Sequential Estimation Research Articles

A Strong Gravitational Lens Is Worth a Thousand Dark Matter Halos: Inference on Small-scale Structure Using Sequential Methods

Strong gravitational lenses are a singular probe of the Universe’s small-scale structure—they are sensitive to the gravitational effects of low-mass (<1010 M ⊙) halos even without a luminous counterpart. Recent strong-lensing analyses of dark matter structure rely on simulation-based inference (SBI). Modern SBI methods, which leverage neural networks as density estimators, have shown promise in extracting the halo-population signal. However, it is unclear whether the constraints from these models are limited by the methodology or the data. In this study, we introduce an accelerator-optimized simulation pipeline that can generate lens images with realistic subhalo populations in milliseconds. Leveraging this simulator, we identify the main limitation of our fiducial SBI analysis: training set size. We then adopt a sequential neural posterior estimation (SNPE) approach, allowing us to refine the training distribution to align with the observed data. Using only one-fifth as many mock Hubble Space Telescope images, SNPE matches the constraints on the low-mass halo population produced by our best nonsequential model. Our experiments suggest that an over 3 order-of-magnitude increase in training set size and GPU hours would be required to achieve an equivalent result without sequential methods. While the full potential of the existing lens sample remains to be explored, the notable improvement in constraining power enabled by our sequential approach highlights that current constraints are limited primarily by methodology and not the data itself. Moreover, our results emphasize the need to treat training set generation and model optimization as interconnected stages of any cosmological analysis using SBI.

Co-Estimating State of Charge and Capacity of Automotive Lithium-Ion Batteries Under Deep Degradation Using Multiple Estimators

Since battery systems typically account for over 40% of the cost of an electric vehicle, their mid-life replacements are exceptional. Therefore, the battery’s lifespan must exceed that of the vehicle. To ensure long-term and safe use, accurate state-of-charge (SOC) estimation must be maintained throughout the battery’s lifespan. This requires appropriate updates to parameters, such as capacity, in the battery model. In this context, dual extended Kalman filters, which simultaneously estimate both states and parameters, have gained interest. While existing reports on simultaneous estimators seemed promising, our study found that they performed well under low levels of battery aging but encountered issues at higher levels. Accurately reflecting the actual physicochemical changes of the parameters in aging cells is challenging for two reasons: the limited number of measurements of terminal voltage available for numerous parameters, and the weak observability of the capacity. Therefore, we combined the simultaneous estimator with a capacity estimator operated separately during charging and a sequential estimator specialized for an enhanced self-correcting model, achieving SOC accuracy within 5% even when the SOH decreased by 30%. However, there is still much work to be carried out to implement sequential estimators in battery management systems operating in real time with limited computational resources.

Earth shadow time/accelerometer/GNSS-based geosynchronous transfer orbit determination method for electric propulsion satellite

Autonomous orbital maneuvering of an electric propulsion satellite in geosynchronous transfer orbit (GTO) requires more accurate autonomous orbit determination (OD). Implementing the traditional autonomous OD method for the electric propulsion satellites may result in the accumulation of measurement errors and dynamic errors from orbit extrapolation, which significantly restrict the OD accuracy. Fortunately, an electric propulsion satellite in GTO can sense the transit time in or out of the Earth shadow according to the output power change of the solar array. Therefore, an Earth shadow time/accelerometer/GNSS-based geosynchronous transfer OD method for electric propulsion satellites is proposed in this paper. First, a system state model with dynamics is established for the entire orbit transfer process. Second, measurement models that use the measurement information from the accelerometer, GNSS, and the transit time into or out of the Earth shadow are established. Third, a sequential filtering estimation approach is designed to solve the problem of asynchronous data fusion for autonomous OD. Comparison simulations demonstrate the effectiveness and superiority of the proposed method.

GlyCompute: towards the automated analysis of protein N-linked glycosylation kinetics via an open-source computational framework.

Understanding the complex biosynthetic pathways of glycosylation is crucial for the expanding field of glycosciences. Computer-aided glycosylation analysis has greatly benefited in recent years from the development of tools found in web-based portals and open-source libraries. However, the in silico analysis of cellular glycosylation kinetics is underrepresented in current glycoscience-related tools and databases. This could be partly attributed to the limited accessibility of kinetic models developed using proprietary software and the difficulty in reliably parameterising such models. This work aims to address these challenges by proposing GlyCompute, an open-source framework demonstrating a novel, streamlined approach for the assembly, simulation, and parameterisation of kinetic models of protein N-linked glycosylation. Specifically, given one or more sets of experimentally observed N-glycan structures and their relative abundances, minimum representations of a glycosylation reaction network are generated. The topology of the resulting networks is then used to automatically assemble the material balances and kinetic mechanisms underpinning the mathematical model. To match the experimentally observed relative abundances, a sequential parameter estimation strategy using Bayesian inference is proposed, with stages determined automatically based on the underlying network topology. The proposed framework was tested on a case study involving the simultaneous fitting of the kinetic model to two protein N-linked glycoprofiles produced by the same CHO cell culture, showing good agreement with experimental observations. We envision that GlyCompute could help glycoscientists gain quantitative insights into the effect of enzyme kinetics and their perturbations on experimentally observed glycoprofiles in biomanufacturing and clinical settings.

Relative position estimation using modulated magnetic field for close proximity formation flight

This paper presents a method to estimate relative position vectors between spacecraft equipped with magnetic coils and magnetic field sensors for close proximity operation. Filters can segregate a magnetic field with a particular frequency if spacecraft drive their coils with this specific frequency. The proposed method utilizes the amplitude of the magnetic field with a particular frequency to estimate relative position vectors. The method consists of an initial position estimator and a sequential position estimator, which is an unscented Kalman filter. The initial position estimator provides a coarse estimate for the relative position vectors using the segregated magnetic field. Relation between the magnetic field and relative position vector is derived analytically in this article for the initial position estimator. The unscented Kalman filter refines the estimation accuracy by initializing the filter with the estimate by the initial position estimator. It is shown that a spacecraft can conduct relative position vector estimation using the magnetic field of a target spacecraft, provided that a few conditions clarified in the article are satisfied. Finally, the proposed estimators are evaluated numerically via simulations.

Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost

Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost

SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences

The rapid growth of earthquake catalogs, driven by machine learning-based phase picking and denser seismic networks, calls for the application of a broader range of models to determine whether the new data enhances earthquake forecasting capabilities. Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as inlabru, which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with inlabru. Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n^2)$$\\end{document} to O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n\\log n)$$\\end{document}. This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function.

Saturated load forecasting based on improved logistic regression and affinity propagation

Saturated load forecasting (SLF) is a crucial guarantee for stable operation of power grid. However, insufficient data makes SLF collapse. Although logistic regression (LR) can be employed to tackle this problem, its non-linearity may lead to analytically unsolvable maximum likelihood (ML) function. Due to this dilemma, this paper proposes a sequential LR estimator. It depends on minimum variance unbiased estimator (MVUE) and maximum likelihood estimator (MLE) to form an iterative method: in which a linearized statistical model is established by inverse substitution to reduce complexity. Moreover, a new forecasting framework combining LR estimator with clustering algorithms is constructed. In this framework, load data are clustered based on affinity propagation (AP) before LR. Subsequently, SLF result is obtained from corresponding categories by iteration. Simulation results show that the method proposed in this paper has lower computational complexity and higher prediction accuracy.

Enhanced Characterization of Fractured Zones in Bedrock Using Hydraulic Tomography through Joint Inversion of Hydraulic Head and Flux Data

Hydraulic tomography (HT) is a promising technique for high-resolution imaging of subsurface heterogeneity, which addresses the limitations of traditional methods, such as borehole drilling and geophysical surveys. This study focuses on the application of HT to detect and characterize fractured zones in bedrock and addresses the gap in the understanding of the role of distributed flux data in the joint inversion of hydraulic head and flux data. By conducting synthetic injection tests and using sequential successive linear estimators for inversion, the study explores the effectiveness of combining limited head data with distributed temperature sensing (A-DTS)-derived flux data. The findings highlight the fact that integrating flux data significantly enhances the accuracy of identifying fracture permeability characteristics, even when head data is sparse. This approach not only improves the resolution of hydraulic conductivity fields but also offers a cost-effective strategy for practical field applications. The results underscore the potential of HT to enhance our understanding of groundwater flow and contaminant transport in fractured media, which has important implications for carbon capture, enhanced geothermal systems, and radioactive waste disposal.

A novel sequential estimation framework for battery state of health and remaining useful life based on sparse and limited data

Battery State of Health (SOH) estimation and Remaining Useful Life (RUL) prediction are significant for battery management systems in both electric vehicles and energy storage systems. Various battery Health Indicators (HIs) and abundant health information are generally utilized for SOH and RUL estimation. However, HIs and health information may not be available for various reasons such as sensor installation limitations, computational burden and communication delay of the system. To overcome the issue of sparse and limited data acquisition in real applications, this study proposed a novel battery SOH and RUL sequential estimation framework only utilizing sparse segments of time series voltage data. The Extreme Learning Machine (ELM) and Long Short Term Memory (LSTM) network are applied for SOH estimation and RUL prediction respectively. Locally Weighted Scatterplot Smoothing (LOWESS) is used for both data smoothing and sparse data reconstruction. Three common battery datasets are fully investigated for validation. The experiment results show well estimation accuracies in both battery SOH and RUL, demonstrating the effectiveness of the framework in limited data prediction. Several popular SOH and RUL estimation algorithms and two state-of-the-art works are compared to further elaborate the superiority of the proposed framework.

Grasping Under Uncertainties: Sequential Neural Ratio Estimation for 6-DoF Robotic Grasping

Grasping Under Uncertainties: Sequential Neural Ratio Estimation for 6-DoF Robotic Grasping

Real-time gamma-ray energy spectrum / dose monitor with k-α method based on sequential bayesian estimation

Medical applications of radiation have been widely spread until now. However, the exposure of medical staff is sometimes overlooked, because treatment of patients is the first priority. The purpose of this study is to develop a small and light monitor that can measure the energy spectrum and dose of gamma-rays at the same time in real-time for medical applications. Using the monitor, the medical staff could be guided to be more aware ofthe risk of radiation, and finally the exposure to them could be substantially suppressed. So far, a CsI scintillator has been chosen as a detection device of gamma-rays and combined with a Multi-Pixel Photon Counter (MPPC) to develop a prototype monitor. Then we confirmed its basic performance with standard gamma-ray sources. To achieve the real-time measurement, α method (sequential Bayesian estimation) was adopted and improved to propose a new unfolding process, named k-α method, with which the convergence speed could really be accelerated to realize real-time measurement. Also, gamma-ray measurements with a mixed source of 133Ba, 137Cs and 60Co were carried out to confirm the validity of the present monitor. As a result, it was found that gamma-ray energy spectrum could be estimated successfully in several-tens seconds in the field of around 6 μSv/h. For the dose estimation, the correct values could be estimated just after starting measurement.

Balancing Performance and Portability: A Study on CsI(Tl) Crystal Sizes for Real-Time Gamma-Ray Spectrum and Dose Monitoring

Current radiation dosimeters sometimes face accuracy limitations or provide only cumulative doses over long periods. To contribute to this area, we developed a portable monitor that measures the energy spectrum and dose of gamma rays in real time. To achieve this, we used an improved sequential Bayesian estimation algorithm. The dose rate was then derived from the energy spectrum by applying a flux-to-dose conversion coefficient. The monitor consists mainly of a CsI(Tl) scintillator and a multi-pixel photon counter (MPPC). In developing this device, we focused on striking a balance between measurement accuracy, ease of use, and portability. As an essential aspect of the research, we investigated the influence of the CsI(Tl) crystal size on the performance of the monitor to determine an optimal size. This was accomplished by calculating the detection efficiency and energy resolution through experimental measurements using standard gamma-ray sources and simulations using MCNP5. Within the scope of the research, detector response functions were created for each crystal size for an energy range of 10 keV to 3 MeV. Considering an optimal balance of detection efficiency and energy resolution alongside a compact size suitable for portable applications, the crystal measuring 2.6 × 2.6 × 1.3 cm3 was deemed preferable.

A Possibilistic Formulation of Autonomous Search for Targets.

Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

Watermarking-based remote secure sequential fusion estimation under the event-triggered mechanism

This paper investigates the problem of remote sequential fusion estimation using event-triggered communication mechanism in cyber–physical systems with deception attack interference. The watermarking defense strategy is used to encrypt and decrypt the data transmitted by sensors, which is convenient for the χ2 detector to detect deception attacks. The effectiveness of the χ2 detector is verified for three different attack scenarios. In addition, an event-triggered mechanism is designed based on the prediction error variance, which greatly saves the network resource while guaranteeing the accuracy of sequential fusion estimation. Finally, simulation results are given to illustrate the effectiveness of the proposed sequential fusion estimation method.

Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

Abstract We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. k-EPL considers the joint behaviour of multiple players simultaneously, as opposed to individual responses to other agents’ equilibrium play. This, in addition to reframing the problem from conditional choice probability (CCP) space to value function space, yields a computationally tractable, stable, and efficient estimator. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum-likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum-likelihood estimator at a nearly superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL’s good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data. We apply the estimator to analyse competition in the U.S. wholesale club industry.

Sequential Estimation of Conditional Odds Ratio

Sequential Estimation of Conditional Odds Ratio

Video-based sequential Bayesian homography estimation for soccer field registration

A novel Bayesian framework is proposed, which explicitly relates the homography of one video frame to the next through an affine transformation while explicitly modelling keypoint uncertainty. The literature has previously used differential homography between subsequent frames, but not in a Bayesian setting. In cases where Bayesian methods have been applied, camera motion is not adequately modelled, and keypoints are treated as deterministic. The proposed method, Bayesian Homography Inference from Tracked Keypoints (BHITK), employs a two-stage Kalman filter and significantly improves existing methods. Existing keypoint detection methods may be easily augmented with BHITK. It enables less sophisticated and less computationally expensive methods to outperform the state-of-the-art approaches in most homography evaluation metrics. Furthermore, the homography annotations of the WorldCup and TS-WorldCup datasets have been refined using a custom homography annotation tool that has been released for public use. The refined datasets are consolidated and released as the consolidated and refined WorldCup (CARWC) dataset.

The Sequential estimation of generalized linear model coefficients

Generalized LinearModels (GLM) allows us to model the relationship between a response variable and one or more predictor variables while taking into account the distribution of the response variable. It is a useful tool for modeling data that do not follow a normal distribution and can be applied to a wide range of data types and problem settings. As data becomes increasingly relevant in our daily lives, the use of these models is becoming more important. However, this increase in importance also implies an increase in the complexity of estimation due to the volume of data that must be processed. In contrast, when dealing with laboratory experiments or other situations, we may have limited observations making it challenging to obtain robust estimates. To address these challenges, this paper proposes a simple and efficient method for estimating the coefficients of GLM and provides mathematical proof for the almost sure convergence of this method towards the desired solution. The proposed method is also validated on real-world data, reinforcing its utility and effectiveness.

A photogrammetric approach for real‐time visual SLAM applied to an omnidirectional system

AbstractThe problem of sequential estimation of the exterior orientation of imaging sensors and the three‐dimensional environment reconstruction in real time is commonly known as visual simultaneous localisation and mapping (vSLAM). Omnidirectional optical sensors have been increasingly used in vSLAM solutions, mainly for providing a wider view of the scene, allowing the extraction of more features. However, dealing with unmodelled points in the hyperhemispherical field poses challenges, mainly due to the complex lens geometry entailed in the image formation process. To address these challenges, the use of rigorous photogrammetric models that appropriately handle the geometry of fisheye lens cameras can overcome these challenges. Thus, this study presents a real‐time vSLAM approach for omnidirectional systems adapting ORB‐SLAM with a rigorous projection model (equisolid‐angle). The implementation was conducted on the Nvidia Jetson TX2 board, and the approach was evaluated using hyperhemispherical images captured by a dual‐fisheye camera (Ricoh Theta S) embedded into a mobile backpack platform. The trajectory covered a distance of 140 m, with the approach demonstrating accuracy better than 0.12 m at the beginning and achieving metre‐level accuracy at the end of the trajectory. Additionally, we compared the performance of our proposed approach with a generic model for fisheye lens cameras.