In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat...In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.展开更多
In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state...In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.展开更多
A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of r...A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.展开更多
This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the charact...This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.展开更多
Advanced Receiver Autonomous Integrity Monitoring(ARAIM) is a new technology that will provide worldwide coverage of vertical guidance in aviation navigation. The ARAIM performance and improvement under depleted const...Advanced Receiver Autonomous Integrity Monitoring(ARAIM) is a new technology that will provide worldwide coverage of vertical guidance in aviation navigation. The ARAIM performance and improvement under depleted constellations is a practical problem that needs to be faced and researched further. It is a shortcut that improves the availability in position domain whose key idea is to replace the conventional least squares process with a non-least-squares estimator to lower the integrity risk in exchange for a slight increase in nominal position error. The contributions given in this paper include two parts: First, the impacts of one satellite outage on different constellations are analyzed and compared. The conclusion is that GPS is more sensitive and vulnerable to one satellite outage. Second, a constellation weighted ARAIM(CW-ARAIM)position estimator is proposed. The position solution is replaced by a constellation weighted average solution to eliminate the constellation difference. The new solution will move close to the constellation solutions with respect to the accuracy requirement. The simulation results under baseline GPS and Galileo dual-constellation show that the one GPS satellite outage will knock the availability from 91% to only 50%. The performance remains stable with one Galileo satellite outage. With the assistance of the CW-ARAIM method, the availability can increase from 50% to more than80% under depleted GPS configurations. Even without any satellite outage, the proposed method can effectively improve the availability from 91.29% to 98.75%. The test results under optimistic constellations further verify that a balanced constellation is more important than more satellites on orbit and the superiority of CW-ARAIM method is still effective.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
Sensor-fusion based navigation attracts significant attentions for its robustness and accuracy in various applications. To achieve a versatile and efficient state estimation both indoor and outdoor, this paper present...Sensor-fusion based navigation attracts significant attentions for its robustness and accuracy in various applications. To achieve a versatile and efficient state estimation both indoor and outdoor, this paper presents an improved monocular visual inertial navigation architecture within the Multi-State Constraint Kalman Filter （MSCKF）. In addition, to alleviate the initialization demands by appending enough stable poses in MSCKF, a rapid and robust Initialization MSCKF （I-MSCKF） navigation method is proposed in the paper. Based on the trifocal tensor and sigmapoint filter, the initialization of the integrated navigation can be accomplished within three consecutive visual frames. Thus, the proposed I-MSCKF method can improve the navigation performance when suffered from shocks at the initial stage. Moreover, the sigma-point filter is applied at initial stage to improve the accuracy for state estimation. The state vector generated at initial stage from the proposed method is consistent with MSCKF, and thus a seamless transition can be achieved between the initialization and the subsequent navigation in I-MSCKF. Finally, the experimental results show that the proposed I-MSCKF method can improve the robustness and accuracy for monocular visual inertial navigations.展开更多
Ⅰ. INTRODUCTIONLet X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, …be i. i. d. random variables each having distribution function F（x）, and X<sub>n</sub>, 1≤…≤X<...Ⅰ. INTRODUCTIONLet X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, …be i. i. d. random variables each having distribution function F（x）, and X<sub>n</sub>, 1≤…≤X<sub>n,n</sub> the order statistics of X<sub>1</sub>, …, X<sub>n</sub>. Suppose that there exist constants α<sub>&</sub>gt;O and β<sub>n</sub>∈R and some r∈R such展开更多
We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to...We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.展开更多
文摘In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.
基金the National Basic Research Program under the Grant 2005CB321703the NSFC under the Grants 10571108 and 10441005the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203
文摘In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
文摘A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.
基金supported by the National Science Foundation of China under Grant Nos.11571133 and11461027the Fundamental Research Funds for the Central Universities under Grant No.20205001515
文摘This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.
基金funded by the National Natural Science Foundation of China (Nos. 61533008, 61374115, 61328301 and 61603181)the Funding of Jiangsu Innovation Program for Graduate Education of China (No. KYLX16_0379)the Open Fund of State Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University of China (No.17P02)
文摘Advanced Receiver Autonomous Integrity Monitoring(ARAIM) is a new technology that will provide worldwide coverage of vertical guidance in aviation navigation. The ARAIM performance and improvement under depleted constellations is a practical problem that needs to be faced and researched further. It is a shortcut that improves the availability in position domain whose key idea is to replace the conventional least squares process with a non-least-squares estimator to lower the integrity risk in exchange for a slight increase in nominal position error. The contributions given in this paper include two parts: First, the impacts of one satellite outage on different constellations are analyzed and compared. The conclusion is that GPS is more sensitive and vulnerable to one satellite outage. Second, a constellation weighted ARAIM(CW-ARAIM)position estimator is proposed. The position solution is replaced by a constellation weighted average solution to eliminate the constellation difference. The new solution will move close to the constellation solutions with respect to the accuracy requirement. The simulation results under baseline GPS and Galileo dual-constellation show that the one GPS satellite outage will knock the availability from 91% to only 50%. The performance remains stable with one Galileo satellite outage. With the assistance of the CW-ARAIM method, the availability can increase from 50% to more than80% under depleted GPS configurations. Even without any satellite outage, the proposed method can effectively improve the availability from 91.29% to 98.75%. The test results under optimistic constellations further verify that a balanced constellation is more important than more satellites on orbit and the superiority of CW-ARAIM method is still effective.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
基金the supports of the Beijing Key Laboratory of Digital Design&Manufacturethe Academic Excellence Foundation of Beihang University for Ph.D.Studentsthe MIIT(Ministry of Industry and Information Technology)Key Laboratory of Smart Manufacturing for High-end Aerospace Products
文摘Sensor-fusion based navigation attracts significant attentions for its robustness and accuracy in various applications. To achieve a versatile and efficient state estimation both indoor and outdoor, this paper presents an improved monocular visual inertial navigation architecture within the Multi-State Constraint Kalman Filter （MSCKF）. In addition, to alleviate the initialization demands by appending enough stable poses in MSCKF, a rapid and robust Initialization MSCKF （I-MSCKF） navigation method is proposed in the paper. Based on the trifocal tensor and sigmapoint filter, the initialization of the integrated navigation can be accomplished within three consecutive visual frames. Thus, the proposed I-MSCKF method can improve the navigation performance when suffered from shocks at the initial stage. Moreover, the sigma-point filter is applied at initial stage to improve the accuracy for state estimation. The state vector generated at initial stage from the proposed method is consistent with MSCKF, and thus a seamless transition can be achieved between the initialization and the subsequent navigation in I-MSCKF. Finally, the experimental results show that the proposed I-MSCKF method can improve the robustness and accuracy for monocular visual inertial navigations.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONLet X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, …be i. i. d. random variables each having distribution function F（x）, and X<sub>n</sub>, 1≤…≤X<sub>n,n</sub> the order statistics of X<sub>1</sub>, …, X<sub>n</sub>. Suppose that there exist constants α<sub>&</sub>gt;O and β<sub>n</sub>∈R and some r∈R such
基金The research was partially supported by the National Natural Science Foundation of China(Grant No.10231030)the Excellent Young Teacher Program of the Ministry of Education of China.
文摘We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.
