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Kalman filter design and analysis are discussed, and application of the analysis to multidimensional aircraft navigation problems is considered. The application of perturbation matrices, U-D factors, and filter variance component error source percentages to avionics covariance analysis is suggested. Filter design is divided into four phases, and the procedures applied in each phase are examined.
Purpose: The pharmacokinetic parameters derived from dynamic contrast-enhanced (DCE) MRI have been used in more than 100 phase I trials and investigator led studies. A comparison of the absolute values of these quantities requires an estimation of their respective probability distribution function (PDF). The statistical variation of the DCE-MRI measurement is analyzed by considering the fundamental sources of error in the MR signal intensity acquired with the spoiled gradient-echo (SPGR) pulse sequence. Methods: The variance in the SPGR signal intensity arises from quadrature detection and excitation flip angle inconsistency. The noise power was measured in 11 phantoms of contrast agent concentration in the range [0–1] mM (in steps of 0.1 mM) and in onein vivo acquisition of a tumor-bearing mouse. The distribution of the flip angle was determined in a uniform 10 mM CuSO{sub 4} phantom using the spin echo double angle method. The PDF of a wide range of T1 values measured with the varying flip angle (VFA) technique was estimated through numerical simulations of the SPGR equation. The resultant uncertainty in contrast agent concentration was incorporated in the most common model of tracer exchange kinetics and the PDF of the derived pharmacokinetic parameters was studied numerically. Results: The VFA method is an unbiased technique for measuringT1 only in the absence of bias in excitation flip angle. The time-dependent concentration of the contrast agent measured in vivo is within the theoretically predicted uncertainty. The uncertainty in measuring K{sup trans} with SPGR pulse sequences is of the same order, but always higher than, the uncertainty in measuring the pre-injection longitudinal relaxation time (T1{sub 0}). The lowest achievable bias/uncertainty in estimating this parameter is approximately 20%–70% higher than the bias/uncertainty in the measurement of the pre-injection T1 map. The fractional volume parameters derived from the extended Tofts model were found to be extremely sensitive to the variance in signal intensity. The SNR of the pre-injection T1 map indicates the limiting precision with which K{sup trans} can be calculated. Conclusions: Current small-animal imaging systems and pulse sequences robust to motion artifacts have the capacity for reproducible quantitative acquisitions with DCE-MRI. In these circumstances, it is feasible to achieve a level of precision limited only by physiologic variability.
The Li-Strahler reflectance model, driven by LANDSAT Thematic Mapper (TM) data, provided regional estimates of tree size and density within 20 percent of sampled values in two bioclimatic zones in West Africa. This model exploits tree geometry in an inversion technique to predict average tree size and density from reflectance data using a few simple parameters measured in the field (spatial pattern, shape, and size distribution of trees) and in the imagery (spectral signatures of scene components). Trees are treated as simply shaped objects, and multispectral reflectance of a pixel is assumed to be related only to the proportions of tree crown, shadow, and understory in the pixel. These, in turn, are a direct function of the number and size of trees, the solar illumination angle, and the spectral signatures of crown, shadow and understory. Given the variance in reflectance from pixel to pixel within a homogeneous area of woodland, caused by the variation in the number and size of trees, the model can be inverted to give estimates of average tree size and density. Because the inversion is sensitive to correct determination of component signatures, predictions are not accurate for small areas.
Despite drawing inspiration from biological systems which are inherently noisy and variable, artificial neural networks have been shown to require precise weights to carry out the task which they are trained to accomplish. This creates a challenge when adapting these artificial networks to specialized execution platforms which may encode weights in a manner which restricts their accuracy and/or precision.Reflecting back on the non-idealities which are observed in biological systems, we investigated the effect these properties have on the robustness of spiking neural networks under perturbations to weights. First, we examined techniques extant in conventional neural networks which resemble noisy processes, and postulated they may produce similar beneficial effects in spiking neural networks. Second, we evolved a set of spiking neural networks utilizing biological non-idealities to solve a pole-balancing task, and estimated their robustness. We showed it is higher in networks using noisy neurons, and demonstrated that one of these networks can perform well under the variance expected when a hafnium-oxide based resistive memory is used to encode synaptic weights. Lastly, we trained a series of networks using a surrogate gradient method on the MNIST classification task. We confirmed that these networks demonstrate similar trends in robustness to the evolved networks. We discuss these results and argue that they display empirical evidence supporting the role of noise as a regularizer which can increase network robustness.
Abstract Tidal wetlands provide valuable ecosystem services, including storing large amounts of carbon. However, the net exchanges of carbon dioxide (CO 2 ) and methane (CH 4 ) in tidal wetlands are highly uncertain. While several biogeochemical models can operate in tidal wetlands, they have yet to be parameterized and validated against high‐frequency, ecosystem‐scale CO 2 and CH 4 flux measurements across diverse sites. We paired the Cohort Marsh Equilibrium Model (CMEM) with a version of the PEPRMT model called PEPRMT‐Tidal, which considers the effects of water table height, sulfate, and nitrate availability on CO 2 and CH 4 emissions. Using a model‐data fusion approach, we parameterized the model with three sites and validated it with two independent sites, with representation from the three marine coasts of North America. Gross primary productivity (GPP) and ecosystem respiration (R eco ) modules explained, on average, 73% of the variation in CO 2 exchange with low model error (normalized root mean square error (nRMSE) <1). The CH 4 module also explained the majority of variance in CH 4 emissions in validation sites ( R 2 = 0.54; nRMSE = 1.15). The PEPRMT‐Tidal‐CMEM model coupling is a key advance toward constraining estimates of greenhouse gas emissions across diverse North American tidal wetlands. Further analyses of model error and case studies during changing salinity conditions guide future modeling efforts regarding four main processes: (a) the influence of salinity and nitrate on GPP, (b) the influence of laterally transported dissolved inorganic C on R eco , (c) heterogeneous sulfate availability and methylotrophic methanogenesis impacts on surface CH 4 emissions, and (d) CH 4 responses to non‐periodic changes in salinity.
Tests were conducted to provide flight conditions for qualifying the Viking Decelerator System in a simulated Mars environment. A balloon launched decelerator test (BLDT) vehicle which has an external shape similar to the actual Mars Viking Lander Capsule was used so that the decelerator would be deployed in the wake of a blunt body. An effort was made to simulate the BLDT vehicle flights from the time they were dropped from the balloon, through decelerator deployment, until stable decelerator conditions were reached. The procedure used to simulate these flights using the Statistical Trajectory Estimation Program (STEP) is discussed. Using primarily ground-based position radar and vehicle onboard rate gyro and accelerometer data, the STEP produces a minimum variance solution of the vehicle trajectory and calculates vehicle attitude histories. Using film from cameras in the vehicle along with a computer program, attitude histories for portions of the flight before and after decelerator deployment were calculated independent of the STEP simulation. With the assumption that the vehicle motions derived from camera data are accurate, a comparison reveals that STEP was able to simulate vehicle motions for all flights both before and after decelerator deployment.
Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators is then performed by using a variance (Allan variance, modified Allan variance, or time variance) or a system of several variances (multivariance method). However, in some cases, several samples, or even several sets of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (one minute) and since the timing data sequence is very long (more than ten years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. Different interpolation algorithms (linear interpolation, cubic spline) are used to calculate variances in order to verify that they neither lose information nor add erroneous information. A comparison of the results of the different algorithms is given. Finally, the multivariance method was adapted to the measurement sequence of the millisecond pulsar timing data: the responses of each variance of the system are calculated for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics, and separability of this method is given.
The wind resource assessment community has long had the goal of reducing the bias between wind plant pre-construction energy yield assessment (EYA) and the observed annual energy production (AEP). This comparison is typically made between the 50% probability of exceedance (P50) value of the EYA and the long-term corrected operational AEP (hereafter OA P50), and is known as the P50 bias. The industry has critically lacked an independent analysis of bias reduction investigated across multiple consultants to identify the greatest sources of uncertainty and variance in the EYA process and the best opportunities for uncertainty reduction. The present study addresses this gap by benchmarking consultant methodologies against each other and against operational data at a scale not seen before in industry collaborations. We consider data from 10 wind plants and evaluate discrepancies between eight consultancies in the steps taken from estimates of gross to net energy. Consultants tend to overestimate the gross energy produced at the turbines and then compensate by further overestimating downstream losses, leading to a mean P50 bias near zero, still with significant variability among the individual wind plants. Within our data sample, we find that consultant estimates of all loss categories, except environmental losses, tend to reduce the project-to-project variability of the P50 bias. The disagreement between consultants, however, remains flat throughout the addition of losses. Finally, we find that differences in consultants’ estimates of project performance can lead to differences up to $10/MWh in the levelized cost of energy for a wind plant.
Recent studies of active galactic nuclei (AGNs) found a statistically inverse linear scaling between the X-ray normalized excess variance σ{sub rms}{sup 2} (variability amplitude) and the black hole (BH) mass spanning over M{sub BH}=10{sup 6}−10{sup 9} M{sub ⊙}. Suggested as having a small scatter, this scaling relation may provide a novel method to estimate the BH mass of AGNs. However, a question arises as to whether this relation can be extended to the low-mass regime below ∼10{sup 6} M{sub ⊙}. If confirmed, it would provide an efficient tool to search for AGNs with low-mass BHs using X-ray variability. This paper presents a study of the X-ray excess variances for a sample of AGNs with BH masses in the range of 10{sup 5}−10{sup 6} M{sub ⊙} observed with XMM-Newton and ROSAT, including data both from the archives and from newly preformed observations. It is found that the relation is no longer a simple extrapolation of the linear scaling; instead, the relation starts to flatten at ∼10{sup 6} M{sub ⊙} toward lower masses. Our result is consistent with the recent finding of Ludlam et al. Such a flattening of the M{sub BH}−σ{sub rms}{sup 2} relation is actually expected from the shape of the power spectrum density of AGNs, for which the break frequency is inversely scaled with the mass of BHs.
When defining optimal scanning geometries for scanning lidars for wind energy applications, we found that it is still an active field of research. Our paper evaluates uncertainties associated with arc scan geometries and presents recommendations regarding optimal configurations in the atmospheric boundary layer. The analysis is based on arc scan data from a Doppler wind lidar with one elevation angle and seven azimuth angles spanning 30° and focuses on an estimation of 10-min mean wind speed and direction. When flow is horizontally uniform, this approach can provide accurate wind measurements required for wind resource assessments in part because of its high resampling rate. Retrieved wind velocities at a single range gate exhibit good correlation to data from a sonic anemometer on a nearby meteorological tower, and vertical profiles of horizontal wind speed, though derived from range gates located on a conical surface, match those measured by mast-mounted cup anemometers. Uncertainties in the retrieved wind velocity are related to high turbulent wind fluctuation and an inhomogeneous horizontal wind field. Moreover, the radial velocity variance is found to be a robust measure of the uncertainty of the retrieved wind speed because of its relationship to turbulence properties. It is further shown that the standard error of wind speed estimates can be minimized by increasing the azimuthal range beyond 30° and using five to seven azimuth angles.
The Mars Entry, Descent, and Landing Instrumentation (MEDLI2) sensor suite collected data during entry of the Mars 2020 Perseverance rover into Mars’ atmosphere. This suite included a network of MEDLI2 Instrumented Sensor Plugs (MISPs). Each MISP was comprised of a cylinder made of Thermal Protection System (TPS) material with 1-3 embedded thermocouples (TCs), and it was flush mounted into the heatshield or backshell. Data from these in-depth TCs were used to reconstruct the aeroheating environment of the vehicle throughout entry. Surface heating was posed as an inverse problem, with the goal of estimating the surface heating by minimizing an objective function of the difference between MISP temperature measurements during flight and the temperature predictions derived from the Fully Implicit Ablation and Thermal response (FIAT) program. Given an aerothermal environment, FIAT calculates the material response and provides in-depth temperatures throughout the TPS material. To achieve the reverse, an internal tool called FIAT_Opt runs through multiple different environments until the output temperature at the TC depth closely matches the flight data. 95% confidence intervals on the reconstructed surface heating were obtained using Monte Carlo analysis, in which uncertainties in the thermocouple depth and the TPS material properties (e.g., density, thermal conductivity, heat capacity, emissivity) based on flight-lot material testing were included. A variance decomposition method using Sobol indices was employed to assess the sensitivity of the reconstructed peak heating to the TC placement and material property uncertainties. Variance decomposition was found to require tens of thousands of FIAT_Opt runs in order for the Sobol indices to converge. With a single FIAT_Opt run taking on the order of 40 minutes, the required number of computations would take months to complete, even if using multiple CPUs. To mitigate this problem, three machine learning models (ridge regression with cross-validation, random forest regression, and a deep neural network) were trained and tested using the 2000 Monte Carlo runs that were already completed. A subset of 1600 runs were used to train the model (i.e., training set), while the remaining 400 runs were used as the test set. The predictions from the deep neural network (DNN) on the test set showed nearly perfect agreement to the actual values computed with FIAT_Opt (R2 > 0.99). Using the DNN as a surrogate model, the variance decomposition using 50,000 runs was completed within minutes. The resulting Sobol indices showed that the reconstructed peak surface heating was most sensitive to the uncertainties in the thermal conductivity (ST = 0.37) and heat capacity (ST = 0.26). This method can be leveraged to provide requirements for material property measurements needed to improve the accuracy of surface heating prediction and ultimately lead to the reduction of design margins in the future. This presentation will include background on the MEDLI2 suite; the method used for inverse heating estimation; the way that material property uncertainties were accounted for using Monte Carlo analysis; a brief background on variance decomposition; the motivation for using machine learning in this context; how a neural network was trained on the data to enable variance decomposition in a fraction of the time; and the variance decomposition results for one of the MISPs.
Here, a key challenge for current and upcoming cosmic microwave background lensing measurements is their sensitivity to biases from extragalactic foregrounds, such as Sunyaev-Zel'dovich signals or cosmic infrared background emission. Several methods have been developed to mitigate these lensing foreground biases, dividing broadly into multifrequency cleaning approaches and modifications to the estimator geometry, but how to optimally combine these methods has not yet been explored in detail. In this paper, we examine which combination of lensing foreground mitigation strategies is best able to reduce the impact of foreground contamination for a Simons Observatory-like experiment while preserving maximal signal-to-noise. Although the optimal combination obtained depends on whether bias reduction or variance reduction is prioritized and on whether polarization data is used, generally, we find that combinations involving both geometric (profile hardening, source hardening, or shear) and multifrequency (symmetric cleaning) methods perform best. For lensing power spectrum measurements from temperature (polarization and temperature), our combined estimator methods are able to reduce the bias below σ/4 or 0.3% (0.1%), a factor of 16 (30) lower than the standard quadratic estimator bias, at a modest signal-to-noise cost of only 18% (12%). In contrast, single-method foreground-mitigation approaches struggle to reduce the bias to a negligible level below σ/2 without incurring a large noise penalty. For upcoming and current experiments, our combined methods therefore represent a promising approach for making lensing measurements with negligible foreground bias.
We present a constraint on the tensor-to-scalar ratio, $r$, derived from measurements of cosmic microwave background (CMB) polarization $B$-modes with "delensing,'' whereby the uncertainty on $r$ contributed by the sample variance of the gravitational lensing $B$-modes is reduced by cross-correlating against a lensing $B$-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, BICEP/Keck, and Planck data. We expand the BICEP/Keck likelihood analysis framework to accept a lensing template and apply it to the BICEP/Keck data set collected through 2014 using the same parametric foreground modelling as in the previous analysis. From simulations, we find that the uncertainty on $r$ is reduced by $\sim10\%$, from $\sigma(r)$= 0.024 to 0.022, which can be compared with a $\sim26\%$ reduction obtained when using a perfect lensing template. Applying the technique to the real data, the constraint on $r$ is improved from $r_{0.05} < 0.090$ to $r_{0.05} < 0.082$ (95% C.L.). Furthermore, this is the first demonstration of improvement in an $r$ constraint through delensing.
The bias in the rain estimation from satellites, associated with nonuniformly filled FOVs of spaceborne microwave sensors, were estimated using radar data collected during the GARP Atlantic Tropical Experiment. An approximate formula is derived which shows that this bias is closely related to the variance of rain rate within the FOV of the sensor. By applying simple models of rain field to the formula, it is shown that the formula is consistent with the variation of bias.
The need to include dynamical collision momentum transfer contributions, arising from interacting nuclear and Coulomb fields, to estimates of fragment momentum distributions is discussed. Methods based upon an optical potential model are presented. Comparisons with recent experimental data of the Siegen group for variances of transverse momentum distributions for gold nuclei at 980 A MeV fragmenting on silver foil and plastic nuclear track detector targets are made. The agreement between theory and experiment is good.
The Antarctic ozone hole demonstrates large-scale, man-made affects on our atmosphere. Surface observations now show that human produced ozone depleting substances (ODSs) are declining. The ozone hole should soon start to diminish because of this decline. In this talk we will demonstrate an ozone hole parametric model. This model is based upon: 1) a new algorithm for estimating 61 and Br levels over Antarctica and 2) late-spring Antarctic stratospheric temperatures. This parametric model explains 95% of the ozone hole area's variance. We use future ODS levels to predict ozone hole recovery. Full recovery to 1980 levels will occur in approximately 2068. The ozone hole area will very slowly decline over the next 2 decades. Detection of a statistically significant decrease of area will not occur until approximately 2024. We further show that nominal Antarctic stratospheric greenhouse gas forced temperature change should have a small impact on the ozone hole.
The Antarctic ozone hole demonstrates large-scale, man-made affects on our atmosphere. Surface observations now show that human produced ozone depleting substances (ODSs) are declining. The ozone hole should soon start to diminish because of this decline. Herein we demonstrate an ozone hole parametric model. This model is based upon: 1) a new algorithm for estimating C1 and Br levels over Antarctica and 2) late-spring Antarctic stratospheric temperatures. This parametric model explains 95% of the ozone hole area s variance. We use future ODS levels to predict ozone hole recovery. Full recovery to 1980 levels will occur in approximately 2068. The ozone hole area will very slowly decline over the next 2 decades. Detection of a statistically significant decrease of area will not occur until approximately 2024. We further show that nominal Antarctic stratospheric greenhouse gas forced temperature change should have a small impact on the ozone hole.
Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally. Internal tides can have a signature of several centimeters at the surface with wavelengths of about 50–250 km for the first mode and even smaller scales for higher-order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high-resolution ocean measurements make the correction of these small-scale signals a challenge, as the correction of all tidal variability becomes mandatory to access accurate measurements of other oceanic signals. In this context, several scientific teams are working on the development of new internal-tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal-tide models presented here focus on the coherent internal-tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal-tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents: M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data. The results show a significant altimeter variance reduction when using internal-tide corrections in all ocean regions where internal tides are generating or propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength and some insight into the residual non-stationary part of internal tides in the different regions of interest. This work led to the implementation of a new internal-tide correction (ZARON'one) in the next geophysical data records version-F (GDR-F) standards.