Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when ...Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.展开更多
Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like freq...Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like frequency from such signals is possible,achieving high-precision vibration parameters remains challenging.This paper proposed a novel two-stage off-grid estimation method.It leverages a unique array layout(coprime array)to obtain a regular augmented covariance matrix.Subsequently,parameters in the matrix are recovered using the sparse iterative covariance-based estimation method based on covariance fitting criteria.Finally,high-precision estimates of imprecise parameters are obtained using unconditional maximum likelihood estimation,effectively eliminating the effects of basis mismatch.Through substantial numerical and experimental validation,the proposed method demonstrates significantly higher accuracy compared to classical BTT parameter estimation methods,approaching the lower bound of unbiased estimation variance.Furthermore,due to its immunity to frequency gridding,it can track minor frequency deviations,making it more suitable for indicating blade condition.展开更多
The existence and uniqueness of the maximum likelihood estimator(MLE)of parameter for the exponential-Poisson distribution is discussed by Ku s[2007.A new lifetime distribution.Computational Statistics and Data Analys...The existence and uniqueness of the maximum likelihood estimator(MLE)of parameter for the exponential-Poisson distribution is discussed by Ku s[2007.A new lifetime distribution.Computational Statistics and Data Analysis 51(9):4497-4509]in simple random sampling(SRS).As an alternative to the MLEs in SRS,Joukar et al.[2021.Parameter estimation for the exponential-poisson distribution based on ranked set samples.Communication in Statistics-Theory and Methods 50(3):560-581]discussed the MLE of parameter for this distribution in ranked set sampling(RSS).However,they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS.In this article,we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS.The MLEs will be compared in terms of asymptotic efficiencies.Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.展开更多
Beamspace super-resolution methods for elevation estimation in multipath environment has attracted significant attention, especially the beamspace maximum likelihood(BML)algorithm. However, the difference beam is rare...Beamspace super-resolution methods for elevation estimation in multipath environment has attracted significant attention, especially the beamspace maximum likelihood(BML)algorithm. However, the difference beam is rarely used in superresolution methods, especially in low elevation estimation. The target airspace information in the difference beam is different from the target airspace information in the sum beam. And the use of difference beams does not significantly increase the complexity of the system and algorithms. Thus, this paper applies the difference beam to the beamformer to improve the elevation estimation performance of BML algorithm. And the direction and number of beams can be adjusted according to the actual needs. The theoretical target elevation angle root means square error(RMSE) and the computational complexity of the proposed algorithms are analyzed. Finally, computer simulations and real data processing results demonstrate the effectiveness of the proposed algorithms.展开更多
The calibration of transfer functions is essential for accurate pavement performance predictions in the PavementME design. Several studies have used the least square approach to calibrate these transfer functions. Lea...The calibration of transfer functions is essential for accurate pavement performance predictions in the PavementME design. Several studies have used the least square approach to calibrate these transfer functions. Least square is a widely used simplistic approach based on certain assumptions. Literature shows that these least square approach assumptions may not apply to the non-normal distributions. This study introduces a new methodology for calibrating the transverse cracking and international roughness index(IRI) models in rigid pavements using maximum likelihood estimation(MLE). Synthetic data for transverse cracking, with and without variability, are generated to illustrate the applicability of MLE using different known probability distributions(exponential,gamma, log-normal, and negative binomial). The approach uses measured data from the Michigan Department of Transportation's(MDOT) pavement management system(PMS) database for 70 jointed plain concrete pavement(JPCP) sections to calibrate and validate transfer functions. The MLE approach is combined with resampling techniques to improve the robustness of calibration coefficients. The results show that the MLE transverse cracking model using the gamma distribution consistently outperforms the least square for synthetic and observed data. For observed data, MLE estimates of parameters produced lower SSE and bias than least squares(e.g., for the transverse cracking model, the SSE values are 3.98 vs. 4.02, and the bias values are 0.00 and-0.41). Although negative binomial distribution is the most suitable fit for the IRI model for MLE, the least square results are slightly better than MLE. The bias values are-0.312 and 0.000 for the MLE and least square methods. Overall, the findings indicate that MLE is a robust method for calibration, especially for non-normally distributed data such as transverse cracking.展开更多
In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, an...In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
To estimate the spreading sequence of the direct sequence spread spectrum (DSSS) signal, a fast algorithm based on maximum likelihood function is proposed, and the theoretical derivation of the algorithm is provided. ...To estimate the spreading sequence of the direct sequence spread spectrum (DSSS) signal, a fast algorithm based on maximum likelihood function is proposed, and the theoretical derivation of the algorithm is provided. By simplifying the objective function of maximum likelihood estimation, the algorithm can realize sequence synchronization and sequence estimation via adaptive iteration and sliding window. Since it avoids the correlation matrix computation, the algorithm significantly reduces the storage requirement and the computation complexity. Simulations show that it is a fast convergent algorithm, and can perform well in low signal to noise ratio (SNR).展开更多
To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid sear...To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.展开更多
By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of ...By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.展开更多
Losses due to hazards are inevitable and numerical simulations for estimations are complex.This study proposes a model for estimating correlated seismic damages and losses of a water supply pipeline system as an alter...Losses due to hazards are inevitable and numerical simulations for estimations are complex.This study proposes a model for estimating correlated seismic damages and losses of a water supply pipeline system as an alternative for numerical simulations.The common approach in other research shows average damage spots per mesh estimated statistically independent to one another.Spatially distributed lifeline systems,such as water supply pipelines,are interconnected,and seismic spatial variability affects the damages across the region;thus,spatial correlation of damage spots is an important factor in target areas for portfolio loss estimation.Generally,simulations are used to estimate possible losses;however,these assume each damage behaves independently and uncorrelated.This paper assumed that damages per mesh behave in a Poisson distribution to avoid over-dispersion and eliminate negative losses in estimations.The purpose of this study is to obtain a probabilistic portfolio loss model of an extensive water supply area.The proposed model was compared to the numerical simulation data with the correlated Poisson distribution.The application of the Normal To Anything(NORTA)obtained correlations for Poisson Distributions.The proposed probabilistic portfolio loss model,based on the generalized linear model and central limit theory,estimated the possible losses,such as the Probable Maximum Loss(PML,90%non-exceedance)or Normal Expected Loss(NEL,50%non-exceedance).The proposed model can be used in other lifeline systems as well,though additional investigation is needed for confirmation.From the estimations,a seismic physical portfolio loss for the water supply system was presented.The portfolio was made to show possible outcomes for the system.The proposed method was tested and analyzed using an artificial field and a location-based scenario of a water supply pipeline system.This would aid in pre-disaster planning and would require only a few steps and time.展开更多
Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or h...Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.展开更多
In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under ...In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under exponential distribution. These methods are studied under both perfect and imperfect ranking (with errors in ranking). These estimators are then compared with estimators based on simple random sampling (SRS) and ranked set sampling (RSS) procedures. It is shown that relative efficiencies of the estimators based on MRSSU are better than those of the estimator based on SRS. Simulation results show that efficiency of proposed estimator is better than estimator based on RSS under ranking error.展开更多
The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate ...The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate the DOA (Direction of Arrival), initial velocity and acceleration of a maneuvering target in colocated MIMO radar. The target’s DOA is estimated in the first place, then a Maximum-Likelihood (ML) estimation based on peak search is applied to a two-dimensional grids providing estimation of initial velocity and acceleration. Simulations show that the MIMO radar has a better performance in DOA estimation than the phased array radar. By means of Monte Carlo simulations, the estimation error of initial velocity and acceleration on different SNRs are calculated. The results also suggest the effectiveness of this method.展开更多
Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,b...Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,but also can enhance the performance of tracking radars.A frequency-agile refined maximum likelihood(RML)algorithm based on optimal fusion is proposed.The algorithm constructs an optimization problem,which minimizes the mean square error(MSE)of angle estimation.Thereby,the optimal weight at different frequency points is obtained for fusing the angle estimation.Through theoretical analysis and simulation,the frequency-agile RML algorithm based on optimal fusion can improve the accuracy of angle estimation effectively.展开更多
Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In mos...Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.展开更多
The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communic...The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.展开更多
This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is es...This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is essential for beamforming, where the antenna array radiating pattern is steered to provide faster and reliable data transmission with increased coverage. This work proposes using metaheuristics to improve a maximum likelihood DOA estimator for an antenna array arranged in a uniform cuboidal geometry. The DOA estimation performance of the proposed algorithm was compared to that of MUSIC on different two dimensions scenarios. The metaheuristic algorithms present better performance than the well-known MUSIC algorithm.展开更多
In this paper, an importance sampling maximum likelihood(ISML) estimator for direction-of-arrival(DOA) of incoherently distributed(ID) sources is proposed. Starting from the maximum likelihood estimation description o...In this paper, an importance sampling maximum likelihood(ISML) estimator for direction-of-arrival(DOA) of incoherently distributed(ID) sources is proposed. Starting from the maximum likelihood estimation description of the uniform linear array(ULA), a decoupled concentrated likelihood function(CLF) is presented. A new objective function based on CLF which can obtain a closed-form solution of global maximum is constructed according to Pincus theorem. To obtain the optimal value of the objective function which is a complex high-dimensional integral,we propose an importance sampling approach based on Monte Carlo random calculation. Next, an importance function is derived, which can simplify the problem of generating random vector from a high-dimensional probability density function(PDF) to generate random variable from a one-dimensional PDF. Compared with the existing maximum likelihood(ML) algorithms for DOA estimation of ID sources, the proposed algorithm does not require initial estimates, and its performance is closer to CramerRao lower bound(CRLB). The proposed algorithm performs better than the existing methods when the interval between sources to be estimated is small and in low signal to noise ratio(SNR)scenarios.展开更多
基金supported in part by the National Key Research and Development Program of China(2023YFB3906403)the National Natural Science Foundation of China(62373118,62173105)the Natural Science Foundation of Heilongjiang Province of China(ZD2023F002)
文摘Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.
基金the National Natural Science Foundation of China(Nos.52105117,52222504&51875433)the Funds for Distinguished Young talent of Shaanxi Province,China(No.2019JC-04)。
文摘Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like frequency from such signals is possible,achieving high-precision vibration parameters remains challenging.This paper proposed a novel two-stage off-grid estimation method.It leverages a unique array layout(coprime array)to obtain a regular augmented covariance matrix.Subsequently,parameters in the matrix are recovered using the sparse iterative covariance-based estimation method based on covariance fitting criteria.Finally,high-precision estimates of imprecise parameters are obtained using unconditional maximum likelihood estimation,effectively eliminating the effects of basis mismatch.Through substantial numerical and experimental validation,the proposed method demonstrates significantly higher accuracy compared to classical BTT parameter estimation methods,approaching the lower bound of unbiased estimation variance.Furthermore,due to its immunity to frequency gridding,it can track minor frequency deviations,making it more suitable for indicating blade condition.
基金Supported by the National Natural Science Foundation of China(11901236,12261036)Scientific Research Fund of Hunan Provincial Education Department(21A0328)Young Core Teacher Foundation of Hunan Province([2020]43).
文摘The existence and uniqueness of the maximum likelihood estimator(MLE)of parameter for the exponential-Poisson distribution is discussed by Ku s[2007.A new lifetime distribution.Computational Statistics and Data Analysis 51(9):4497-4509]in simple random sampling(SRS).As an alternative to the MLEs in SRS,Joukar et al.[2021.Parameter estimation for the exponential-poisson distribution based on ranked set samples.Communication in Statistics-Theory and Methods 50(3):560-581]discussed the MLE of parameter for this distribution in ranked set sampling(RSS).However,they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS.In this article,we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS.The MLEs will be compared in terms of asymptotic efficiencies.Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.
基金supported by the Fund for Foreign Scholars in University Research and Teaching Programs (B18039)。
文摘Beamspace super-resolution methods for elevation estimation in multipath environment has attracted significant attention, especially the beamspace maximum likelihood(BML)algorithm. However, the difference beam is rarely used in superresolution methods, especially in low elevation estimation. The target airspace information in the difference beam is different from the target airspace information in the sum beam. And the use of difference beams does not significantly increase the complexity of the system and algorithms. Thus, this paper applies the difference beam to the beamformer to improve the elevation estimation performance of BML algorithm. And the direction and number of beams can be adjusted according to the actual needs. The theoretical target elevation angle root means square error(RMSE) and the computational complexity of the proposed algorithms are analyzed. Finally, computer simulations and real data processing results demonstrate the effectiveness of the proposed algorithms.
基金the Michigan Department of Transportation (MDOT) for the financial support of this study (report no. SPR1723)。
文摘The calibration of transfer functions is essential for accurate pavement performance predictions in the PavementME design. Several studies have used the least square approach to calibrate these transfer functions. Least square is a widely used simplistic approach based on certain assumptions. Literature shows that these least square approach assumptions may not apply to the non-normal distributions. This study introduces a new methodology for calibrating the transverse cracking and international roughness index(IRI) models in rigid pavements using maximum likelihood estimation(MLE). Synthetic data for transverse cracking, with and without variability, are generated to illustrate the applicability of MLE using different known probability distributions(exponential,gamma, log-normal, and negative binomial). The approach uses measured data from the Michigan Department of Transportation's(MDOT) pavement management system(PMS) database for 70 jointed plain concrete pavement(JPCP) sections to calibrate and validate transfer functions. The MLE approach is combined with resampling techniques to improve the robustness of calibration coefficients. The results show that the MLE transverse cracking model using the gamma distribution consistently outperforms the least square for synthetic and observed data. For observed data, MLE estimates of parameters produced lower SSE and bias than least squares(e.g., for the transverse cracking model, the SSE values are 3.98 vs. 4.02, and the bias values are 0.00 and-0.41). Although negative binomial distribution is the most suitable fit for the IRI model for MLE, the least square results are slightly better than MLE. The bias values are-0.312 and 0.000 for the MLE and least square methods. Overall, the findings indicate that MLE is a robust method for calibration, especially for non-normally distributed data such as transverse cracking.
基金Undergraduate Education High land Construction Project of Shanghaithe Key Course Construction of Shanghai Education Committee (No.20075302)the Key Technology R&D Program of Shanghai Municipality (No.08160510600)
文摘In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金supported by Joint Foundation of and China Academy of Engineering Physical (10676006)
文摘To estimate the spreading sequence of the direct sequence spread spectrum (DSSS) signal, a fast algorithm based on maximum likelihood function is proposed, and the theoretical derivation of the algorithm is provided. By simplifying the objective function of maximum likelihood estimation, the algorithm can realize sequence synchronization and sequence estimation via adaptive iteration and sliding window. Since it avoids the correlation matrix computation, the algorithm significantly reduces the storage requirement and the computation complexity. Simulations show that it is a fast convergent algorithm, and can perform well in low signal to noise ratio (SNR).
基金supported by the National Natural Science Foundation of China (No. 61002026)
文摘To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.
文摘By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.
文摘Losses due to hazards are inevitable and numerical simulations for estimations are complex.This study proposes a model for estimating correlated seismic damages and losses of a water supply pipeline system as an alternative for numerical simulations.The common approach in other research shows average damage spots per mesh estimated statistically independent to one another.Spatially distributed lifeline systems,such as water supply pipelines,are interconnected,and seismic spatial variability affects the damages across the region;thus,spatial correlation of damage spots is an important factor in target areas for portfolio loss estimation.Generally,simulations are used to estimate possible losses;however,these assume each damage behaves independently and uncorrelated.This paper assumed that damages per mesh behave in a Poisson distribution to avoid over-dispersion and eliminate negative losses in estimations.The purpose of this study is to obtain a probabilistic portfolio loss model of an extensive water supply area.The proposed model was compared to the numerical simulation data with the correlated Poisson distribution.The application of the Normal To Anything(NORTA)obtained correlations for Poisson Distributions.The proposed probabilistic portfolio loss model,based on the generalized linear model and central limit theory,estimated the possible losses,such as the Probable Maximum Loss(PML,90%non-exceedance)or Normal Expected Loss(NEL,50%non-exceedance).The proposed model can be used in other lifeline systems as well,though additional investigation is needed for confirmation.From the estimations,a seismic physical portfolio loss for the water supply system was presented.The portfolio was made to show possible outcomes for the system.The proposed method was tested and analyzed using an artificial field and a location-based scenario of a water supply pipeline system.This would aid in pre-disaster planning and would require only a few steps and time.
基金supported by the National Natural Science Foundation of China(Grant No.11961035)Jiangxi Provincial Natural Science Foundation(Grant No.20224BCD41001).
文摘Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.
文摘In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under exponential distribution. These methods are studied under both perfect and imperfect ranking (with errors in ranking). These estimators are then compared with estimators based on simple random sampling (SRS) and ranked set sampling (RSS) procedures. It is shown that relative efficiencies of the estimators based on MRSSU are better than those of the estimator based on SRS. Simulation results show that efficiency of proposed estimator is better than estimator based on RSS under ranking error.
文摘The estimation of target parameters in MIMO radar signal processing is one of the most important research topics. An efficient implementation of the Maximum Likelihood estimator is presented in this paper to estimate the DOA (Direction of Arrival), initial velocity and acceleration of a maneuvering target in colocated MIMO radar. The target’s DOA is estimated in the first place, then a Maximum-Likelihood (ML) estimation based on peak search is applied to a two-dimensional grids providing estimation of initial velocity and acceleration. Simulations show that the MIMO radar has a better performance in DOA estimation than the phased array radar. By means of Monte Carlo simulations, the estimation error of initial velocity and acceleration on different SNRs are calculated. The results also suggest the effectiveness of this method.
基金supported by the Fund for Foreign Scholars in University Research and Teaching Programs(the 111 Project)(B18039).
文摘Low elevation estimation,which has attracted wide attention due to the presence of specular multipath,is essential for tracking radars.Frequency agility not only has the advantage of strong anti-interference ability,but also can enhance the performance of tracking radars.A frequency-agile refined maximum likelihood(RML)algorithm based on optimal fusion is proposed.The algorithm constructs an optimization problem,which minimizes the mean square error(MSE)of angle estimation.Thereby,the optimal weight at different frequency points is obtained for fusing the angle estimation.Through theoretical analysis and simulation,the frequency-agile RML algorithm based on optimal fusion can improve the accuracy of angle estimation effectively.
文摘Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.
基金the National Natural Science Foundation of China(62071144,61971159,61871149).
文摘The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.
文摘This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is essential for beamforming, where the antenna array radiating pattern is steered to provide faster and reliable data transmission with increased coverage. This work proposes using metaheuristics to improve a maximum likelihood DOA estimator for an antenna array arranged in a uniform cuboidal geometry. The DOA estimation performance of the proposed algorithm was compared to that of MUSIC on different two dimensions scenarios. The metaheuristic algorithms present better performance than the well-known MUSIC algorithm.
基金supported by the basic research program of Natural Science in Shannxi province of China (2021JQ-369)。
文摘In this paper, an importance sampling maximum likelihood(ISML) estimator for direction-of-arrival(DOA) of incoherently distributed(ID) sources is proposed. Starting from the maximum likelihood estimation description of the uniform linear array(ULA), a decoupled concentrated likelihood function(CLF) is presented. A new objective function based on CLF which can obtain a closed-form solution of global maximum is constructed according to Pincus theorem. To obtain the optimal value of the objective function which is a complex high-dimensional integral,we propose an importance sampling approach based on Monte Carlo random calculation. Next, an importance function is derived, which can simplify the problem of generating random vector from a high-dimensional probability density function(PDF) to generate random variable from a one-dimensional PDF. Compared with the existing maximum likelihood(ML) algorithms for DOA estimation of ID sources, the proposed algorithm does not require initial estimates, and its performance is closer to CramerRao lower bound(CRLB). The proposed algorithm performs better than the existing methods when the interval between sources to be estimated is small and in low signal to noise ratio(SNR)scenarios.
