Estimation Problem Research Articles

Least Squares Estimation of Multifactor Uncertain Differential Equations with Applications to the Stock Market

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields.

Intangible cultural heritage based on finite element analysis: force analysis of Chinese traditional garden rockery construction

In traditional Chinese rockery stacking, the peculiarity of the materials and reliance on the personal experience of artisans during the construction process make it challenging to scientifically quantify the structural stress and use scientific methods to ensure the stability of rockery structures and the safety of the construction process. Therefore, the intangible cultural heritage of rockery stacking technology faces the problem of scientific structural inspection and risk estimation during the construction process. This study uses a finite element analysis to evaluate the structural stress of the rockery-stacking site to contribute to the sustainable development and protection of this intangible cultural heritage. After establishing a three-dimensional digital model, mechanical calculations are carried out for the overall structure of the rockery and its different parts. The analysis identifies three types of structural factors in artificial rockeries: contact, structure, and load. It also effectively and intuitively identifies the weak points in the rockery structures and provides an assessment of risks, offering valuable insights for risk prevention and for the construction and maintenance of the structures. These results contribute to the structural safety inspection of traditional Chinese rockery stacking and the structural evaluation of existing rockery heritage.

Inference Based on Sequential Order Statistics with Lindley Distribution

In this paper, we consider the problem of estimation of parameters of Lindley distribution based on sequential order statistics under conditional proportional hazard rate model. Maximum Likelihood and Bayesian estimation techniques are applied for estimating the unknown parameters. Markov Chain Monte Carlo method is implemented for obtaining the Bayes estimators. An intensive simulation study is carried out to assess the performance of different estimators discussed in this paper. A real data analysis is also performed for illustrative purposes.

Prediction of the health state of lithium-ion power batteries using machine learning

Faced with the increasingly urgent issues of energy depletion and environmental pollution, various countries are actively supporting the new energy vehicle industry, making electric vehicle technology a focus of widespread attention among researchers. The Battery Management System (BMS) plays a crucial role in overseeing the power battery's operational parameters, with the estimation of the State of Health (SOH) being a pivotal function. Accurate estimation of SOH can improve the utilization efficiency and endurance of power batteries, extend their service life, and help users achieve the best balance between system safety and economic benefits. Machine learning methods provide a new solution to the SOH estimation problem. Without analyzing the complex aging mechanisms inside the battery, online SOH estimation can be completed by learning from historical aging data. In this study, the lithium battery dataset provided by NASA is used and trained through multiple linear regression models and support vector machine models to predict the SOH of lithium-ion batteries. The results demonstrate the accuracy and reliability of both methods in predicting SOH. Simultaneously, the prediction results of different feature values are compared to obtain the most accurate combination of feature values.

Convergence analysis of state estimation for UAV formation under GPS‐denied environments

AbstractIn this article, we focus on the state estimation and formation control problem for a multi‐UAV system, where only parts of UAVs have GPS measurements, that is, the anchors, and the other UAVs measure their relative positions with anchors. With a second‐order discrete‐time model of each UAV in the formation, we analyze the convergence of state estimation (including its expectation and covariance) for commonly used consensus‐based formation control protocols, under the effect of control and measurement noise. More specifically, based on the discrete‐time stability analysis, we obtain the sufficient and necessary conditions for the expectation stability of the formation control. Using the fixed point theorem in positive symmetric matrix subspace and observability analysis, we rigorously prove that the covariance of estimation is bounded if and only if the anchor node set is globally reachable. Based on our analysis, the formation control parameters and system topology can be designed to satisfy sufficient conditions, such that the desired formation pattern can be achieved for the multi‐UAV dynamic system under GPS‐denied environments. Simulation results corroborate the effectiveness of our theoretical results.

Accelerometer static state detection (SSD)-assisted GNSS/accelerometer bridge monitoring algorithm

Abstract In the field of structural health monitoring (SHM), a loosely coupled (LC) Kalman filtering algorithm that accounts for baseline drift errors is commonly used to integrate GNSS data with accelerometer data. In the LC algorithm, the baseline drift errors are considered unknown parameters that need to be estimated. In scenario of continuous float solutions, the estimation of baseline drift error is often inaccurate, leading to the divergence of monitoring results. Theoretically, as a type of motion sensor, accelerometers are expected to qualitatively determine the priori state of bridges, whether dynamic or static. Utilizing the inherent characteristics of accelerometers and the principle of zero-velocity detection in integrated navigation, we originally propose a bridge static state detection (SSD) method based on low-cost accelerometer, and introduces this prior SSD information as a constraint in GNSS/accelerometer LC algorithm, called SSD-LC bridge monitoring algorithm. Through a simulation platform and real-world bridge monitored tests, the effectiveness of our proposed SSD method has been verified. Furthermore, our proposed SSD-LC bridge monitoring algorithm can effectively mitigate the divergence problem in baseline drift estimation that occurs with continuous GNSS float solutions in traditional algorithms, which can effectively avoid misjudgments and false alarms in bridge monitoring during GNSS anomalies.

State of energy estimation of lithium-ion battery based on long short-term memory optimization Adaptive Cubature Kalman filter.

State of energy (SOE) is an important parameter to ensure the safety and reliability of lithium-ion battery (LIB) system. The safety of LIBs, the development of artificial intelligence, and the increase in computing power have provided possibilities for big data computing. This article studies SOE estimation problem of LIBs, aiming to improve the accuracy and adaptability of the estimation. Firstly, in the SOE estimation process, adaptive correction is performed by iteratively updating the observation noise equation and process noise equation of the Adaptive Cubature Kalman Filter (ACKF) to enhance the adaptive capability. Meanwhile, the adoption of high-order equivalent models further improves the accuracy and adaptive ability of SOE estimation. Secondly, Long Short-term Memory (LSTM) is introduced to optimize Ohmic internal resistance (OIR) and actual energy (AE), further improving the accuracy of SOE estimation. Once again, in the process of OIR and AE estimation, the iterative updating of the observation noise equation and process noise equation of ACKF were also adopted to perform adaptive correction and enhance the adaptive ability. Finally, this article establishes a SOE estimation method based on LSTM optimized ACKF. Validate the LSTM optimized ACKF method through simulation experiments and compare it with individual ACKF methods. The results show that the ACKF estimation method based on LSTM optimization has an SOE estimation error of less than 0.90% for LIB, regardless of the SOE at 100%, 65%, and 30%, which is more accurate than the SOE estimation error of ACKF alone. It can be seen that this study has improved the accuracy and adaptability of LIB's SOE estimation, providing more accurate data support for ensuring the safety and reliability of lithium batteries.

Set-membership state estimation for time-varying complex networks: two zonotopic design methods

This article studies the zonotopic set-membership state estimation problem for linear time-varying complex networks with unknown-but-bounded (UBB) noises, where the UBB noises are contained by a set of zonotopes. The objective of the addressed problem is to give two design methods, namely the correction matrix method and the state observer method, where a time-varying zonotopic sequence containing all possible states of the system is obtained. The expressions of the correction matrix and the observer gain are given under the F-radius criterion, and the desired minimum zonotopes are obtained. In addition, a state observer based on the measured output at the current moment is designed to analyze the equivalence between the above two methods. Finally, in order to demonstrate the effectiveness of the proposed state estimation algorithms, two simulation examples are presented.

Distributionally robust origin–destination demand estimation

Gaining a good understanding of the travel demands of a city or region is extremely important for many transportation applications. For stochastic origin–destination (OD) estimation problems, an accurate distribution assumption or observation of OD estimates or data is usually desired but not always available. In this paper, we establish a novel two-stage OD estimation framework based on distributionally robust optimization (DRO) and quasi-sparsity property of large-scale OD demand matrices. The proposed two-stage Distributionally Robust Quasi-Sparsity OD estimation (DR-QSOD) model does not require an accurate or complete distribution assumption of estimates/data. Numerical results demonstrate that DR-QSOD model outperforms stochastic QSOD model in estimating OD demands when the distribution assumption of data is biased. This paper also discusses two different approaches to solve the DR-QSOD model as well as compares their computational efficiency. In addition, DR-QSOD model is shown to keep relatively high quasi-sparsity consistency, which also brings lots of meaningful practical insights.

Nonparametric estimation for periodic stochastic differential equations driven by [formula omitted]-Brownian motion

The paper is concerned with the nonparametric estimation problem for periodic stochastic differential equations driven by G-Brownian motion based on continuous observations. The consistency and asymptotic distribution of the nonparametric estimator are discussed. Computer simulations are performed to illustrate our theory.

Expectation-Maximization enables Phylogenetic Dating under a Categorical Rate Model.

Dating phylogenetic trees to obtain branch lengths in time unit is essential for many downstream applications but has remained challenging. Dating requires inferring substitution rates that can change across the tree. While we can assume to have information about a small subset of nodes from the fossil record or sampling times (for fast-evolving organisms), inferring the ages of the other nodes essentially requires extrapolation and interpolation. Assuming a distribution of branch rates, we can formulate dating as a constrained maximum likelihood (ML) estimation problem. While ML dating methods exist, their accuracy degrades in the face of model misspecification where the assumed parametric statistical distribution of branch rates vastly differs from the true distribution. Notably, most existing methods assume rigid, often unimodal, branch rate distributions. A second challenge is that the likelihood function involves an integral over the continuous domain of the rates and often leads to difficult non-convex optimization problems. To tackle these two challenges, we propose a new method called Molecular Dating using Categorical-models (MD-Cat). MD-Cat uses a categorical model of rates inspired by non-parametric statistics and can approximate a large family of models by discretizing the rate distribution into k categories. Under this model, we can use the Expectation- Maximization (EM) algorithm to co-estimate rate categories and branch lengths in time units. Our model has fewer assumptions about the true distribution of branch rates than parametric models such as Gamma or LogNormal distribution. Our results on two simulated and real datasets of Angiosperms and HIV and a wide selection of rate distributions show that MD-Cat is often more accurate than the alternatives, especially on datasets with exponential or multimodal rate distributions.

Estimating dementia incidence in insured older Asian Americans and Pacific Islanders in California: an application of inverse odds of selection weights.

Literature shows heterogeneous age-standardized dementia incidence rates across US Asian American, Native Hawaiian, and Pacific Islanders (AANHPI), but no estimates of population-representative dementia incidence exist due to lack of AANHPI longitudinal probability samples. We compared harmonized characteristics between AANHPI Kaiser Permanente Northern California members (KPNC cohort) and the target population of AANHPI 60+ with private or Medicare insurance using the California Health Interview Survey. We used stabilized inverse odds of selection weights (sIOSW) to estimate ethnicity-specific crude and age-standardized dementia incidence rates and cumulative risk by age 90 in the target population. Differences between the KPNC cohort and target population varied by ethnicity. sIOSW eliminated most differences in larger ethnic groups; some differences remained in smaller groups. Estimated crude dementia incidence rates using sIOSW (versus unweighted) were similar in Chinese, Filipinos, Pacific Islanders and Vietnamese, and higher in Japanese, Koreans, and South Asians. Unweighted and weighted age-standardized incidence rates differed for South Asians. Unweighted and weighted cumulative risk were similar for all groups. We estimated the first population-representative dementia incidence rates and cumulative risk in AANHPI ethnic groups. We encountered some estimation problems and weighted estimates were imprecise, highlighting challenges using weighting to extend inferences to target populations.

Time of week intensity estimation from partly interval censored data with applications to police patrol planning

Law enforcement agencies are tasked with crime prevention and crime reduction under limited resources. Having an accurate temporal estimate of the crime rate would be valuable to achieve such a goal. However, estimation is usually complicated by the interval censored nature of crime data. We cast the problem of intensity estimation as a Poisson regression using an EM algorithm to estimate the parameters. Two special penalties are added that provide smoothness over the time of day and day of week. This approach provides accurate intensity estimates and can also uncover day of week clusters that share the same intensity patterns. Both simulated and real crime data gathered from the city of Cincinnati and the city of Dallas are used to demonstrate the effectiveness of the proposed model.

CGNSDE: Conditional Gaussian neural stochastic differential equation for modeling complex systems and data assimilation

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

Divergences based Bayesian inference with censored data

. In this work, we deal with some Bayesian inference problems in the presence of right censored data. First, we propose a dual ϕ−divergence Bayes type estimators for parametric models and we establish their asymptotic normality. To establish this result, we need a uniform strong law of large numbers that we prove as well. Then, we consider the problem of prior distributions construction for model selection using ϕ−divergences. Finally, we consider the problem of the predictive density estimation on the basis of ϕ−divergences. We apply an expansion result of the generalized Bayesian predictive density on two parametric models widely used in survival analysis, namely the Weibull and the inverse Weibull model, under right censoring. We also check the performances of our proposed methods through simulations and real data applications. The results of these studies show that our proposed dual ϕ−divergence Bayes type estimators are more robust than other Bayesian estimators. Moreover, the generalized Bayesian predictive density performs better than the classical estimative density especially for the inverse Weibull model.

Super-resolution delay-Doppler estimation for OTFS-based automotive radar

In this paper, we consider the problem of joint delay-Doppler estimation in an automotive radar based on orthogonal time frequency space (OTFS) modulation. We propose a super-resolution estimation approach that operates in the continuous domain and employs a two-dimensional atomic norm carrying delay and Doppler shift information to mitigate the off grid errors. The estimation task of target parameters is reformulated as a semidefinite program (SDP) problem. To solve this problem in an efficient way, we leverage the alternating direction method of multipliers (ADMM) and adopt an iterative procedure to obtain the optimal solution. The effectiveness of the proposed method is confirmed by theoretical analyses. Numerical results are presented to demonstrate the superior performance of the proposed method in comparison with the state-of-the-arts.

On Alpha-Expansion-Based Graph-Cut Optimization for Decoder-Side Depth Estimation

In order to achieve high realism an acceptable level of user experience in immersive videos, it is crucial to provide both the best possible quality of depth maps and minimize computational time. In this paper, we propose a new approach to the decoder-side depth estimation (DSDE) problem, which uses the hierarchical alpha-expansion algorithm with additional improvements for the estimation designed to be more robust to compressed video artifacts and limited computational resources. As shown by the experimental results, the proposal simultaneously results in reduction of computation time of the estimation process (by almost 40%) and an improvement of quality of estimated depth maps. The increased quality is demonstrated by more than 6% Bjøntegaard delta gain compared to the Moving Picture Experts Group (MPEG) immersive video state-of-the-art DSDE method.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Problems of Estimation of Microbial Biomass in Soddy-Podzolic Soils (Forests of the Protected Areas of Moscow Region)

Problems of Estimation of Microbial Biomass in Soddy-Podzolic Soils (Forests of the Protected Areas of Moscow Region)

State estimation based on measurement from a part of nodes for a delayed Itô type of complex network with Markovian mode-dependent parameters

This article is devoted to coping with the state estimate problem for a class of Itô stochastic complex network. The target network under consideration is a hybrid system involving Markovian jumping parameters and mode-dependent distributed time-delays, and the system noise is characterized by the Brownian Motion. The problem addressed is to design a state estimator to track the states of target network under the assumption that the network outputs are from only a portion of network nodes. By utilizing the Lyapunov stability method and the Itô stochastic differential equation theory, sufficient conditions are educed so that the state estimation error of the estimator is mean-square exponentially ultimately bounded. In particular, in the case that the system is noise-free, the derived conditions can ensure the state estimation error is mean-square exponentially stable. Furthermore, the estimator design can be made by solving a set of matrix inequalities. Lastly, a numerical example is exploited to indicates the validity of the theoretical results.