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
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
In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood ...In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.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
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 the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fi...In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.展开更多
Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degrad...Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.展开更多
Vehicle positioning with the global navigation satellite system （GNSS） in urban environments faces two problems which are attenuation and dynamic. For traditional GNSS receivers hardly able to track dynamic weak sig...Vehicle positioning with the global navigation satellite system （GNSS） in urban environments faces two problems which are attenuation and dynamic. For traditional GNSS receivers hardly able to track dynamic weak signals, the coupling between all visible satellite signals is ignored in the absence of navigation state feedback, and thermal noise error and dynamic stress threshold are contradictory due to non-coherent discriminators. The vector delay/frequency locked loop （VDFLL） with navigation state feedback and the joint vector tracking loop （JVTL） with coherent discriminator which is a synchronization parameter tracking loop based on maximum likelihood estimation （MLE） are proposed to improve the tracking sensitivity of GNSS receiver in dynamic weak signal environments. A joint vector position tracking loop （JVPTL） directly tracking user position and velocity is proposed to further improve tracking sensitivity. The coherent navigation parameter discriminator of JVPTL, being able to ease the contradiction between thermal noise error and dynamic stress threshold, is based on MLE according to the navigation parameter based linear model of received baseband signals. Simulation results show that JVPTL, which combines the advantages of both VDFLL and JVTL, performs better than both VDFLL and JVTL in dynamic weak signal environments.展开更多
In the signal processing for metrewave radar, the reflection paths of target echoes can cause severe error in the elevation estimation for the low-angle target tracking. The exact angles of the reflection paths are un...In the signal processing for metrewave radar, the reflection paths of target echoes can cause severe error in the elevation estimation for the low-angle target tracking. The exact angles of the reflection paths are unknown beforehand, and therefore, the reflection paths can not be suppressed easily. Therefore, in this article, an improved reflection paths suppression approach is presented. A block matrix aggregate is constructed based on the possible angles of the reflection paths. Combined with the beamforming-like processing, a generalized maximum likelihood estimation is derived to optimize the estimation. Moreover, the noise reduction method based on the Toeplitz covariance matrix is used for better performance. This approach is applied to the real data collected by the low-angle tracking radar with 8-channel vertical array. The experiment results show that the reflection effects are reduced and the accuracy of the elevation estimate is improved.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and lea...The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.展开更多
This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and m...This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.展开更多
A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and rel...A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.展开更多
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).
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In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.
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.
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.
基金supported by the National Natural Science Foundation of China(1150143371473187)the Natural Science Basic Research Plan in Shaanxi Province of China(2016JQ1014)
文摘In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.
基金Projects(51475462,61374138,61370031)supported by the National Natural Science Foundation of China
文摘Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.
基金supported by the National Natural Science Foundation for Young Scientists of China(61201190)
文摘Vehicle positioning with the global navigation satellite system （GNSS） in urban environments faces two problems which are attenuation and dynamic. For traditional GNSS receivers hardly able to track dynamic weak signals, the coupling between all visible satellite signals is ignored in the absence of navigation state feedback, and thermal noise error and dynamic stress threshold are contradictory due to non-coherent discriminators. The vector delay/frequency locked loop （VDFLL） with navigation state feedback and the joint vector tracking loop （JVTL） with coherent discriminator which is a synchronization parameter tracking loop based on maximum likelihood estimation （MLE） are proposed to improve the tracking sensitivity of GNSS receiver in dynamic weak signal environments. A joint vector position tracking loop （JVPTL） directly tracking user position and velocity is proposed to further improve tracking sensitivity. The coherent navigation parameter discriminator of JVPTL, being able to ease the contradiction between thermal noise error and dynamic stress threshold, is based on MLE according to the navigation parameter based linear model of received baseband signals. Simulation results show that JVPTL, which combines the advantages of both VDFLL and JVTL, performs better than both VDFLL and JVTL in dynamic weak signal environments.
文摘In the signal processing for metrewave radar, the reflection paths of target echoes can cause severe error in the elevation estimation for the low-angle target tracking. The exact angles of the reflection paths are unknown beforehand, and therefore, the reflection paths can not be suppressed easily. Therefore, in this article, an improved reflection paths suppression approach is presented. A block matrix aggregate is constructed based on the possible angles of the reflection paths. Combined with the beamforming-like processing, a generalized maximum likelihood estimation is derived to optimize the estimation. Moreover, the noise reduction method based on the Toeplitz covariance matrix is used for better performance. This approach is applied to the real data collected by the low-angle tracking radar with 8-channel vertical array. The experiment results show that the reflection effects are reduced and the accuracy of the elevation estimate is improved.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
基金Project(71371182) supported by the National Natural Science Foundation of China
文摘The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.
基金supported by the National Natural Science Foundation of China(1127301761401207+2 种基金6147119661501240)the College Graduate Scientific Research Innovation Fund in Jiangsu Province of China(KYLX16_0447)
基金the National Natural Science Foundation of China (No. 79970041).
文摘This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.
基金supported by the Research Center of the Female Scientific and Medical Colleges,Deanship of Scientific Research,King Saud University
文摘A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.
