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Results for “mean squared error”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Mean-square error bounds for reduced-error linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗
NASA NTRS1987

Mean-square-error bounds for reduced-order linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗
NASA NTRS2013

Estimating Root Mean Square Errors in Remotely Sensed Soil Moisture over Continental Scale Domains

Root Mean Square Errors (RMSE) in the soil moisture anomaly time series obtained from the Advanced Scatterometer (ASCAT) and the Advanced Microwave Scanning Radiometer (AMSR-E; using the Land Parameter Retrieval Model) are estimated over a continental scale domain centered on North America, using two methods: triple colocation (RMSETC ) and error propagation through the soil moisture retrieval models (RMSEEP ). In the absence of an established consensus for the climatology of soil moisture over large domains, presenting a RMSE in soil moisture units requires that it be specified relative to a selected reference data set. To avoid the complications that arise from the use of a reference, the RMSE is presented as a fraction of the time series standard deviation (fRMSE). For both sensors, the fRMSETC and fRMSEEP show similar spatial patterns of relatively highlow errors, and the mean fRMSE for each land cover class is consistent with expectations. Triple colocation is also shown to be surprisingly robust to representativity differences between the soil moisture data sets used, and it is believed to accurately estimate the fRMSE in the remotely sensed soil moisture anomaly time series. Comparing the ASCAT and AMSR-E fRMSETC shows that both data sets have very similar accuracy across a range of land cover classes, although the AMSR-E accuracy is more directly related to vegetation cover. In general, both data sets have good skill up to moderate vegetation conditions.

Remotely sensed soil moisture validation↗
NASA NTRS2009

Decomposition of the Mean Squared Error and NSE Performance Criteria: Implications for Improving Hydrological Modelling

The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE), are the two criteria most widely used for calibration and evaluation of hydrological models with observed data. Here, we present a diagnostically interesting decomposition of NSE (and hence MSE), which facilitates analysis of the relative importance of its different components in the context of hydrological modelling, and show how model calibration problems can arise due to interactions among these components. The analysis is illustrated by calibrating a simple conceptual precipitation-runoff model to daily data for a number of Austrian basins having a broad range of hydro-meteorological characteristics. Evaluation of the results clearly demonstrates the problems that can be associated with any calibration based on the NSE (or MSE) criterion. While we propose and test an alternative criterion that can help to reduce model calibration problems, the primary purpose of this study is not to present an improved measure of model performance. Instead, we seek to show that there are systematic problems inherent with any optimization based on formulations related to the MSE. The analysis and results have implications to the manner in which we calibrate and evaluate environmental models; we discuss these and suggest possible ways forward that may move us towards an improved and diagnostically meaningful approach to model performance evaluation and identification.

Gupta, Hoshin V.↗
NASA NTRS1991

Test functions for the moment method which yield the minimum mean square error

The method of moments has found extensive applications in the solution of a wide class of electromagnetic problems. Additionally, there are a number of basis functions which have found favor and with them different types of testing methods. This work examines the selection of test functions, given a selected set of basis functions, which serve to minimize the mean square error. These test functions will guarantee equal or lesser error compared with any other test function. Additionally, these test functions provide a monotonic improvement of the approximation as the increase in the order of the system. Hence while these test functions require the application of the differential or integral operator one additional time, they provide an absolute lower bound to the mean square error in the approximation and a means to systematically improve accuracy with each increase in the order of the unknowns.

Shamansky, H.↗
NASA NTRS1990

Digital image gathering and minimum mean-square error restoration

Most digital image restoration algorithms are inherently incomplete because they are conditioned on a discrete-input, discrete-output model which only accounts for blurring during image gathering and additive noise. For those restoration applications where sampling and reconstruction are important, the restoration algorithm should be based on a more comprehensive end-to-end model which also accounts for the potentially important noiselike effects of aliasing and the low-pass filtering effects of interpolative reconstruction. It is demonstrated that although the mathematics of this more comprehensive model is more complex, the increase in complexity is not so great as to prevent a complete development and analysis of the associated minimum mean-square error (Wiener) restoration filter.

Park, Stephen K.↗
NASA NTRS1974

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Long, S. A. T.↗
NASA NTRS1989

Measured and predicted root-mean-square errors in square and triangular antenna mesh facets

Deflection shapes of square and equilateral triangular facets of two tricot-knit, gold plated molybdenum wire mesh antenna materials were measured and compared, on the basis of root mean square (rms) differences, with deflection shapes predicted by linear membrane theory, for several cases of biaxial mesh tension. The two mesh materials contained approximately 10 and 16 holes per linear inch, measured diagonally with respect to the course and wale directions. The deflection measurement system employed a non-contact eddy current proximity probe and an electromagnetic distance sensing probe in conjunction with a precision optical level. Despite experimental uncertainties, rms differences between measured and predicted deflection shapes suggest the following conclusions: that replacing flat antenna facets with facets conforming to parabolically curved structural members yields smaller rms surface error; that potential accuracy gains are greater for equilateral triangular facets than for square facets; and that linear membrane theory can be a useful tool in the design of tricot knit wire mesh antennas.

Fichter, W. B.↗
NASA NTRS1993

Neural self-tuning adaptive control of non-minimum phase system

The motivation of this research came about when a neural network direct adaptive control scheme was applied to control the tip position of a flexible robotic arm. Satisfactory control performance was not attainable due to the inherent non-minimum phase characteristics of the flexible robotic arm tip. Most of the existing neural network control algorithms are based on the direct method and exhibit very high sensitivity, if not unstable, closed-loop behavior. Therefore, a neural self-tuning control (NSTC) algorithm is developed and applied to this problem and showed promising results. Simulation results of the NSTC scheme and the conventional self-tuning (STR) control scheme are used to examine performance factors such as control tracking mean square error, estimation mean square error, transient response, and steady state response.

Ho, Long T.↗
NASA NTRS1993

Adaptive control strategies for flexible robotic arm

The motivation of this research came about when a neural network direct adaptive control scheme was applied to control the tip position of a flexible robotic arm. Satisfactory control performance was not attainable due to the inherent non-minimum phase characteristics of the flexible robotic arm tip. Most of the existing neural network control algorithms are based on the direct method and exhibit very high sensitivity if not unstable closed-loop behavior. Therefore a neural self-tuning control (NSTC) algorithm is developed and applied to this problem and showed promising results. Simulation results of the NSTC scheme and the conventional self-tuning (STR) control scheme are used to examine performance factors such as control tracking mean square error, estimation mean square error, transient response, and steady state response.

Bialasiewicz, Jan T.↗
NASA NTRSDate not supplied

Expanding the Spatiotemporal Range of Soil Moisture Analysis Utilizing NASA Earth Observations and In Situ Measurements

Drought can cause immense agricultural and ecological damage resulting in high mitigation and compensation costs. Climate variability in future decades is expected to cause severe drought conditions and threaten necessary water resources. Stakeholders seek to implement effective drought assessments in preparation for potential economic and environmental damage invoked by drought. Although in-situ measurements are accurate, the current infrastructure is spatially limited and costly to maintain. A framework was created to compare modeled, satellite and in-situ data in drought monitoring. Here we show that the comparison of in-situ and remotely sensed soil moisture (SM) measurements can increase the spatiotemporal range of SM assessments. Data collected between 2003 and 2021 by NASA’s SPoRT Land Information System (SPoRT-LIS) and Soil Moisture Active Passive (SMAP) mission were standardized and compared with in-situ data provided through the Illinois Climate Network (WARM). Statistical analysis results including the Pearson correlation coefficient (r), root mean squared error, mean absolute error and others were calculated to compare the WARM measurements to the SMAP and SPoRT-LIS products. Results indicate that both satellite products demonstrate seasonally variable bias that is not present in the in-situ measurements. Bias was highest in the winter months and lowest in the late summer and early fall months in both satellite datasets. Overall, WARM-SPoRT comparisons resulted in lower seasonal variability. However, on average, the SMAP comparison demonstrated higher correlation values and lower error values. The WARM-SMAP average correlation (r) was 0.61 compared to the WARM-SPoRT average correlation (r) value of 0.54. Average mean absolute error values calculated for the SMAP and SPoRT comparisons were 0.07 and 0.08 percent soil moisture by volume, respectively. These analyses suggest integrating in-situ measurements and those provided by NASA Earth observations can be utilized in a multi-faceted SM evaluation, a valuable contribution to drought monitoring and water resource decision making.

Emma P Myrick↗
NASA NTRS2019

Evaluation Analysis of NASA SMAP L3 and L4 and SPoRT-LIS Soil Moisture Data in the United States

Soil moisture has a critical role in the development, frequency and persistence of climatic and hydrologic extremes such as drought, heat wave and flooding events. In situ soil moisture data are uneven and sparse in time and space. This highlights the need to utilize other soil moisture sources to fill this spatiotemporal gap. The goal of this study is to validate one satellite-based and two model-based soil moisture datasets with in situ data across the United States. Soil moisture information from the Soil Moisture Active Passive (SMAP) enhanced level 3 (L3) (SMAP L3) and modeled level 4 (L4) (SMAP L4) data at 9-km resolution and Short-term Prediction Research and Transition-Land Information System (SPoRT-LIS) modeled at 3-km resolution were selected for evaluation. SPoRT-LIS is a near real-time, high resolution operational land analysis data. Ground-based data were obtained from the North American Soil Moisture Database (NASMD) for 362 stations. Seven statistical indicators including anomaly, Spearman, and Pearson correlation coefficients, the systematic error (Bias), root mean square error (RMSE), unbiased root mean square error (ubRMSE), and normalized standard deviation (SDV) were used to evaluate the satellite- and model-derived soil moisture data. In addition, the triple collocation (TC) error model was used to measure the error among SMAP L4, SPoRT-LIS and ground-based data. This study assesses which satellite or modeled dataset is most appropriate for specific times and locations to use as a surrogate for in situ observations. Temporal and spatial analysis demonstrated that, overall, SMAP L4 performed better than SMAP L3 and SPoRT-LIS. Strong agreement was observed between SMAP L4 and in situ observations (ρ = 0.53, Bias = −0.006) in all seasons and most regions with various land covers, especially in winter and in the central regions of the United States. For croplands, SMAP L4 presented the best agreement with in situ data, analyzing all period (ρ = 0.60) and non-winter period (ρ = 0.61) separately.

Tavakol, Ameneh↗