Quadratic Estimation Research Articles

Efficient computation of the super-sample covariance for stage IV galaxy surveys

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the ∼15% level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3×2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30%.

Inference of gravitational lensing and patchy reionization with future CMB data

We develop an optimal Bayesian solution for jointly inferring secondary signals in the cosmic microwave background (CMB) originating from gravitational lensing and from patchy screening during the epoch of reionization. This method is able to extract full information content from the data, improving upon previously considered quadratic estimators for lensing and screening. We forecast constraints using the marginal unbiased score expansion method, and show that they are largely dominated by CMB polarization, and depend on the exact details of reionization. For models consistent with current data which produce the largest screening signals, a detection ($3\text{ }\ensuremath{\sigma}$) of the cross-correlation between lensing and screening is possible with SPT-3G and a detection of the autocorrelation is possible with CMB-S4. Models with the lowest screening signals evade the sensitivity of SPT-3G but are still possible to detect with CMB-S4 via their lensing cross-correlation.

Snow Height and Snow Water Equivalent Estimation from Snow Cover Fraction Using Sentinel-2 Satellite Images in North Kazakhstan

Climate change's influence on snowpack can significantly affect natural and anthropogenic processes. Water resources and agri-business, which depend on winter precipitation, are highly affected by variations in a snowbank and melting regimes. This paper demonstrates the comparison results of the snowpack thickness estimation in the LLP "North Kazakhstan AES" adopting distinctive techniques (quadratic, exponential, and linear functions) for assessing Fractional Snow Cover (SCF) and demonstrating Snow Water Equivalent (SWE) on the one hand, and in-situ perspective on the other. Between the 26–29 of February 2020, a field measurement was managed on the territory of 25,000 hectares. Accordingly, the thickness of the snowpack was surveyed at 560 points, and its density was measured at 70 points. Applying existing methodologies of SCF computation, it became apparent that the quadratic equation provides more reliable results at RMSE of 0.01 m, followed by linear -0.12 m and exponential -0.13 m methods. This work showed a strong correlation between snow height and SCF, namely the quadratic function in Northern Kazakhstan. Thus, we strongly suggest using Sentinel-2 MSI and the quadratic SCF estimation function for snow cover estimation, further spring flood forecasting, and other hydrological studies. Keywords: snow height, snow cover fraction, normalized-difference snow index, snow water equivalent, Sentinel-2 MSI, North Kazakhstan

Estimation Method Based on Extended Kalman Filter for Uncertain Phase Shifts in Phase-Measuring Profilometry

Phase-measuring profilometry (PMP) is increasingly applied in high-accuracy three-dimensional shape measurement. However, various factors may result in the uncertainty of phase shift values in the PMP system, and phase errors induced by actual phase shift often bring about the reconstruction failure of a measured object. A quadratic phase estimation method using the extended Kalman filter is proposed to remove the phase error introduced by uncertain phase shift. After eliminating the background and fringe modulation, the state estimation is employed to evaluate the quadratic phase coefficients in a selected mask window, and the phase shifts of adjacent fringe patterns can be estimated to compute the unwrapping phase. This paper presents a novel method for improving the accuracy of the PMP system influenced by phase shift errors, and the proposed region-wise method significantly enhances the reconstruction quality and efficiency. Experimental results show that the proposed algorithm effectively evaluates the actual phase shift and directly compensates the phase error, and has the advantages of high speed, high accuracy, and robustness.

Optimizing foreground mitigation for CMB lensing with combined multifrequency and geometric methods

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 $\ensuremath{\sigma}/4$ 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 $\ensuremath{\sigma}/2$ 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.

Testing quadratic maximum likelihood estimators for forthcoming Stage-IV weak lensing surveys

ABSTRACTHeadline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new fast implementation of the Quadratic Maximum Likelihood (QML) estimator, optimal for Gaussian fields, to test the performance of Pseudo-Cℓ estimators for upcoming weak lensing surveys and quantify the gain from a more optimal method. Through the use of realistic survey geometries, noise levels, and power spectra, we find that there is a decrease in the errors in the statistics of the recovered E-mode spectra to the level of $\sim \!\! 20\, {{\ \rm per\ cent}}$ when using the optimal QML estimator over the Pseudo-Cℓ estimator on the largest angular scales, while we find significant decreases in the errors associated with the B-modes. This raises the prospects of being able to constrain new physics through the enhanced sensitivity of B-modes for forthcoming surveys that our implementation of the QML estimator provides. We test the QML method with a new implementation that uses conjugate-gradient and finite-differences differentiation methods resulting in the most efficient implementation of the full-sky QML estimator yet, allowing us to process maps at resolutions that are prohibitively expensive using existing codes. In addition, we investigate the effects of apodization, B-mode purification, and the use of non-Gaussian maps on the statistical properties of the estimators. Our QML implementation is publicly available and can be accessed from GitHub.

Velocity reconstruction with the cosmic microwave background and galaxy surveys

The kinetic Sunyaev Zel'dovich (kSZ) and moving lens effects, secondary contributions to the cosmic microwave background (CMB), carry significant cosmological information due to their dependence on the large-scale peculiar velocity field. Previous work identified a promising means of extracting this cosmological information using a set of quadratic estimators for the radial and transverse components of the velocity field. These estimators are based on the statistically anisotropic components of the cross-correlation between the CMB and a tracer of large scale structure, such as a galaxy redshift survey. In this work, we assess the challenges to the program of velocity reconstruction posed by various foregrounds and systematics in the CMB and galaxy surveys, as well as biases in the quadratic estimators. To do so, we further develop the quadratic estimator formalism and implement a numerical code for computing properly correlated spectra for all the components of the CMB (primary/secondary blackbody components and foregrounds) and a photometric redshift survey, with associated redshift errors, to allow for accurate forecasting. We create a simulation framework for generating realizations of properly correlated CMB maps and redshift binned galaxy number counts, assuming the underlying fields are Gaussian, and use this to validate a velocity reconstruction pipeline and assess map-based systematics such as masking. We highlight the most significant challenges for velocity reconstruction, which include biases associated with: modelling errors, characterization of redshift errors, and coarse graining of cosmological fields on our past light cone. Despite these challenges, the outlook for velocity reconstruction is quite optimistic, and we use our reconstruction pipeline to confirm that these techniques will be feasible with near-term CMB experiments and photometric galaxy redshift surveys.

Real-world CMB lensing quadratic estimator power spectrum response

I describe a method to estimate response matrices of Cosmic Microwave Background (CMB) lensing power spectra estimators to the true sky power under realistic conditions. Applicable to all lensing reconstruction pipelines based on quadratic estimators (QE), it uses a small number of Gaussian CMB Monte-Carlos and specially designed QE's in order to obtain sufficiently accurate matrices with little computational effort. This method may be used to improve the modelling of CMB lensing band-powers by incorporating at least some of the non-idealities encountered in CMB lensing reconstruction. These non-idealities always include masking, and often inhomogeneous filtering, either in the harmonic domain or pixel space. I obtain these matrices for Planck latest lensing reconstructions, and then show that the residual couplings induced by masking explain very well the residual multiplicative bias seen on the Planck simulations, removing the need for an empirical correction.

Maximum likelihood kinetic Sunyaev-Zel’dovich velocity reconstruction

The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background (CMB) temperature anisotropies induced by the scattering of CMB photons from free electrons, will be measured by near-term CMB experiments at high significance. By combining CMB temperature anisotropies with a tracer of structure, such as a galaxy redshift survey, previous literature introduced a number of techniques to reconstruct the radial velocity field. This reconstructed radial velocity field encapsulates the majority of the cosmological information contained in the kSZ temperature anisotropies, and can provide powerful new tests of the standard cosmological model and theories beyond it. In this paper, we introduce a new estimator for the radial velocity field based on a coarse-grained maximum likelihood fit for the kSZ component of the temperature anisotropies, given a tracer of the optical depth. We demonstrate that this maximum likelihood estimator yields a higher fidelity reconstruction than existing quadratic estimators in the low-noise and high-resolution regime targeted by upcoming CMB experiments. We describe implementations of the maximum likelihood estimator in both harmonic space and map space, using either direct measurements of the optical depth field or a galaxy survey as a tracer. We comment briefly on the impact of biases introduced by imperfect reconstruction of the optical depth field.

A non-linear Kalman filter for track parameters estimation in high energy physics

The Kalman Filter is a widely used approach for the linear quadratic estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks. Implementations of this formalism often make assumptions on the linearity of the underlying dynamic system and the Gaussian nature of the process noise and measurement model, which are violated in a number of track reconstruction applications. This paper introduces an implementation of a Non-Linear Kalman Filter (NLKF) within the ACTS track reconstruction toolkit. The NLKF addresses the issue of non-linearity by using a set of representative sample points during the projection of the track state to the measurement. In a typical use case, the NLKF outperforms the so-called Extended Kalman Filter in the accuracy and precision of the track parameter estimates obtained, with an increase in CPU time below a factor of two. It is therefore a promising approach for use in applications where precise estimation of track parameters is a key concern.

Distributed estimation for multi‐agent systems with relative measurements and quantized communication: A feedback quadratic framework

SummaryIn this paper, the feedback quadratic distributed state estimation problem is investigated for a class of linear discrete time‐varying multi‐agent systems subject to non‐Gaussian noises. For the multi‐agent systems, each agent has access to not only the local measurements but the relative states to its adjacent agents as well. Due to the bandwidth constraints of the digital communication networks, the signals are quantized and then exchanged between two adjacent agents, where the probabilistic uniform quantizations are taken into account. The purpose of the addressed problem is to design a novel quadratic distributed estimator for each agent based on the local information and the predictions received from the neighbors. In particular, an output injection term is introduced to handle the unstable systems. By means of the state/measurement augmentation approach, the underlying system is transformed into an augmented one, which aggregates the original vector and its second‐order Kronecker power. Accordingly, a distributed estimator is constructed such that an upper bound is ensured for the estimation error covariance and the suboptimal estimator parameters, which minimize such an upper bound, are subsequently calculated in terms of the solutions to certain matrix difference equations. Finally, an illustrative example is provided to verify the effectiveness and superiority of the proposed quadratic estimation scheme.

The nonlinear effects of air pollution on criminal behavior: evidence from Mexico City and New York

This article proposes an inverted U-shape relationship between air pollution and criminal behavior. Exposure increases criminality by raising criminals’ taste for risk and violent behavior while also reducing it by changing the number of felons and crime opportunities in the market through exacerbated morbidity and avoidance behavior. I illustrate both mechanisms with an expected utility model of the decision to delict and a simplified search and matching frictions model between criminals and crime opportunities. Linear, quadratic, and nonparametric Poisson pseudo-maximum likelihood estimator panel models confirm this bell-shaped relationship for Mexico City and New York, suggesting that the linear association between pollution and criminality uncovered by late studies may be better estimated with nonlinear models.

A Survey of LQE and MPC Discrete-Control for Acrobot

This paper surveys the Linear Quadratic Estimation (LQE) and Model Predictive Control (MPC) discrete control methods applied to the Acrobot system. Both techniques aim to achieve and maintain a balanced position for the Acrobot. Through evaluation and comparison, we highlight their strengths, limitations, and potential applications, offering insights for future robotic control research.

Is Government Spending an Important Factor in Economic Growth? Nonlinear Cubic Quantile Nexus from Eastern Europe and Central Asia (EECA)

This study rigorously investigates the non-monotonic phenomenon of the government spending–growth nexus in the EECA. Using panel data from 19 countries over the period 1995–2019, a nonlinear quadratic estimator and cubic nonlinear estimator were applied to quantile regressions. The preliminary findings revealed a negative linear nexus of government spending and economic growth using a linear model, while the nonlinear models (i.e., quadratic and cubic nonlinear estimators) indicated evidence of nonlinearity in the nexus in the EECA over the study period. Furthermore, the study found strong evidence of the existence of an inverted “N-shaped” (nonlinear cubic) nexus between government spending and growth, which can be interpreted as the typical credit-driven boom-and-bust cycle in most EECA countries. Finally, in elucidating the nexus between government spending and economic growth, the study found that most macroeconomic and governance variables are relaxing in explaining GS.

Towards optimal foreground mitigation strategies for interferometric H i intensity mapping in the low-redshift Universe

Abstract We conduct the first case study towards developing optimal foreground mitigation strategies for neutral hydrogen (H i) intensity mapping using radio interferometers at low redshifts. A pipeline for simulation, foreground mitigation, and power spectrum estimation is built, which can be used for ongoing and future surveys using MeerKAT and Square Kilometre Array Observatory. It simulates realistic sky signals to generate visibility data-given instrument and observation specifications, which is subsequently used to perform foreground mitigation and power spectrum estimation. A quadratic estimator formalism is developed to estimate the temperature power spectrum in visibility space. Using MeerKAT telescope specifications for observations in the redshift range, $z$ ∼ 0.25–0.30, corresponding to the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey, we present a case study, where we compare different approaches of foreground mitigation. We find that component separation in visibility space provides a more accurate estimation of H i clustering when compared with foreground avoidance, with the uncertainties being 30 per cent smaller. Power spectrum estimation from image is found to be less robust with larger bias and more information loss when compared with estimation in visibility. We conclude that for the considered sub-band of $z$ ∼ 0.25–0.30, the MIGHTEE survey will be capable of measuring the H i power spectrum from $k\sim 0.5$ to $k\sim 10\, {\rm Mpc^{-1}}$ with signal-to-noise ratio being ∼3. We are the first to show that, at low redshift, component separation in visibility space suppresses foreground contamination at large line-of-sight scales, allowing measurement of H i power spectrum closer to the foreground wedge, crucial for data analysis towards future detections.

Recursive state estimation for stochastic nonlinear non-Gaussian systems using energy-harvesting sensors: A quadratic estimation approach

In this paper, the recursive quadratic state estimation problem is investigated for a class of stochastic nonlinear systems (SNSs) subject to non-Gaussian noises through energy-harvesting sensors. Stochastic nonlinearities are taken into account in both state and measurement equations. The energy-harvesting technique is employed to mitigate the phenomenon of energy depletion and supply energy for data transmissions between the sensors and the remote estimator. By augmenting the state/measurements and their respective second-order Kronecker powers, the original SNS is converted into a new nonlinear system that exploits more information about the non-Gaussian noises, and the resultant quadratic estimator can then be designed by developing an efficient recursive variance-minimization algorithm. Subsequently, an upper bound is proven to exist on the estimation error covariance matrix via solving certain matrix difference equations, and such an upper bound is minimized by resorting to the design of appropriate gain parameters of the quadratic estimator. Moreover, we analyze the monotonicity of the trace of the minimal upper bound with respect to the probability of measurement transmission. Finally, a simulation example is given to demonstrate the effectiveness of the proposed quadratic estimation algorithm.

Quadratic regression estimation of hybridized nanoliquid flow using Galerkin finite element technique considering shape of nano solid particles

Because of its multivariate particle suspension approach, the developing class of fluid has a better level of stability as well as increased heat transfer. In this regard, hybrid nanofluid outperforms ordinary fluid and even well-known nanofluid. In a slick environment, we investigate its fluidity and heat transfer qualities. Nano-leveled particle morphologies, porousness materials, variable thermal conductivity, slippage velocity, and thermal radiative effects are all being studied. The Galerkin finite element method is a numerical methodology for numerically solving the governing equations (G-FEM). For this analysis, a Powell-Eyring hybrid nanofluid (PEHNF) flowing via a permeable stretchable surface is used, which comprises two types of nanoparticles (NP), copper (Cu), and titanium alloy (Ti6Al4V) dispersed in sodium alginate (C6H9NaO7). The heat transfer ratio of PEHNF (Ti6Al4V-Cu/C6H9NaO7) remained much greater than that of conventional nanofluids (Cu-C6H9NaO7), with a range of 43%–54%. When lamina particles are present, the thermal conductivity of the boundary layer increases dramatically, while spherical nanoparticles have the lowest thermal conductivity. As nanoparticles are added under their fractional sizes, radiative heat conductance, and flexible heat conductance, the system’s entropy increases. The flow system’s ability to transport mass decreases when molecule diffusivity decreases dramatically. This is theoretically related to a rise in Schmidt number against molecular diffusivity.

On Powell-Eyring hybridity nanofluidic flow based Carboxy-Methyl-Cellulose (CMC) with solar thermal radiation: A quadratic regression estimation

Examining the thorough double-hybrid nanofluid mode Yamada-Ota and Xue provide a detailed description of the Powell-Eyring fluid model (PEFM) with the grouping of the base streaming Carboxy-Methyl-Cellulose (CMC) and doubly changed Carbon nanotubes CNTs (Single-walled carbon nanotubes (SWCNT), Multi-walled carbon nanotubes (MWCNT)). The coordinate systems are considered normal vectors, which are all regarded to be components of the spinning cone system in which this fluid is thought to movement. The PEFM move and thermal characteristics are governed by the sliding boundary conditions, the porous medium, and buoyancy. Similarity transformations are employed to derive a set of ordinary differential equations (ODEs) indicated by the accurate initial requirement. These ODEs are after that numerically solved using a particular technique called the Galerkin finite element method (GFEM). In addition to the thermal dispersion, this investigation consumes likewise shaped graphical consequences for the velocity in different 2D-directions. Along with the dimensionless Nusselt number, the outcomes of the skin friction constants are tabulated under the influence of pertinent regulating factors. According to the findings, radiation increases the current field while the Darcy-Forchheimer limitation increases the movement of the 2D-axis. The frictional coefficient is additionally increased together with the x- and y-components by the buoyancy ratio parameter. Additionally, by controlling elements approximating radioactivity, absorbency, and sliding boundary conditions, the dimensionless Nusselt number is reduced (velocity and temperature). Furthermore, regarding the frictional factor Cfx, after testing with 100 combinations of Powell-Eyring-II parameter (β2) and speed slippage constrain (γ1) in between the 20% and 110%, it was noted that those constrains tends to resist frictional factor.

Research on Underwater Sound Source Localization Based on NLM-EEMD and FCM-Generalized Quadratic Correlation

The accuracy of underwater sound source localization depends on the preprocessing effect of signal denoising and delay estimation performance. In order to meet the needs of high-precision underwater positioning, this article studies a time delay estimation method based on nonlocal mean-enforced mean empirical mode decomposition (NLM-EEMD) autocorrelation denoising preprocessing and fuzzy C-means clustering (FCM)-generalized quadratic for underwater sound source localization technology. The theories such as NLM, EEMD, FCM, and generalized quadratic correlation delay estimation are studied in detail, and the speech signal of the test library in the TIMIT standard library is selected for simulation analysis, which verifies the correctness of the delay estimation method. Experiments were carried out in a larger outdoor pool. The analysis results show that the NLM-EEMD adaptive denoising method effectively reduces noise interference and improves the quality of EEMD decomposition and the FCM-generalized quadratic correlation method increases the correlation between two signals. The time delay estimation accuracy is improved, and the positioning accuracy is 48.66% higher than that of the direct generalized cross-correlation method.

Quadratic Pose Estimation Problems: Globally Optimal Solutions, Solvability/Observability Analysis, and Uncertainty Description

Pose estimation problems are fundamental in robotics. Most of these problems are challenging due to the nonconvex nature. This also sets up an obstacle for uncertainty description that is essential for pose integration and quality control. In this article, we show that a large class of related problems can be categorized as the quadratic pose estimation problems (QPEPs) and we propose a general quaternion-based mathematical model to unify these problems. To solve the nonconvex QPEPs, a Gröbner-basis method is investigated to derive their globally optimal and robust solutions. Furthermore, we develop the rules for characterizing the solvability and observability of these solutions. In addition, the uncertainty description, i.e., covariance matrix, as an important piece of information in robotic state estimation frameworks, is analyzed in detail. Theoretical results show that the covariance can be estimated via online optimization, in an efficient and unbiased manner. In this way, both the solution and covariance are guaranteed to be globally optimal. Through simulations and experiments, we show that the proposed QPEP-based solver is not only accurate, robust, and efficient but outperforms the representatives for covariance estimation. The designed algorithms are also assembled as a C++/MATLAB/Octave/ROS library, while these developed interfaces are built for main stream platforms and simultaneous localization and mapping schemes.