Uncertainty Covariance Matrix Research Articles

Multivariate Uncertainty in Deep Learning.

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes filters are typically assumed to be a fixed covariance matrix. This assumption is risky, particularly for "black box" deep learning models, in which uncertainty can vary dramatically and unexpectedly. Accurate quantification of multivariate uncertainty will allow for the full potential of deep learning to be used more safely and reliably in these applications. We show how to model multivariate uncertainty for regression problems with neural networks, incorporating both aleatoric and epistemic sources of heteroscedastic uncertainty. We train a deep uncertainty covariance matrix model in two ways: directly using a multivariate Gaussian density loss function and indirectly using end-to-end training through a Kalman filter. We experimentally show in a visual tracking problem the large impact that accurate multivariate uncertainty quantification can have on the Kalman filter performance for both in-domain and out-of-domain evaluation data. We additionally show, in a challenging visual odometry problem, how end-to-end filter training can allow uncertainty predictions to compensate for filter weaknesses.

The Pantheon+ Analysis: SuperCal-fragilistic Cross Calibration, Retrained SALT2 Light-curve Model, and Calibration Systematic Uncertainty

We present a recalibration of the photometric systems in the Pantheon+ sample of Type Ia supernovae (SNe Ia) including those in the SH0ES distance-ladder measurement of H 0. We utilize the large and uniform sky coverage of the public Pan-STARRS stellar photometry catalog to cross calibrate against tertiary standards released by individual SN Ia surveys. The most significant updates over the “SuperCal” cross calibration used for the previous Pantheon and SH0ES analyses are: (1) expansion of the number of photometric systems (now 25) and filters (now 105), (2) solving for all filter offsets in all systems simultaneously to produce a calibration uncertainty covariance matrix for cosmological-model constraints, and (3) accounting for the change in the fundamental flux calibration of the Hubble Space Telescope CALSPEC standards from previous versions on the order of 1.5% over a Δλ of 4000 Å. We retrain the SALT2 model and find that our new model coupled with the new calibration of the light curves themselves causes a net distance modulus change (d μ/dz) of 0.04 mag over the redshift range 0 < z < 1. We introduce a new formalism to determine the systematic impact on cosmological inference by propagating the covariance in the fitted calibration offsets through retraining simultaneously with light-curve fitting and find a total calibration uncertainty impact of σ w = 0.013; roughly half the size of the sample statistical uncertainty. Similarly, we find the systematic SN calibration contribution to the SH0ES H 0 uncertainty is less than 0.2 km s−1 Mpc−1, suggesting that SN Ia calibration cannot resolve the current level of the “Hubble Tension.”

A novel feedback correction-adaptive Kalman filtering method for the whole-life-cycle state of charge and closed-circuit voltage prediction of lithium-ion batteries based on the second-order electrical equivalent circuit model

Accurate state of charge (SOC) and closed-circuit voltage (CCV) prediction is essential for lithium-ion batteries and their model performance. In this study, a novel feedback correction-adaptive Kalman filtering (FC-AKF) method is proposed for the online battery state co-prediction, which is adaptive to the whole-life-cycle of the lithium-ion battery based on the improved second-order equivalent circuit model (SO-ECM). For the feedback correction strategy, the optimized iterative state initialization is conducted using the uncertainty covariance matrix of the prior three-time points with the convergence of the updating process. The experimental results show that the SOC prediction error of the proposed FC-AKF method is 0.0099% and 0.975% compared with the ampere-hour integral method under the dynamic stress test (DST) and the Beijing bus dynamic stress test (BBDST) working conditions, respectively. Also, the CCV traction by the SO-ECM is 0.80 V and has fast initial convergence and quick prediction error reduction characteristics. The constructed iterative calculation model promotes the accurate SOC and CCV co-prediction effect, improving the safety and longevity of lithium-ion batteries with high precision and fast convergence advantages.

Uncertainty of atmospheric microwave absorption model: impact on ground-based radiometer simulations and retrievals

Abstract. This paper presents a general approach to quantify absorption model uncertainty due to uncertainty in the underlying spectroscopic parameters. The approach is applied to a widely used microwave absorption model (Rosenkranz, 2017) and radiative transfer calculations in the 20–60 GHz range, which are commonly exploited for atmospheric sounding by microwave radiometer (MWR). The approach, however, is not limited to any frequency range, observing geometry, or particular instrument. In the considered frequency range, relevant uncertainties come from water vapor and oxygen spectroscopic parameters. The uncertainty of the following parameters is found to dominate: (for water vapor) self- and foreign-continuum absorption coefficients, line broadening by dry air, line intensity, the temperature-dependence exponent for foreign-continuum absorption, and the line shift-to-broadening ratio; (for oxygen) line intensity, line broadening by dry air, line mixing, the temperature-dependence exponent for broadening, zero-frequency line broadening in air, and the temperature-dependence coefficient for line mixing. The full uncertainty covariance matrix is then computed for the set of spectroscopic parameters with significant impact. The impact of the spectroscopic parameter uncertainty covariance matrix on simulated downwelling microwave brightness temperatures (TB) in the 20–60 GHz range is calculated for six atmospheric climatology conditions. The uncertainty contribution to simulated TB ranges from 0.30 K (subarctic winter) to 0.92 K (tropical) at 22.2 GHz and from 2.73 K (tropical) to 3.31 K (subarctic winter) at 52.28 GHz. The uncertainty contribution is nearly zero at 55–60 GHz frequencies. Finally, the impact of spectroscopic parameter uncertainty on ground-based MWR retrievals of temperature and humidity profiles is discussed.

Consistency between GRUAN sondes, LBLRTM and IASI

Abstract. Radiosonde soundings from the GCOS Reference Upper-Air Network (GRUAN) data record are shown to be consistent with Infrared Atmospheric Sounding Instrument (IASI)-measured radiances via LBLRTM (Line-By-Line Radiative Transfer Model) in the part of the spectrum that is mostly affected by water vapour absorption in the upper troposphere (from 700 hPa up). This result is key for climate data records, since GRUAN, IASI and LBLRTM constitute reference measurements or a reference radiative transfer model in each of their fields. This is specially the case for night-time radiosonde measurements. Although the sample size is small (16 cases), daytime GRUAN radiosonde measurements seem to have a small dry bias of 2.5 % in absolute terms of relative humidity, located mainly in the upper troposphere, with respect to LBLRTM and IASI. Full metrological closure is not yet possible and will not be until collocation uncertainties are better characterized and a full uncertainty covariance matrix is clarified for GRUAN.

Nonparametric Uncertainty Estimation and Propagation for Noise Robust ASR

We consider the framework of uncertainty propagation for automatic speech recognition (ASR) in highly nonstationary noise environments. Uncertainty is considered as the variance of speech distortion. Yet, its accurate estimation in the spectral domain and its propagation to the feature domain remain difficult. Existing methods typically rely on a single uncertainty estimator and propagator fixed by mathematical approximation. In this paper, we propose a new paradigm where we seek to learn more powerful mappings to predict uncertainty from data. We investigate two such possible mappings: linear fusion of multiple uncertainty estimators/propagators and nonparametric uncertainty estimation/propagation. In addition, a procedure to propagate the estimated spectral-domain uncertainty to the static Mel frequency cepstral coefficients (MFCCs), to the log-energy, and to their first- and second-order time derivatives is proposed. This results in a full uncertainty covariance matrix over both static and dynamic MFCCs. Experimental evaluation on Tracks 1 and 2 of the 2nd CHiME Challenge resulted in up to 29% and 28% relative keyword error rate reduction with respect to speech enhancement alone.

The importance of uncertainty covariance tuning for steady-state data reconciliation in mineral and metal processing

Data reconciliation is widely applied in metallurgical plants for steady-state estimation of process variables. Algorithms are mainly based on mass and energy conservation equations that could be mostly extracted from process flow diagrams. An important difficulty is to characterize uncertainties about the plant behavior. Usually, the Gaussian context is assumed and a Maximum-Likelihood estimator is retained. In practice, tuning the weighting matrix, i.e. selecting the variances of modeling and measurement errors, is a challenging task that is sometimes overlooked. The objective of the paper is to illustrate the impact of correctly choosing uncertainty covariance matrices. Effects of matrix structures are investigated to assess the sensitivity of data reconciliation to uncertainty. Analyses are supported by simulation of basic case-studies including a combustion chamber, a hydrocyclone, a flotation circuit and a separation unit. Results show that adjustment of the uncertainty covariance matrix has a significant impact on the precision of estimates. A correct selection is highly valuable for subsequent uses of reconciled data.

Enthalpy and entropy changes in formation of gas phase sulfnric acid monohydrates and dihydrates as a result of fitting to experimental pressure data

The values of enthalpy change ΔH1 = −44.3 kJ/mol and entropy change ΔS1 = −94.6 J/mol in the gas phase addition of a water molecule to a sulfuric acid molecule and entropy change ΔS2 = −145 J/mol in hydration of a sulfuric acid monohydrate are obtained by a fitting procedure. The procedure uses experimental data from the literature on total pressure of sulfuric acid hydrates and free molecules. The enthalpy change in monohydrate hydration is taken, based on the results of ab initio calculations given in literature, to be ΔH2 = ΔH1 ‐ 10 kJ/mol. The estimate of covariance matrix of uncertainties of these values is obtained. The standard errors of estimates of ΔH1, ΔS1, and ΔS2 are 43%, 63%, and 45% of the above values, respectively. Uncertainties are strongly correlated. The sulfuric acid hydration model is proposed for geophysical applications. The model converts total acid to free acid in accordance with experimental measurements and increases the predicted values of sulfuric acid‐water nucleation rate by 102–107 times compared with the classical liquid drop hydrate model.

A new approach to the characterisation of rock formations for use in logging tool calibration facilities

A novel approach to the characterization of rock formations for the calibration of neutron porosity tools was developed using the SPARTAN sandstone test pits. The responses measured with different tools and their sensitivities to formation characteristics were calculated with the McBend Monte Carlo code. Consistent values of the porosity, grain density, and macroscopic thermal neutron absorption cross-section of the sandstone were derived from physical measurements together with their uncertainty covariance matrix. For this purpose it was necessary to supplement the chemical composition with the trace element concentrations obtained from prompt gamma analysis. Maximum likelihood adjustments were made to all parameters using the new code DATAK. Very close agreement between measurement and calculation had been obtained before making these adjustments, indicating that the uncertainties had originally been overestimated. While the magnitude of the adjustments was correspondingly small, the uncertainties on all the parameters were reduced, leading to a refined description of the formation characteristics. >

An analytical approach to Monte Carlo spectrum unfolding

The Monte Carlo spectrum unfolding method offers model-independent means for extracting the maximum information from the measurement data together with their uncertainties. The uncertainty of the unfolded spectrum, including correlations, can also be obtained. Its main shortcoming is the huge number of calculations which must be carried out. The analytical unfolding method proposed reduces the amount of calculations by orders of magnitude. It essentially consists in replacing the most appropriate a priori probability distribution required for drawing sample spectra from it at random for the Monte Carlo statistics with a certain exponential distribution from which the desired spectrum and its uncertainty covariance matrix can be analytically calculated. By taking into account the principle of maximum entropy, only a few-parameter, non-linear optimization problem remains to be solved. The results are equivalent to those obtained by the Monte Carlo unfolding in the limiting case of an infinite number of energy groups.

Error analysis of spatial representation and estimation of mobile robots

The problem of estimating the location of a mobile robot in an unstructured environment is discussed. This work extends earlier results in two important ways. First, the bias and variance of the estimation are analytically derived as functions of the angular error and distance between frames. Second, the uncertainty covariance matrix is derived and is compared to the first-order approximation previously used to estimate the result of compounding uncertain transformations to provide a framework in which the appropriateness of the first-order estimate can be formally studied. A simulation study, showing how the biases and expected distance between the estimate and true position of the robot vary as a function of measurement errors and different path plannings, is presented. Some possible improvements of the estimation method and future research topics are also given.