve remote sensing agricultural estimates

Satellite estimates of agricultural characteristics often are not sufficiently precise for reliable use in small geographical regions. The precision of estimates of agricultural characteristics such as crop proportions and leaf area indexes can be increased by modeling ground observations as a function of satellite estimates. Linear regression models using least squares estimators of the model parameters are most often advocated as an appropriate methodology; however, least squares estimation requires that the predictor variables are measured without error, an unreasonable assumption for this application. An alternative estimation methodology which assumes that both the response variables (ground observations) and the predictor variables (satellite estimates) are measured with error involves the use of linear structural models. The application of linear structural models to the estimation of agricultural characteristics using satellite spectral measurements is examined.

Gunst, R. F.↗
NASA NTRS1985

Time-resolved speckle effects on the estimation of laser-pulse arrival times

A maximum-likelihood (ML) estimator of the pulse arrival in laser ranging and altimetry is derived for the case of a pulse distorted by shot noise and time-resolved speckle. The performance of the estimator is evaluated for pulse reflections from flat diffuse targets and compared with the performance of a suboptimal centroid estimator and a suboptimal Bar-David ML estimator derived under the assumption of no speckle. In the large-signal limit the accuracy of the estimator was found to improve as the width of the receiver observational interval increases. The timing performance of the estimator is expected to be highly sensitive to background noise when the received pulse energy is high and the receiver observational interval is large. Finally, in the speckle-limited regime the ML estimator performs considerably better than the suboptimal estimators.

Tsai, B.-M.↗
NASA NTRS1985

Evaluation of crop acreage estimation methods using Landsat data as auxiliary input

The regression and ratio estimators are studied in the context of improving upon the ground survey estimates of crop acreages by utilizing Landsat data. The approach is to formulate analytically the estimation problem that utilizes ground survey data, as collected by the U.S. Department of Agriculture, and Landsat data, which provide a complete coverage for an area of interest, and then to conduct simulation studies. It is shown over a wide range of conditions that the regression estimator is the most efficient unless there is a low correlation between the actual and estimated crop acreages in the sampled area segments, in which case a ratio type estimator is superior. Estimation of the variance of the regression estimator is also investigated.

Chhikara, R. S.↗
NASA NTRS1987

Aircraft parameter estimation

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated example are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and space shuttle vehicles.

Kenneth W Iliff↗
NASA NTRS1987

Aircraft parameter estimation

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated examples are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and Space Shuttle vehicles.

Iliff, Kenneth W.↗
NASA NTRS1989

Kalman estimation for SEDS measurements

The first on-orbit experiment of the Small Expendable Deployer System (SEDS) for tethered satellites will collect telemetry data for tethered length, rate of deployment, and tether tension. The post-flight analysis will use this data to reconstruct the deployment history and determine payload position and tether shape. Two Kalman estimator algorithms were written, and output using simulated measurement data was compared. Both estimators exhibited the same estimated state histories, indicating that numerical instability in the traditional algorithm was not the cause of filter divergence. Estimation of acceleration biases was added, which reduced the error but did not correct the divergence. An add-a-bead estimator that adds lumped masses as the tether is deployed was written, which provides a state model that matches the BEADSIM simulation providing the true measurements and states. This twenty-one bead estimator produced state histories similar to those of the two-bead estimator, indicating that the filter divergence was not caused by a reduced-order model. The noise models used to date are relatively simple and may be the source of estimator divergence. The investigation of colored noise models, cross-correlated measurement and process covariances, and noise-adaptive filter techniques is recommended.

Carrington, Connie K.↗
NASA NTRS1990

Multistage estimation of received carrier signal parameters under very high dynamic conditions of the receiver

A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), 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, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.

Kumar, Rajendra↗
NASA NTRS1991

On the estimation of climatological Z-R relationships

A statistical framework for climatological Z-R parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that Z-R parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological Z-R estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate Z-R parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of Z-R model parameter estimates. These results are particularly useful for error analysis of precipitation products that are derived using climatological Z-R relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.

Krajewski, Witold F.↗
NASA NTRS1992

An analysis of I/O efficient order-statistic-based techniques for noise power estimation in the HRMS sky survey's operational system

Noise power estimation in the High-Resolution Microwave Survey (HRMS) sky survey element is considered as an example of a constant false alarm rate (CFAR) signal detection problem. Order-statistic-based noise power estimators for CFAR detection are considered in terms of required estimator accuracy and estimator dynamic range. By limiting the dynamic range of the value to be estimated, the performance of an order-statistic estimator can be achieved by simpler techniques requiring only a single pass of the data. Simple threshold-and-count techniques are examined, and it is shown how several parallel threshold-and-count estimation devices can be used to expand the dynamic range to meet HRMS system requirements with minimal hardware complexity. An input/output (I/O) efficient limited-precision order-statistic estimator with wide but limited dynamic range is also examined.

Zimmerman, G. A.↗