Maximum Likelihood Estimation Algorithm Research Articles

Iterative maximum-likelihood estimation algorithm for clock offset and skew correction in UWB systems assisted by 5G NR multipath

High-precision location services such as unmanned driving, indoor navigation, and mine positioning have been benefiting significantly with the breakthroughs in Fifth-Generation (5G) technology. This paper proposes a collaborative Time of Flight (TOF) measurement framework for 5G New Radio (NR) in Release 17 and Ultra-Wideband (UWB). The method proposed improves the positioning accuracy by tackling the issues of UWB clock offset and clock skew. To this end, we have designed an innovative correction algorithm that effectively utilizes 5G multipath measurement and Timing Error Group (TEG) identifiers. The algorithm employs a low-complexity iterative maximum likelihood estimation (MLE) method to accurately estimate error parameters and calibrate UWB TOF measurement results. Simulation results show that this algorithm significantly enhances positioning precision and robustness. It reduces positioning error by 24 % and 35 % compared to the baseline algorithm in two representative scenarios. These improvements make it suitable for UWB systems in real-time and complex environments.

Interval-Censored Linear Quantile Regression

Censored quantile regression has emerged as a prominent alternative to classical Cox’s proportional hazards model or accelerated failure time model in both theoretical and applied statistics. While quantile regression has been extensively studied for right-censored survival data, methodologies for analyzing interval-censored data remain limited in the survival analysis literature. This article introduces a novel local weighting approach for estimating linear censored quantile regression, specifically tailored to handle diverse forms of interval-censored survival data. The estimation equation and the corresponding convex objective function for the regression parameter can be constructed as a weighted average of quantile loss contributions at two interval endpoints. The weighting components are nonparametrically estimated using local kernel smoothing or ensemble machine learning techniques. To estimate the nonparametric distribution mass for interval-censored data, a modified EM algorithm for nonparametric maximum likelihood estimation is employed by introducing subject-specific latent Poisson variables. The proposed method’s empirical performance is demonstrated through extensive simulation studies and real data analyses of two HIV/AIDS datasets. Supplementary materials for this article are available online.

Intermittent fault detection in nonstationary processes via a Wald‐based control chart

SummaryIn this article, the problem of intermittent fault (IF) detection is investigated for nonstationary processes in the multivariate statistics framework. By combining the moving window technique with maximum likelihood estimation (MLE), the moving window Wald‐based control chart is proposed to realize the detection of IFs in nonstationary processes. The computational efficiency and the convergence properties are discussed for the designed iterative algorithm of MLE. Then, necessary and sufficient conditions are presented to guarantee the detectability of IFs with the consideration of window lengths. Moreover, the alarm delays are analyzed for the appearance and disappearance of IFs. In virtue of the above analysis, the optimal window length is derived by minimizing the supremum of alarm delays. In order to estimate the time of IFs' appearance and disappearance, an algorithm is designed with the inspiration of simulated annealing strategy. Finally, a simulation on rotary steerable drilling tool system is provided to verify the effectiveness of the proposed method.

A nonparametric degradation modeling method for remaining useful life prediction with fragment data

Condition-based maintenance (CBM) is an effective way to keep the safety of industrial equipment by predicting the remaining useful life (RUL) and scheduling the maintenance plan before failure. Condition monitoring data is the basis of health state evaluation and RUL prediction. In ideal cases, the monitoring data are collected consecutively starting from the healthy stage until the end of the lifetime. In real industrial cases, however, fragment data often exist due to the interruption of monitoring and/or the loss of sensor readings. The major characteristic of fragment data is that they only record a random period of degradation process. The initial degradation time information is generally lost. Therefore, it is unable to be modeled using the common time-dependent modeling framework. To deal with the above issue, this paper proposes a nonparametric degradation modeling method for RUL prediction with fragment data. In this method, a new state-dependent degradation modeling framework is constructed via two-step axis transform. It formulates the RUL using a function depending on the health state. Based on functional principle component analysis (FPCA), a principal analysis via maximum likelihood estimation (PAMLE) algorithm is developed to recover the missing data of failed units. In addition, a RUL prediction-oriented optimization (POO) algorithm is proposed to predict the RUL of in-service units based on a piece of fragment data. Consequently, the proposed method is capable of dealing with the issues of both data recovery and RUL prediction. The effectiveness of the method is demonstrated using a fatigue crack growth dataset and a lithium-ion (Li-ion) battery degradation dataset.

Fusion of diverse data sources for flood extent mapping and risk assessment in Sindh: A comparative study of inundation mapping approaches

Accurate and timely mapping of flood extent is crucial for effective disaster response and management. However, existing methods often face challenges in integrating diverse data sources and leveraging advanced techniques for precise inundation mapping. This research aimed to address this gap by proposing and evaluating four different methods for improving flood extent mapping in Sindh, Pakistan, by integrating various data sources, including precipitation, Synthetic Aperture Radar (SAR), buildings, population, and optical data. The first strategy involves categorizing post-flood SAR data immediately using non-parametric (Support Vector Machine (SVM) and Random Forest (RF)), parametric (Maximum Likelihood Estimation (MLE)), and cluster (ISO) algorithms for Vertical transmit and Vertical received (VV) and Vertical transmit and Horizontal received (VH) polarisations. The second method relies on Otsu's method for automatic thresholding on post-flood event VH and VV data. The third approach utilizes both pre- and post-flood event data by creating a stack of Pre-event VH, Pre-event VV, Post-event VH, and Post-event VV data, which is then classified using the SVM, RF, MLE, and ISO algorithms. Lastly, the fourth method employs the stack of Principal Component Analysis (PCA) bands, consisting of PCA components 1, 2, and 3, to categorize data for flooding using the SVM, RF, MLE, and ISO algorithms. The rationale behind evaluating these diverse methods was to identify the most effective approach for accurately mapping flood extent by exploiting the strengths of different algorithms and data processing techniques. The accuracy and precision of these approaches were rigorously evaluated using Landsat-9 Normalized Difference Water Index (NDWI) as a reference dataset, along with error matrix and compound value (Cv) metrics. The findings show that a PCA-based technique with SVM is marginally superior (based on the overall accuracy and Kappa coefficient with a value of 92.20 % and kappa coefficient 0.821) than the other approaches tested in the study. By reducing the dimensionality of the dataset while preserving relevant information, PCA offers a computationally efficient approach to flood extent mapping. Among all the approaches, the collective performance of the algorithms was computed using the Cv metric. The SVM algorithm with a Cv of 1.25 demonstrated the best performance, followed by the RF algorithm with Cv of 1.5, and the MLE algorithm with Cv of 2.5. The worst performing algorithm among all is found to be ISO with Cv of 4. It comes into view that first and second approach underperformed in VH polarisation compared to the VV polarisation and provide a more accurate representation of flooded area in VV polarisation. The flood extent with highest accuracy, together with the world's gridded population, latest Microsoft's Global ML Building Footprints, and OpenStreetMap building data are used in conjunction to estimate the number of people and buildings at risk within the study area.

Estimating the size of a closed population by modeling latent and observed heterogeneity.

The paper extends the empirical likelihood (EL) approach of Liu etal. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

GNSS direct position estimation-inspired positioning with pseudorange correlogram for urban navigation

Multipath (MP) reception has been among the main issues for accurate and reliable positioning in urban environments. It has been shown to introduce positioning errors of up to tens of meters for conventional two-step (2SP) receivers. The direct position estimation (DPE) has been introduced as a more robust positioning algorithm compared to the conventional two-step (2SP) receivers in terms of MP mitigation. However, its high computational load prevents DPE from real-time positioning for commercial receivers. Thus, we present a novel grid-based maximum likelihood estimation (MLE) algorithm based on DPE by making use of pseudorange measurements to obtain the correlogram on a predefined searching space. Unlike DPE, which performs correlations at the intermediate frequency (IF) level, correlations are done by directly comparing the code phase of each candidate position, velocity, and timing with the incoming pseudorange. This way, the proposed method retains MP mitigation properties from DPE through the use of MLE from DPE and allows for a significantly reduced computational load compared to DPE. The proposed method was tested with both open-sourced datasets collected in urban environments as well as IF simulation data, and its performance is evaluated against a 2SP receiver. Results show that the proposed method manages to acquire the MP mitigation capability of DPE and outperforms 2SP by up to around 23% in the tested urban datasets and 91% in the simulation data, at a much-reduced computational time. The resilience of our proposed method against MP and NLOS could even potentially offer applications in geodetic networks, where robust estimators are traditionally employed to counteract outliers.

Estimation of regime-switching diffusions via Fourier transforms

In this article, an algorithm for maximum-likelihood estimation of regime-switching diffusions is proposed. The proposed approach uses a Fourier transform to numerically solve the system of Fokker–Planck or forward Kolmogorow equations for the temporal evolution of the state densities. Monte Carlo simulations confirm the theoretically expected consistency of this approach for moderate sample sizes and its practical feasibility for certain regime-switching diffusions used in economics and biology with moderate numbers of states and parameters. An application to animal movement data serves as an illustration of the proposed algorithm.

Second-based queue length estimation with fusing MMW and low penetration rate CAV trajectory data

This paper combines millimeter-wave radar (MMW) data with connected autonomous vehicle (CAV) trajectory data to estimate queue length on a second-by-second basis. Firstly, queued vehicles on multiple lanes with the same traffic movement are mapped to a virtual lane. Then, the presence of CAV or human-driven vehicle (HDV) for any given queueing index is determined. A Bayesian joint probability model is subsequently established for queue length expectation, considering the existence of the queued vehicle type as a condition. The average time headway and dissipation speed distribution are derived from departure timestamps, which allows for the calculation of the prior probability ratio of queue length. Lastly, the maximum likelihood estimation (EM) algorithm is employed for iteratively estimating the CAV penetration rate. Simulation results demonstrate the method offers a compelling trade-off between precision and second-based real-time performance, while field test results further confirm the wide applicability under various traffic conditions.

A Technique for Efficient Estimation of Dynamic Structural Equation Models: A Case Study

Dynamic structural equation models (DSEM) are designed for time series analysis of latent structures. Inherent to the application of DSEM is model parameter estimation, which has to be addressed in many applications by a single time series. In this context, however, the methods currently available either lack estimation quality or are computationally inefficient. Given the era of big data, the necessity for a trade-off between these properties may be detrimental to the applicability of DSEM. The paper is aimed at tackling this trade-off by proposing a novel estimator recursioning technique (ER technique) that facilitates the development of computationally efficient raw-data maximum likelihood estimation algorithms through data transformation, covariance matrix block decomposition, likelihood function reduction, and estimator recursioning steps. The ER technique is introduced by applying it to a special case of the general dynamic structural equation model that encompasses a noisy Wiener-process-type structure with input from the factor-analytic model. The resulting algorithm has been verified through a number of numerical experiments as well as implemented in a brand new R package EMLI, which is available on CRAN.

Comparison of the Meta-Heuristic Algorithms for Maximum Likelihood Estimation of the Exponentially Modified Logistic Distribution

Generalized distributions have been studied a lot recently because of their flexibility and reliability in modeling lifetime data. The two-parameter Exponentially-Modified Logistic distribution is a flexible modified distribution that was introduced in 2018. It is regarded as a strong competitor for widely used classical symmetrical and non-symmetrical distributions such as normal, logistic, lognormal, log-logistic, and others. In this study, the unknown parameters of the Exponentially-Modified Logistic distribution are estimated using the maximum likelihood method. Five meta-heuristic algorithms, including the genetic algorithm, particle swarm optimization algorithm, grey wolf optimization algorithm, whale optimization algorithm, and sine cosine algorithm, are applied in order to solve the nonlinear likelihood equations of the study model. The efficiencies of all maximum likelihood estimates for these algorithms are compared via an extensive Monte Carlo simulation study. The performance of the maximum likelihood estimates for the location and scale parameters of the Exponentially-Modified Logistic distribution developed with the genetic algorithm and grey wolf optimization algorithms is the most efficient among others, according to simulation findings. However, the genetic algorithm is two times faster than grey wolf optimization and can be considered better than grey wolf optimization considering the computation time criterion. Six real datasets are analyzed to show the flexibility of this distribution.

Alternative modified Cholesky decomposition of the precision matrix of longitudinal data

The correlation matrix might be of scientific interest for longitudinal data. However, few studies have focused on both robust estimation of the correlation matrix against model misspecification and robustness to outliers in the data, when the precision matrix possesses a typical structure. In this paper, we propose an alternative modified Cholesky decomposition (AMCD) for the precision matrix of longitudinal data, which results in robust estimation of the correlation matrix against model misspecification of the innovation variances. A joint mean-covariance model with multivariate normal distribution and AMCD is established, the quasi-Fisher scoring algorithm is developed, and the maximum likelihood estimators are proven to be consistent and asymptotically normally distributed. Furthermore, a double-robust joint modeling approach with multivariate Laplace distribution and AMCD is established, and the quasi-Newton algorithm for maximum likelihood estimation is developed. The simulation studies and real data analysis demonstrate the effectiveness of the proposed AMCD method.

Two New Algorithms for Maximum Likelihood Estimation of Sparse Covariance Matrices With Applications to Graphical Modeling

Two New Algorithms for Maximum Likelihood Estimation of Sparse Covariance Matrices With Applications to Graphical Modeling

A Study of Business English Translation Skills Based on Parallel Corpus

Abstract In this paper, the support vector machine is used as the overall classification of the paragraph alignment method. The paragraph length relationship is taken as an essential feature of the business English paragraph alignment model, the CRFs discriminative model is used as the word alignment task model, and the maximum likelihood estimation algorithm is used for model parameter training. Aiming at the real-time alignment needs at the sentence or paragraph level in Business English, the word alignment algorithm based on semantic similarity calculation is proposed, and the evaluation indexes of English-Chinese EC, Chinese-English CE unidirectional alignment and bi-directional fusion alignment, and semantic extension alignment are compared. Adding traditional business English translation techniques, comparing the effects of conventional translation techniques on business English sentence and paragraph translation versus parallel corpus-based translation techniques. The dynamic chunking accuracy of two-way fusion alignment and semantic expansion alignment is 94.57% and 94.32%, respectively, and the accuracy of semantic expansion alignment is 6.85% and 8.17% higher than that of EC one-way alignment. Meanwhile, the number of errors in business English translation works based on parallel corpora is reduced, which can help translators overcome the interference of Chinese chapter structures and improve the quality of their translation works.

A Quantitative Impact Assessment of English Translation Errors on the Authenticity of News Dissemination

Abstract To improve the accuracy of news communication between readers and audiences, it is necessary to avoid the errors generated in the process of news translation so as to make the English translation of news content expression more in line with the actual situation, thus ensuring the authenticity of news dissemination. In this paper, the MapReduce multiple regression model is constructed by optimizing the classical multiple linear regression model in terms of maximum likelihood estimation and gradient descent algorithm with the aim of reducing the errors in the process of English translation of news. This model is used to analyze the errors generated by the English translation process and finally proposes a method for improving translation accuracy based on the factors causing the errors. After testing, the F-value, P-value, and R² of the degree of fit of the MapReduce model are 54.39, 0.005, and 0.893, respectively. Furthermore, the model passed the significance test. The Pearson coefficients of the 4 types of translation errors in the MapReduce multiple linear regression model were −0.673, −0.622, −0.584, and −0.736, respectively, all of which were significantly negatively correlated with the truthfulness of news dissemination at the 1% level. The model analyzes that the three kinds of translation errors are basically between 2%-4%, 7%-20%, and 2%-4%, and puts forward reasonable opinions on the avoidance of the four kinds of errors, namely, “pragmatic translation, cultural translation, linguistic translation and text-specific translation”, which generate errors in the process of the English translation of news.

Digging the Underlying Layers of Intelligent Transportation System Networks by Mobile Crowdsourcing

Understanding the underlying topologies of networks is very important for improving their performance and security, especially in Intelligent Transportation Systems (ITS). Anonymous router identification recognizes and merges anonymous interfaces belonging to the same router in the traceroute measurement data, which is regarded as one of the critical issues for recovering the router-level topologies of networks. In this paper, we studied the problem of recovering the router-level topologies of networks with mobile crowdsourcing and proposed a method based on graph embedding (called <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE)</monospace> for accurate identification of anonymous network routers from traceroute measurement data. We first use the graph embedding method to capture the connection characteristics of different interfaces of anonymous routers from the traceroute data and then, evaluate the distances between interfaces based on the extracted connection characteristics. Finally, we identify the interfaces that belong to the same anonymous router by using a heuristic maximum likelihood estimation algorithm that we have developed. Compared to the existing methods, <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE</monospace> is more felxible in ITS because it identifies anonymous network routers without requiring manually predefined subgraphs (or patterns). In the evaluation, we simulated a variety of scenarios to generate the measurement data and compared <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE</monospace> to two state-of-the-art methods (the neighborhood matching method and the graph induction-based method). The results suggest that <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE</monospace> can significantly improve the accuracy of anonymous router identification (with an average improvement of over 20%) at a slight identification rate loss (less than 4%).

A novel efficient estimator for three‐dimensional bearings‐only source localisation with unknown sensor altitude and systematic measurement errors

AbstractA novel two‐stage profile maximum likelihood estimator is proposed to estimate the source location and the systematic errors jointly, with the aim of addressing the problem of source localisation using angle‐only measurements from a single sensor with unknown sensor altitude and systematic measurement errors. The proposed two‐stage profile maximum likelihood estimator algorithm is capable of decoupling the azimuth and elevation angle measurements while transforming the original maximum likelihood optimisation problem into two sub‐problems, that is, two‐dimensional‐projected maximum likelihood estimator and relative altitude maximum likelihood estimator. In terms of the two‐dimensional‐projected maximum likelihood estimator, an algorithm combining pseudo‐linear estimating and Kalman filtering is proposed to generate an initial estimate. Subsequently, a Gauss–Newton iterative method is developed to estimate the two‐dimensional‐projected target location and the azimuth systematic error jointly. The relative height maximum likelihood estimator is initialised using a pseudo‐linear estimator. Next, a Gauss–Newton iterative algorithm is adopted to estimate the elevation systematic error and the relative height. As indicated by the result of the simulation studies, the proposed algorithm exhibits an estimation performance close to the Cramér–Rao lower bound with unknown sensor altitude and systematic measurement errors.

Improved slot synchronization method for high-speed photon-counting communication based on SNSPD arrays

In optical communication systems based on photon-counting protocols, using highly efficient superconducting nanowire single-photon detectors (SNSPDs) is currently considered an effective solution for achieving high communication rates. However, in the process of increasing the communication channel throughput by reducing the slot width, as the slot frequency increases to the GHz level, the sub-nanosecond-level jitter caused by detection systems becomes non-negligible relative to the entire signal slot and greatly affects the accuracy of slot synchronization. To accurately characterize the photon arrival distribution of SNSPDs and further reduce communication error rates, we constructed a system. Through data analysis, we discovered that the photon arrival intensity distribution under the influence of jitter conforms to a non-homogeneous Poisson process (NHPP) and proposed a correction model for the photon arrival distribution and provided the corrected expression for the maximum likelihood estimation (MLE) algorithm. In subsequent experiments, combined with a blind search strategy, we enhanced the robustness of the model under different slot offset states and reduced the hardware complexity of existing synchronization schemes. The results show that at signal photons Ks=1.624 and background noise photons Kb=0.016 per symbol, the ideal Poisson model's hard decision error rate is 10.56 %, while the corrected model achieves an error rate close to the ideal synchronization performance at 8.9 %.

Experimental 3D super-localization with Laguerre–Gaussian modes

Improving three-dimensional (3D) localization precision is of paramount importance for super-resolution imaging. By properly engineering the point spread function (PSF), such as utilizing Laguerre–Gaussian (LG) modes and their superposition, the ultimate limits of 3D localization precision can be enhanced. However, achieving these limits is challenging, as it often involves complicated detection strategies and practical limitations. In this work, we rigorously derive the ultimate 3D localization limits of LG modes and their superposition, specifically rotation modes, in the multi-parameter estimation framework. Our findings reveal that a significant portion of the information required for achieving 3D super-localization of LG modes can be obtained through feasible intensity detection. Moreover, the 3D ultimate precision can be achieved when the azimuthal index l is zero. To provide a proof-of-principle demonstration, we develop an iterative maximum likelihood estimation (MLE) algorithm that converges to the 3D position of a point source, considering the pixelation and detector noise. The experimental implementation exhibits an improvement of up to two-fold in lateral localization precision and up to twenty-fold in axial localization precision when using LG modes compared to Gaussian mode. We also showcase the superior axial localization capability of the rotation mode within the near-focus region, effectively overcoming the limitations encountered by single LG modes. Notably, in the presence of realistic aberration, the algorithm robustly achieves the Cramér-Rao lower bound. Our findings provide valuable insights for evaluating and optimizing the achievable 3D localization precision, which will facilitate the advancements in super-resolution microscopy.

Local polynomial software reliability models and their application

In this paper, we propose local polynomial software reliability models (SRMs), which can be categorized into a semi-parametric modeling framework. Our models belong to the common non-homogeneous Poisson process (NHPP)-based SRMs, but possess a flexible structure to approximate an arbitrary mean value function by controlling the polynomial degree. More specifically, we develop two types of local polynomial NHPP-based SRMs; finite-failure (type-I) and infinite-failure (type-II) SRMs, which are substantial extensions of the existing NHPP-based SRMs in the similar categories. We also develop two maximum likelihood estimation algorithms in both estimation and prediction phases, where the former is used for the testing period experienced in the past, and the latter for the prediction in the future. In numerical experiments with actual 8 software fault count time-interval data sets, we compare our local polynomial NHPP-based SRMs with the well-known existing parametric NHPP-based SRMs in terms of goodness-of-fit and predictive performances. Finally, it can be concluded that our local polynomial NHPP-based SRMs with lower polynomial degrees could outperform the existing NHPP-based SRMs in several cases and should be listed as candidates for the representative NHPP-based SRMs in software reliability analysis.