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At least 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

A Method and Model to Predict Initial Failure Rates

It has long been well known that actual system reliability typically falls well short of early estimates. Failure rates are often ten or more times higher than anticipated. Many reasons have been given for this, but over-optimism is the fundamental cause of too-favorable reliability predictions. Most forecasts of reliability are essentially best-case scenarios, as are predictions of budget and schedule. Confident engineers assemble estimates bottom-up, including the known factors and ignoring problems that they hope won't happen. Traditional reliability estimation is based on simply summing up the component failure rates. This ignores most actual failure causes. The way to reduce over-optimism is to use the historical system level failure rate from similar projects. Adjustments should not be made based purely on engineering judgment, but only if there is so logical quantitative justification. The traditional component-based reliability estimate is useful as a lower bound on the system failure rate. The difference between this lower bound component-based reliability and the historical system level reliability indicates how much of the total failure rate is due to system level problems rather than component failures

Jones, Harry W.↗
DOE OSTI2020

A robust dynamic state estimation approach against model errors caused by load changes

Dynamic state estimation (DSE) plays an important role in power system security monitoring and online control. In practice, there are two approaches to implementing DSE. The first approach is distributed DSE, which is based on the assumption that the terminal bus of each generator can be measured by PMUs (phasor measurement units). The assumption cannot be satisfied currently, however, because PMUs usually are installed at important high-voltage buses such as 500-kV buses installed in portions of the grid overseen by the Western Electricity Coordinating Council. Another issue of this approach is that performance of DSE is vulnerable to bad measurement data. The reason for this vulnerability is that DSE is performed separately through measurements at each terminal bus, and measurements at terminal buses are the only measurement upon which DSE can rely. Therefore, important redundant measurements are not included in this approach. The second approach is centralized DSE. This approach does not have the requirement for PMU location, and redundant measurements can be considered fully. However, load changes and grid topology changes impact centralized DSE. In this paper, we propose a new approach for handling the impact of load changes on DSE. We have developed a new algorithm that includes two sequential steps. In the first step, errors caused by load changes are detected by analyzing the difference between prediction results and measured results. In the second step, once model error is detected, a model optimization procedure is run to correct the error so the state estimation error can be mitigated. Simulation results from the IEEE 68 bus system show that the proposed approach can effectively handle model errors caused by load changes.

robust dynamic state estimation, load change, powe↗
NASA NTRS1996

Subsonic Wing Optimization for Handling Qualities Using ACSYNT

The capability to accurately and rapidly predict aircraft stability derivatives using one comprehensive analysis tool has been created. The PREDAVOR tool has the following capabilities: rapid estimation of stability derivatives using a vortex lattice method, calculation of a longitudinal handling qualities metric, and inherent methodology to optimize a given aircraft configuration for longitudinal handling qualities, including an intuitive graphical interface. The PREDAVOR tool may be applied to both subsonic and supersonic designs, as well as conventional and unconventional, symmetric and asymmetric configurations. The workstation-based tool uses as its model a three-dimensional model of the configuration generated using a computer aided design (CAD) package. The PREDAVOR tool was applied to a Lear Jet Model 23 and the North American XB-70 Valkyrie.

Soban, Danielle Suzanne↗
DOE OSTI2023

Assessment of Potential Pennycress Availability and Suitable Sites for Sustainable Aviation Fuel Refineries in Ohio

Pennycress grain has a relatively high oil content (25–36%) and it is considered a desirable feedstock to produce sustainable aviation fuel (SAF). Pennycress crop can be integrated into the corn–soybean rotation as a winter cover crop in the midwestern U.S. to provide both ecosystem services and economic benefits for the farmers, while serving as a promising feedstock for SAF production. For pennycress-based SAF biorefineries to be established at the commercial scale, a sustainable design of the supply system is required to provide reliable information on feedstock availability and optimal facility locations. The objectives of this research were to assess the pennycress production potential in Ohio, and to identify the best locations to establish the SAF biorefineries. To estimate the pennycress production potential in Ohio, a geographic information system (GIS)-based model was developed using the spatially explicit six-year historical data on areas that were planted in the corn–soybean rotation for the period of 2013 through 2018, pennycress yield estimates from field-based experiments reported in the literature, and the soil productivity index for the region of study. Optimal SAF biorefinery locations were identified using a GIS-based location-allocation model. Annual land potentially available for pennycress production in Ohio was estimated to be ~0.6 million ha, which could produce ~1.1 million metric tons of pennycress grain as feedstock to produce ~210 million liters of SAF, depending on the pennycress yield level, oil content, and conversion efficiencies. In addition, the optimum locations for 12 biorefineries, each at an annual capacity of 18.9 million liters of SAF, were identified, and the average transportation distance was estimated to be 35 and 58 km for maximizing attendance and coverage conditions, respectively. The outcomes of this research would help minimize the risks associated with feedstock supply and cost variabilities for pennycress-based SAF production in the region.

Mousavi-Avval, Seyed Hashem↗
NASA NTRS2015

Integration of Uncertain Ramp Area Aircraft Trajectories and Generation of Optimal Taxiway Schedules at Charlotte Douglas (CLT) Airport

The integration of aircraft maneuver characteristics into an optimal taxiway scheduling solution is challenging due to the uncertainties that are intrinsic to ramp area aircraft trajectories. To address the challenge, we build a stochastic model of ramp area aircraft trajectories that is used to generate a probabilistic measure of conflict within the Charlotte Douglas International Airport (CLT) ramp area. Parameters of the conflict distributions are estimated and passed to a Mixed Integer Linear Program that solves for an optimal taxiway schedule constrained to be conflict free in the presence of trajectory uncertainties. Here we extend our previous research by accounting for departing and arriving aircraft whereas our prior formulation only accounted for departing aircraft.

taxiway schedule↗
NASA NTRS2011

Principal Component Noise Filtering for NAST-I Radiometric Calibration

The National Polar-orbiting Operational Environmental Satellite System (NPOESS) Airborne Sounder Testbed- Interferometer (NAST-I) instrument is a high-resolution scanning interferometer that measures emitted thermal radiation between 3.3 and 18 microns. The NAST-I radiometric calibration is achieved using internal blackbody calibration references at ambient and hot temperatures. In this paper, we introduce a refined calibration technique that utilizes a principal component (PC) noise filter to compensate for instrument distortions and artifacts, therefore, further improve the absolute radiometric calibration accuracy. To test the procedure and estimate the PC filter noise performance, we form dependent and independent test samples using odd and even sets of blackbody spectra. To determine the optimal number of eigenvectors, the PC filter algorithm is applied to both dependent and independent blackbody spectra with a varying number of eigenvectors. The optimal number of PCs is selected so that the total root-mean-square (RMS) error is minimized. To estimate the filter noise performance, we examine four different scenarios: apply PC filtering to both dependent and independent datasets, apply PC filtering to dependent calibration data only, apply PC filtering to independent data only, and no PC filters. The independent blackbody radiances are predicted for each case and comparisons are made. The results show significant reduction in noise in the final calibrated radiances with the implementation of the PC filtering algorithm.

Tian, Jialin↗
NASA NTRS2011

Optimal Asteroid Mass Determination from Planetary Range Observations: A Study of a Simplified Test Model

Mars ranging observations are available over the past 10 years with an accuracy of a few meters. Such precise measurements of the Earth-Mars distance provide valuable constraints on the masses of the asteroids perturbing both planets. Today more than 30 asteroid masses have thus been estimated from planetary ranging data (see [1] and [2]). Obtaining unbiased mass estimations is nevertheless difficult. Various systematic errors can be introduced by imperfect reduction of spacecraft tracking observations to planetary ranging data. The large number of asteroids and the limited a priori knowledge of their masses is also an obstacle for parameter selection. Fitting in a model a mass of a negligible perturber, or on the contrary omitting a significant perturber, will induce important bias in determined asteroid masses. In this communication, we investigate a simplified version of the mass determination problem. Instead of planetary ranging observations from spacecraft or radar data, we consider synthetic ranging observations generated with the INPOP [2] ephemeris for a test model containing ~25000 asteroids. We then suggest a method for optimal parameter selection and estimation in this simplified framework.

asteroids↗
NASA NTRSDate not supplied

OCO-2 Satellite-imposed Constraints on Terrestrial Biospheric CO2 Flux over South Asia

The spatiotemporal variability of terrestrial biospheric carbon dioxide (CO2) flux over South Asia is poorly understood. The inverse model “top-down” CO2 flux estimates which rely on atmospheric CO2 observational data are impeded by sparse in situ measurements over this region. The Orbiting Carbon Observatory 2 (OCO-2) provides much needed global retrievals of column-average CO2 dry-air mole fraction (XCO2) with the finest spatial and temporal resolution and highest sensitivity to surface fluxes available to-date. This study conducted global inverse model simulations as part of the second OCO-2 Multi-model Intercomparison Project assimilating version 9 of the OCO-2 XCO2 retrievals in land nadir (LN) and land glint (LG) observing modes and global in situ (IS) measurements. The four-dimensional variational assimilation system with the GEOS-Chem global chemical transport model was used to estimate CO2 fluxes from 2015 to 2018. We then assessed the spatiotemporal variability of optimized CO2 Net ecosystem Exchange (NEE) fluxes aggregated over the South Asia region. The most robust result found by assimilating OCO-2 observations was the constraints imposed on the seasonal cycle of terrestrial biospheric fluxes over South Asia. The seasonality of South Asian NEE estimated by assimilating OCO-2 or global IS data showed a larger seasonal cycle compared to the current understanding of NEE in this region (represented by the prior NEE used in the model). The satellite-in situ joint inversion (IS + LN + LG) led to land flux seasonal amplitude (absolute magnitude of the difference between peak and trough of monthly mean values over a year) of 4.0 PgC yr-1, compared to the prior model (1.5 PgC yr-1). Moreover, OCO-2 data imposed a phase shift in the seasonal cycle, resulting in a large CO2 source in April and a large uptake in September. Most of the features in the seasonal cycle imposed by OCO-2 data are in agreement with previous “top-down” studies assimilating regional aircraft observations. Nevertheless, we recommend a closer examination of the novel features highlighted by the OCO-2 column data over South Asia in future studies by conducting regional inverse modelling with denser in situ and vertically-resolved regional observations along with satellite data.

OCO-2↗
NASA NTRS2011

Filtering Methods for Error Reduction in Spacecraft Attitude Estimation Using Quaternion Star Trackers

Precision attitude determination for recent and planned space missions typically includes quaternion star trackers (ST) and a three-axis inertial reference unit (IRU). Sensor selection is based on estimates of knowledge accuracy attainable from a Kalman filter (KF), which provides the optimal solution for the case of linear dynamics with measurement and process errors characterized by random Gaussian noise with white spectrum. Non-Gaussian systematic errors in quaternion STs are often quite large and have an unpredictable time-varying nature, particularly when used in non-inertial pointing applications. Two filtering methods are proposed to reduce the attitude estimation error resulting from ST systematic errors, 1) extended Kalman filter (EKF) augmented with Markov states, 2) Unscented Kalman filter (UKF) with a periodic measurement model. Realistic assessments of the attitude estimation performance gains are demonstrated with both simulation and flight telemetry data from the Lunar Reconnaissance Orbiter.

Calhoun, Philip C.↗
DOE OSTI2020

Optimization of the electron transport layer in quantum dot light-emitting devices

Quantum dot light-emitting devices have emerged as an important technology for display applications. Their emission is a result of recombination between positive and negative charge carriers that are transported through the hole and electron conductive layers, respectively. The selection of electron or hole transport materials in these devices not only demands the alignment of energy levels between the layers but also balances the flow of electrons and holes toward the recombination sites. In this work, we examine a method for device optimization through control of the charge carrier kinetics. We employ impedance spectroscopy to examine the mobility of charge carriers through each of the layers. The derived mobility values provide a path to estimate the transition time of each charge carrier toward the emitting layer. We suggest that an optimal device structure can be obtained when the transition times of both charge carriers toward the active layer are similar. Finally, we examine our hypothesis by focusing on thickness optimization of the electron transport layer.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Battery Evaluation Profiles for X-57 and Future Urban Electric Aircraft

Battery energy density is one of the most critical design parameters for sizing all-electric aircraft, however it’s easily overestimated. Establishing the effective, usable energy density is confused by varying degrees of margin needed to account for structural and thermal management between different cell chemistry and pack designs. Therefore, a better methodology is needed to fairly compare emerging battery technologies for electric aircraft. Currently, there is a loss of critical information when vehicle trade studies are performed using “nominal” published cell-level performance metrics. Aircraft power demands rarely match these nominal power profiles, and aircraft designers lack the ability to accurately simulate the battery performance and temperature off-nominally unless the battery chemistry is well established. Conversely, battery suppliers have no generalized reference cases to publish more realistic performance metrics. This can lead to poor assumptions, such as aircraft studies assuming a fixed discharge efficiency of a battery, when in reality the usable energy in a pack is dependent on the power and thermal profile. Information needed to properly assess weight penalties for thermal management is also typically poorly characterized when assessing candidate batteries. This paper serves to better inform battery development, and similarly, provide aircraft designers with more realistic assumptions for applying knockdown margins in their designs. Detailed power and thermal performance estimates are provided, which provide a starting point for sizing power and thermal budgets using experimentally derived battery models. Results show that the X-57 battery-to-shaft efficiency is 77.3% for a particular optimized mission. Considering a 25% reserve on the battery capacity, this means that only roughly half of the original 55.3kWh ‘nominal’ pack energy can be converted to useful work during a mission. Further estimates on a clean-sheet VTOL optimization show an average 82.7% battery-to-shaft efficiency, using 98% peak efficiency inverters and 97.4% peak efficiency motors. Although higher battery efficiencies are possible, the resulting weight penalty negates improvement in vehicle performance. These trade-offs and resulting power profiles are provided as a starting point to better assess future battery designs.

Battery Electric Aircraft↗
NASA NTRSDate not supplied

Battery Evaluation Profiles for X-57 and Future Urban Electric Aircraft

Battery energy density is one of the most critical design parameters for sizing all-electric aircraft, however it’s easily overestimated. Establishing the effective, usable energy density is confused by varying degrees of margin needed to account for structural and thermal management between different cell chemistry and pack designs. Therefore, a better methodology is needed to fairly compare emerging battery technologies for electric aircraft. Currently, there is a loss of critical information when vehicle trade studies are performed using “nominal” published cell-level performance metrics. Aircraft power demands rarely match these nominal power profiles, and aircraft designers lack the ability to accurately simulate the battery performance and temperature off-nominally unless the battery chemistry is well established. Conversely, battery suppliers have no generalized reference cases to publish more realistic performance metrics. This can lead to poor assumptions, such as aircraft studies assuming a fixed discharge efficiency of a battery, when in reality the usable energy in a pack is dependent on the power and thermal profile. Information needed to properly assess weight penalties for thermal management is also typically poorly characterized when assessing candidate batteries. This paper serves to better inform battery development, and similarly, provide aircraft designers with more realistic assumptions for applying knockdown margins in their designs. Detailed power and thermal performance estimates are provided, which provide a starting point for sizing power and thermal budgets using experimentally derived battery models. Results show that the X-57 battery-to-shaft efficiency is 77.3% for a particular optimized mission. Considering a 25% reserve on the battery capacity, this means that only roughly half of the original 55.3kWh ‘nominal’ pack energy can be converted to useful work during a mission. Further estimates on a clean-sheet VTOL optimization show an average 82.7% battery-to-shaft efficiency, using 98% peak efficiency inverters and 97.4% peak efficiency motors. Although higher battery efficiencies are possible, the resulting weight penalty negates improvement in vehicle performance. These trade-offs and resulting power profiles are provided as a starting point to better assess future battery designs.

Battery↗
DOE OSTI2021

An Algebra of Machine Learners with Applications

Machine learning (ML) methods are increasingly being applied to solve complex, data-driven problems in diverse areas, by exploiting the physical laws derived from first principles such as thermal hydraulics and the abstract laws developed recently for data and computing infrastructures. These physical and abstract laws encapsulate, typically in compact algebraic forms, the critical knowledge that complements data-driven ML models. We present a unified perspective of these laws and ML methods using an abstract algebra (A;⊕,Ⓧ), wherein the performance estimation and classification tasks are characterized by the additive ⊕ operations, and the diagnosis, reconstruction, and optimization tasks are characterized by the difference Ⓧ operations. This abstraction provides ML codes and their performance characterizations that are transferable across different areas. We describe practical applications of these abstract operations using examples of throughput profile estimation tasks in data transport infrastructures, and power-level and sensor error estimation tasks in nuclear reactor systems.

Rao, Nageswara↗
DOE OSTI2025

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Reverse Osmosis (RO) are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in (ultra-filtration) UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square error (RMSE) metric. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent covariates across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is studied for both direct and recursive RF modelling approaches across increasing forecast horizons. Accurate prediction of initial TMP is critical for optimizing RO operations, as it enables the development of robust modelling frameworks by accurately estimating membrane fouling trends, thereby enhancing process efficiency and long-term reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗
DOE OSTI2020

The Beam Dump eXperiment

Hadronic matter makes about 14% of the known universe. The remaining 86% is Dark Matter (DM). Since it does not interact with the ordinary matter via electromagnetic force, DM is not visible and, to date, it escaped detection. The search for Dark Matter (DM) is one of the hottest topic in modern physics. Despite the increasing number of astrophysical and cosmological observations proving the existence, so far no particle physics experiment has detected DM yet. Up to now, most of the experimental efforts have been focused on the so called WIMP (Weakly Interacting Massive Particle) paradigm, which predicts heavy DM (10 GeV-10 TeV mass range) interacting with Standard Model (SM) particles via the weak force mediators (W or Z bosons). More recently, due to the lack of clear evidence of WIMPs, other models of DM gained the interest of the physics community. These models consider Light DM particles (LDM), in MeV-GeV mass range. Among LDM theories, the Dark Photon theory predicts the existence of a Dark Sector interacting with SM particles via a new massive vector boson (Dark Photon, Heavy Photon or A0), mediator of a new force. This scenario, despite being theoretically well motivated, is remarkably experimentally unexplored. The Beam Dump eXperiment (BDX), is an approved experiment at Jefferson Lab (JLab), aiming to discover the DM predicted witihn the Dark Photon theory. The experiment uses the CEBAF (Continuous Electron Beam Accelerator Facility) 11 GeV electron beam, impinging on the JLab Hall-A beam-dump, to produce a beam of DM particles, detected by a ~ 1 m3 detector made of thallium doped cesium iodide (CsI(Tl)) crystals located ~ 20 m downstream. In order to achieve excellent background rejection, the experimental setup includes active vetos and passive shielding surrounding CsI(Tl) crystals. Given the weakness of the DM-SM interaction, the scattering of a DM particle in the BDX detector is a rare event. Therefore, the characterization of the expected background is a critical aspect of the experiment. Both cosmogenic and penetrating SM particles produced by the beam interaction in the dump contribute to the background of the experiment. While the cosmogenic contribution can be measured during the experiment when the beam is off, beam-related background can only be estimated via Monte Carlo (MC) simulations. Therefore, a careful assessment of possible systematics introduced by the MC is needed. The beam-correlated background characterization was made by measuring the muon flux produced by the interaction of the CEBAF beam with Hall-A dump in a dedicated experimental campaign in spring 2018 [1]. The comparison to the ?ux predicted by MC allowed us to validate the BDX simulation framework. The reach of BDX, i.e. the region that the experiment can probe in the LDM theory parameter space, depends critically on the background rejection capability and signal detection effciency. For this reason, the detector setup was fine-tuned through a dedicated study. The response to LDM and background events was evaluated for different setups and selection cuts. As a result of this procedure, the configuration resulting in the best sensitivity was selected [2]. The reach calculation was performed taking into account the different LDM production mechanisms, including the contribution of secondary particles produced in the beam-dump. In particular, the effect of the secondary positrons annihilation was found to be extremely significant. In the majority of the sensitivity studies, this contribution is neglected, but recent results [3] [4] demonstrated that this process significantly enhances the sensitivity of lepton beam-dump experiments. Currently, the BDX collaboration is focused on the deployment and operation of a small detector, called BDX-MINI, built to perform a preliminary physics measurement searching for LDM at JLab. This test will pave the way to the realization of the full BDX experiment. The measurement is currently ongoing but results are expected by the end of this year. During my PhD I was involved in all aspects of the BDX experiment: design, simulation, prototyping and data analysis. The main results of my work are reported in this thesis. This manuscript is organized as follows: the first Chapter provides an introduction to the theory of LDM, with particular attention to the Dark Photon paradigm; the second Chapter illustrates the BDX experimental setup, the LDM production and detection mechanisms and the expected backgrounds; Chapter 3 and 4 describe, respectively, the BDX-HODO measurement, with a detailed description of the simulations, and the BDX experimental setup and analysis cuts optimization. Chapter 5 reports about BDXMINI detector characterization, calibration and sensitivity estimate. Finally, Chapter 6 describes in detail the calculation of the secondary positron annihilation contribution to the sensitivity of BDX and other electron-beam thick-target experiment.

Marsicano, Luca↗
DOE OSTI2022

Dynamic, resilient sensing system for automatic cyber-attack neutralization

An industrial asset may have monitoring nodes that generate current monitoring node values. An abnormality detection computer may determine that an abnormal monitoring node is currently being attacked or experiencing fault. A dynamic, resilient estimator constructs, using normal monitoring node values, a latent feature space (of lower dimensionality as compared to a temporal space) associated with latent features. The system also constructs, using normal monitoring node values, functions to project values into the latent feature space. Responsive to an indication that a node is currently being attacked or experiencing fault, the system may compute optimal values of the latent features to minimize a reconstruction error of the nodes not currently being attacked or experiencing a fault. The optimal values may then be projected back into the temporal space to provide estimated values and the current monitoring node values from the abnormal monitoring node are replaced with the estimated values.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Analysis of a spatial tracking subsystem for optical communications

Spatial tracking plays a very critical role in designing optical communication systems because of the small angular beamwidth associated with the optical signal. One possible solution for spatial tracking is to use a nutating mirror which dithers the incoming beam at a rate much higher than the mechanical disturbances. A power detector then senses the change in detected power as the signal is reflected off the nutating mirror. This signal is then correlated with the nutator driver signals to obtain estimates of the azimuth and elevation tracking signals to control the fast scanning mirrors. A theoretical analysis is performed for a spatial tracking system using a nutator disturbed by shot noise and mechanical vibrations. Contributions of shot noise and mechanical vibrations to the total tracking error variance are derived. Given the vibration spectrum and the expected signal power, there exists an optimal amplitude for the nutation which optimizes the receiver performance. The expected performance of a nutator based system is estimated based on the choice of nutation amplitude.

Win, Moe Z.↗
NASA NTRS1984

On Estimating the Phase of Periodic Waveform in Additive Gaussian Noise, Part 2

Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.

Rauch, L. L.↗