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Battlefield surveillance radar is usually 2-D radar, which cannot realize target three-dimensional localization, leading to poor resolution for the air target in the elevation dimension. Previous researchers have used the Traditional Height Finder Radar (HFR) or multiple 2-D radar networking to estimate the target three-dimensional location. However, all of them face the problems of high cost, poor real-time performance and high requirement of space–time registration. In this paper, Reconfigurable Intelligent Surfaces (RISs) with low cost are introduced into the 2-D radar to realize the target three-dimensional localization. Taking advantage of the wide beam of 2-D radar in the elevation dimension, several Unmanned Aerial Vehicles (UAVs) carrying RISs are set in the receiving beam to form multiple auxiliary measurement channels. In addition, the traditional 2-D radar measurements combined with the auxiliary channel measurements are used to realize the target three-dimensional localization by solving a nonlinear least square problem with a convex optimization method. For the proposed RIS-assisted target three-dimensional localization problem, the Cramer–Rao Lower Bound (CRLB) is derived to measure the target localization accuracy. Simulation results verify the effectiveness of the proposed 3-D localization method, and the influences of the number, the positions and the site errors of the RISs on the localization accuracy are covered.

The establishment of failure risk assessment on the secondary system in smart substation can help power gird company timely arrange maintenance when the failure risk of equipment accumulates to a certain extent,thus effectively preventing systematic failure. In this paper,a probabilistic failure model is established through Weibull probability distribution function from a perspective of reliability engineering. According to the type tests and various daily operation statistics of secondary equipment,the regression equation calculated by the average rank method and least square estimation can obtain the model parameter estimation. By doing so,the equipment failure model close to the real operation condition can be obtained. Moreover,the relationship between the failures of the secondary system and a single equipment is established through the fault tree. Therefore,the risk probability distribution function of top event in secondary system can be calculated quantitatively,which can provide auxiliary decision for risk warning and state overhaul. Finally,it is verified by the numerical results that the proposed secondary equipment failure model can provide a reference for accurate time arrangement for system maintenance.

The mathematical characteristics of the mixture of Lindley model with 2-component (2-CMLM) are discussed. In this paper, we investigate both the practical and theoretical aspects of the 2-CMLM. We investigate several statistical features of the mixed model like probability generating function, cumulants, characteristic function, factorial moment generating function, mean time to failure, Mills Ratio, mean residual life. The density, hazard rate functions, mean, coefficient of variation, skewness, and kurtosis are all shown graphically. Furthermore, we use appropriate approaches such as maximum likelihood, least square and weighted least square methods to estimate the pertinent parameters of the mixture model. We use a simulation study to assess the performance of suggested methods. Eventually, modelling COVID-19 patient data demonstrates the effectiveness and utility of the 2-CMLM. The proposed model outperformed the two component mixture of exponential model as well as two component mixture of Weibull model in practical applications, indicating that it is a good candidate distribution for modelling COVID-19 and other related data sets.

The coronavirus disease outbreak in 2019 (COVID-19) has caused major economic and healthcare problems worldwide. At this time, the worldwide outbreak has passed its peak, while the greatest number of cases has been in the USA, Brazil, and India. Measures and policies for controlling the outbreak have been developed by authorities to protect the population of each country, and forecasting the number of infectious people is an important factor for developing them. This research was conducted to identify a suitable forecasting model for estimating the cumulative daily number of infectious people worldwide. Sample countries with severe outbreaks were selected from each continent. Herein, forecasting models based on logistic, Richards, and Gompertz growth curves are derived and their suitability for forecasting the COVID-19 rates in each sample country and worldwide are analyzed. Moreover, estimating the growth curve parameters is based on the least-squares method. The results show that the Gompert growth curve is the most suitable for estimating the cumulative number of infectious people worldwide.

In recent years, statisticians have grown increasingly engaged in research of mixture models, particularly in the previous decade, without adequate consideration of challenge of estimating the parameters of mixture models from a frequentist perspective. Except for maximum likelihood estimation, this study addresses this vacuum by discussing the two other classical methods of estimation for mixture model. We commence by briefly describing the three frequentist approaches, namely maximum likelihood, ordinary, and weighted least squares, and then comparing them through extensive numerical simulations. The model’s applicability is illustrated by its application to simulated and real-world data, which yields promising results in terms of enhanced estimation.

In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and the unit-Gompertz model, which we named the half-logistic unit Gompertz type-I distribution. The key feature of such a novel model is that it adds a new tuning parameter to the unit-Gompertz model using the type-I half-logistic family in order to make the unit-Gompertz model more flexible. Diagrams and numerical results are used to look at the new model’s mathematical and statistical aspects. The efficiency of estimating the distribution parameters is measured using a variety of well-known classical methodologies, including Anderson–Darling, maximum likelihood, least squares, weighted least squares, right tail Anderson–Darling, and Cramer–von Mises estimation. Finally, using the maximum likelihood estimation method, the flexibility and ability of the proposed model are illustrated by means of re-analyzing two real datasets, and comparisons are provided with the fit accomplished by the unit-Gompertz, Kumaraswamy, unit-Weibull, and Kumaraswamy beta distributions for illustrative purposes.

We propose a new model with flexible failure rate called complementary Poisson generalized half logistic (CPGHL). Various properties of the model are explored and examine numerically such as the explicit expressions of the moments, mean deviations, Bonferroni and Lorenz curves, Shannon and Renyi entropy. The distribution of mixture of two CPGHL and some related models based on the log-transform of CPGHL are discussed. The asymptotic of moments of residual life and asymptotic distribution of order statistics are obtained. The characterization of Poisson half logistic (PHL) by truncated moments of a certain function of a random variable is discussed. Estimation of the model parameters was approached by maximum likelihood, least square, and percentile methods. Further, the estimation by maximum likelihood for right censored data of the model were considered. The proposed estimation techniques were assessed by simulation studies. Three data applications are provided one of them is a censored data to demonstrate how the new model outperforms some other existing distribution in practice.

To extract valid results from time series analysis of tides observations, noise reduction is vital. This study aimed to use a precise statistical model to investigate noise types. Noise component amplitude of the proposed model was studied by Least Square Estimation (LS-VCE) through different statistical models: (1) white noise and auto-regressive noise, (2) white noise and Flicker noise, (3) white noise and random walk noise, (4) white noise and Flicker noise and random walk, and (5) auto-regressive noise and Flicker noise. Based on the values obtained for the Likelihood Function, it was concluded that the noise model that can be considered for observations of the Buoy time series includes two white and Flicker noises. In addition, tide forecasting for all stations was done by extracting important frequency calculated in two cases: (1) the first case in which matrix of observation weight matrix was considered as the unit matrix or the noise model was just a white noise (2) the case in which matrix of observation weight matrix was considered as a combination of white and Flicker noises. The results show that use of precise observation weight matrix resulted in 11 millimeter difference compared to the case in which observation with unit weight matrix was used.

In this paper, we propose a two-component mixture of Akash model (TC-MAM). The behavior of TC-MAM distribution has been presented graphically. Moment-based measures, including skewness, index of dispersion, kurtosis, and coefficient of variation, have been determined and hazard rate functions are presented graphically. The probability generating function, Mills ratio, characteristic function, cumulants, mean time to failure, and factorial moment generating function are all statistical aspects of the mixed model that we explore. Furthermore, we figure out the relevant parameters of the mixture model using the most suitable methods, such as least square, weighted least square, and maximum likelihood mechanisms. Findings of simulation experiments to examine behavior of these estimates are graphically presented. Finally, a set of data taken from the real world is examined in order to demonstrate the new model’s practical perspectives. All of the metrics evaluated favor the new model and the superiority of proposed distribution over mixture of Lindley, Shanker, and exponential distributions.

In this paper we have adapted a delayed dengue model to Zika. By assuming that the epidemic starts by a single infected individual entering a disease-free population at some initial time t0 we have used the least squares parameter estimation technique in R to estimate the initial time t0 using observed Zika data from Brazil as well as the transmission probabilities of Zika in Brazil between humans and mosquitoes and vice-versa. Different values of Aedes aegypti (A. aegypti) biting rate are used throughout the paper. We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy. We started off with a non-age-structured model then introduced age-structure into the model. However in reality seasonality, in particular temperature and rainfall, have a great impact on the population size of A. aegypti. Hence we repeat both the non-age-structured and age-structured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.

Underwater localization is an important and fundamental part of the Underwater Acoustic Networks (UANs). The problem we must face is that radio waves and optical waves are heavily attenuated underwater, so acoustic signals become the most common form of communication. However, the speed of sound wave is not constant and will be affected by the environmental factors. The inaccurate sound velocity will have a serious impact on the traditional positioning results. Therefore, the symmetry correction based on least square estimation (SC-LSE) is proposed in this paper. SC-LSE mitigates the influence of the imprecise velocity estimation on the localization by means of a special symmetrical relationship. We consider a realistic case, where the actual speed of sound is uncertain and the unknown nodes may be moving. The simulation results exhibit that our algorithm can achieve good performance and is not sensitive to the change of sound velocity and node movement.

The fusion of a hyperspectral image (HSI) and multispectral image (MSI) can significantly improve the ability of ground target recognition and identification. The quality of spatial information and the fidelity of spectral information are normally contradictory. However, these two properties are non-negligible indicators for multi-source remote-sensing images fusion. The smoothing filter-based intensity modulation (SFIM) method is a simple yet effective model for image fusion, which can improve the spatial texture details of the image well, and maintain the spectral characteristics of the image significantly. However, traditional SFIM has a poor effect for edge information sharpening, leading to a bad overall fusion result. In order to obtain better spatial information, a spatial filter-based improved LSE-SFIM algorithm is proposed in this paper. Firstly, the least square estimation (LSE) algorithm is combined with SFIM, which can effectively improve the spatial information quality of the fused image. At the same time, in order to better maintain the spatial information, four spatial filters (mean, median, nearest and bilinear) are used for the simulated MSI image to extract fine spatial information. Six quality indexes are used to compare the performance of different algorithms, and the experimental results demonstrate that the LSE-SFIM based on bilinear (LES-SFIM-B) performs significantly better than the traditional SFIM algorithm and other spatially enhanced LSE-SFIM algorithms proposed in this paper. Furthermore, LSE-SFIM-B could also obtain similar performance compared with three state-of-the-art HSI-MSI fusion algorithms (CNMF, HySure, and FUSE), while the computing time is much shorter.

The paper presents the results of research on improving the accuracy of aircraft positioning using RTK-OTF (Real Time Kinematic–On The Fly) technique in air navigation. The paper shows a new solution of aircraft positioning for the application of the differential RTK-OTF technique in air navigation. In particular, a new mathematical model is presented which makes it possible to determine the resultant position of an aircraft based on the solution for the method of least squares in a stochastic process. The developed method combines in the process of alignment of GPS (Global Positioning System) observations, three independent solutions of the aircraft position in OTF mode for geocentric coordinates XYZ of the aircraft. Measurement weights as a function of the vector length and the mean vector length error, respectively, were used in the calculations. The applied calculation method makes it possible to determine the resultant position of the aircraft with high accuracy: better than 0.039 m with using the measurement weight as a function of the vector length and better than 0.009 m with the measurement weight as a function of the mean error of the vector length, respectively. In relation to the classical RTK-OTF solution as a model of the arithmetic mean, the proposed method makes it possible to increase the accuracy of determination of the aircraft position by 45–46% using the measurement weight as a function of the vector length, and 86–88% using the measurement weight as a function of the mean error of the vector length, respectively. The obtained test results show that the developed method improves to significantly improve the accuracy of the RTK-OTF solution as a method for determining the reference position in air navigation.

At the end of 2019, an outbreak of the novel coronavirus (COVID-19) made a profound impact on the country’s production and people’s daily lives. Up until now, COVID-19 has not been fully controlled all over the world. Based on the clinical research progress of infectious diseases, combined with epidemiological theories and possible disease control measures, this paper establishes a Susceptible Infected Recovered (SIR) model that meets the characteristics of the transmission of the new coronavirus, using the least square estimation (LSE) method to estimate the model parameters. The simulation results show that quarantine and containment measures as well as vaccine and drug development measures can control the spread of the epidemic effectively. As can be seen from the prediction results of the model, the simulation results of the epidemic development of the whole country and Nanjing are in agreement with the real situation of the epidemic, and the number of confirmed cases is close to the real value. At the same time, the model’s prediction of the prevention effect and control measures have shed new light on epidemic prevention and control.

A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.

Polarization curves are of paramount importance for the detection of toxic components in microbial fuel cell (MFC) based biosensors. In this study, polarization curves were made under non-toxic conditions and under toxic conditions after the addition of various concentrations of nickel, bentazon, sodiumdodecyl sulfate and potassium ferricyanide. The experimental polarization curves show that toxic components have an effect on the electrochemically active bacteria in the cell. (Extended) Butler Volmer Monod (BVM) models were used to describe the polarization curves of the MFC under nontoxic and toxic conditions. It was possible to properly fit the (extended) BVM models using linear regression techniques to the polarization curves and to distinguish between different types of kinetic inhibitions. For each of the toxic components, the value of the kinetic inhibition constant Ki was also estimated from the experimental data. The value of Ki indicates the sensitivity of the sensor for a specific component and thus can be used for the selection of the biosensor for a toxic component.

This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, notions of variance and covariance of set-valued and interval-valued random variables are introduced. Then, we give the definition of the interval-valued linear model and its least square estimator (LSE), as well as some properties of the LSE. Thirdly, we show that, whereas the best linear unbiased estimation does not exist, the best binary linear unbiased estimator exists and it is the LSE. Finally, we present simulation experiments and an application example regarding temperatures of cities affected by their latitude, which illustrates the application of the proposed model.