By constructing a mcan-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear d...By constructing a mcan-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts： a real-valued non-random recurrence equation and the standard Kalman filtering.展开更多
This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot＇s position ...This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot＇s position correctly. However, for each mobile robot, it is impossible to know its own position correctly. Therefore, each mobile robot estimates its position from the data of sensor equipped on it. Generally, the sensor data is incorrect since there is sensor noise, etc. This research considers two types of the sensor data errors from omnidirectional camera. One is the error of white noise of the image captured by omnidirectional camera and so on. Another is the error of position and posture between two omnidirectional cameras. To solve the error of latter case, we proposed a self-position estimation algorithm for multiple mobile robots using two omnidirectional cameras and an accelerometer. On the other hand, to solve the error of the former case, this paper proposed an algorithm of cooperative position estimation for multiple mobile robots. In this algorithm, each mobile robot uses two omnidirectional cameras to observe the surrounding mobile robot and get the relative position between mobile robots. Each mobile robot estimates its position with only measurement data of each other mobile robots. The algorithm is based on a Bayesian filtering. Simulations of the proposed cooperative position estimation algorithm for multiple mobile robots are performed. The results show that position estimation is possible by only using measurement value from each other robot.展开更多
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades o...This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.展开更多
This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic sy...This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic systemanalysis and the multi-dimensional spectral estimation. The results show that the variations of the beach volume arecharaCterized by the multiband oscillations with a dominant semimonth period. Upwards the low tide level, the beachtends to be stable. The estimates of the partial coherences and the partial phases indicate that the variations of thebeach volumes are mainly the results of the direct actions of the waves which are influenced by the tidal level changesand driven by the wind stress. The simulation results of the beach volume series for different beach heart zones bythreshold mixed regressive models indicate that the influence of the tide on the variations of the beach volumes is weakened and the direct actions of the wave energy and the wind stress are apparently enhanced with the increase of thebeach height.(This project was supported by the National Natural Science Foundation of China.)展开更多
This paper proposed an algorithm on simultaneous position estimation and calibration of omnidirectional camera parameters for a group of multiple mobile robots. It is aimed at developing of exploration and information...This paper proposed an algorithm on simultaneous position estimation and calibration of omnidirectional camera parameters for a group of multiple mobile robots. It is aimed at developing of exploration and information gathering robotic system in unknown environment. Here, each mobile robot is not possible to know its own position. It can only estimate its own position by using the measurement value including white noise acquired by two omnidirectional cameras mounted on it. Each mobile robot is able to obtain the distance to those robots observed from the images of two omnidirectional cameras while making calibration during moving but not in advance. Simulation of three robots moving straightly shows the effectiveness of the proposed algorithm.展开更多
In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochasti...In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.展开更多
Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family ...Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family of unbiased stochastic gradient estimators that encompasses existing estimators from the literature and identify a gradient estimator that not only maintains unbiasedness but also achieves minimal variance.Compared with the existing estimator used in SGD algorithms,the proposed estimator demonstrates a significant reduction in variance.By utilizing this stochastic gradient estimator to approximate the full gradient,we propose two mini-batch stochastic conjugate gradient algorithms with minimal variance.Under the assumptions of strong convexity and smoothness on the objective function,we prove that the two algorithms achieve linear convergence rates.Numerical experiments validate the effectiveness of the proposed gradient estimator in reducing variance and demonstrate that the two stochastic conjugate gradient algorithms exhibit accelerated convergence rates and enhanced stability.展开更多
This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimati...This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.展开更多
The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a sing...The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.展开更多
基金Project 60374022 supported by the National Natural Science Foundation of China.
文摘By constructing a mcan-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts： a real-valued non-random recurrence equation and the standard Kalman filtering.
文摘This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot＇s position correctly. However, for each mobile robot, it is impossible to know its own position correctly. Therefore, each mobile robot estimates its position from the data of sensor equipped on it. Generally, the sensor data is incorrect since there is sensor noise, etc. This research considers two types of the sensor data errors from omnidirectional camera. One is the error of white noise of the image captured by omnidirectional camera and so on. Another is the error of position and posture between two omnidirectional cameras. To solve the error of latter case, we proposed a self-position estimation algorithm for multiple mobile robots using two omnidirectional cameras and an accelerometer. On the other hand, to solve the error of the former case, this paper proposed an algorithm of cooperative position estimation for multiple mobile robots. In this algorithm, each mobile robot uses two omnidirectional cameras to observe the surrounding mobile robot and get the relative position between mobile robots. Each mobile robot estimates its position with only measurement data of each other mobile robots. The algorithm is based on a Bayesian filtering. Simulations of the proposed cooperative position estimation algorithm for multiple mobile robots are performed. The results show that position estimation is possible by only using measurement value from each other robot.
文摘This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.
文摘This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic systemanalysis and the multi-dimensional spectral estimation. The results show that the variations of the beach volume arecharaCterized by the multiband oscillations with a dominant semimonth period. Upwards the low tide level, the beachtends to be stable. The estimates of the partial coherences and the partial phases indicate that the variations of thebeach volumes are mainly the results of the direct actions of the waves which are influenced by the tidal level changesand driven by the wind stress. The simulation results of the beach volume series for different beach heart zones bythreshold mixed regressive models indicate that the influence of the tide on the variations of the beach volumes is weakened and the direct actions of the wave energy and the wind stress are apparently enhanced with the increase of thebeach height.(This project was supported by the National Natural Science Foundation of China.)
文摘This paper proposed an algorithm on simultaneous position estimation and calibration of omnidirectional camera parameters for a group of multiple mobile robots. It is aimed at developing of exploration and information gathering robotic system in unknown environment. Here, each mobile robot is not possible to know its own position. It can only estimate its own position by using the measurement value including white noise acquired by two omnidirectional cameras mounted on it. Each mobile robot is able to obtain the distance to those robots observed from the images of two omnidirectional cameras while making calibration during moving but not in advance. Simulation of three robots moving straightly shows the effectiveness of the proposed algorithm.
文摘In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27010101)the Beijing Natural Science Foundation(Grant No.Z220004)+1 种基金the Chinese NSF(Grant No.12021001)the Fundamental Research Funds for the Central Universities(Grant No.2023ZCJH02)。
文摘Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family of unbiased stochastic gradient estimators that encompasses existing estimators from the literature and identify a gradient estimator that not only maintains unbiasedness but also achieves minimal variance.Compared with the existing estimator used in SGD algorithms,the proposed estimator demonstrates a significant reduction in variance.By utilizing this stochastic gradient estimator to approximate the full gradient,we propose two mini-batch stochastic conjugate gradient algorithms with minimal variance.Under the assumptions of strong convexity and smoothness on the objective function,we prove that the two algorithms achieve linear convergence rates.Numerical experiments validate the effectiveness of the proposed gradient estimator in reducing variance and demonstrate that the two stochastic conjugate gradient algorithms exhibit accelerated convergence rates and enhanced stability.
基金supported by the National Natural Science Foundation of China under Grant Nos.60934006, 61174042,and 61120106011
文摘This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.
基金the National Natural Science Foundation of China(NSFC)under Grant 72022001,92146003,71901003the Air Force Office of Scientific Research under Grant FA95502010211by Discover GrantRGPIN-2018-05795fromNSERCCanada.
文摘The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.
