Inconsistency is a fundamental problem in simultaneous localization and mapping(SLAM).Previous works from predecessors have studied the inconsistent problem of extended Kalman filter(EKF)SLAM algorithm focusing on the...Inconsistency is a fundamental problem in simultaneous localization and mapping(SLAM).Previous works from predecessors have studied the inconsistent problem of extended Kalman filter(EKF)SLAM algorithm focusing on the linearization errors.In this paper,we studied the inconsistency issue of EKF SLAM in theory based on measurement noise and observation time.In a simplified situation,we deduced some useful theorems of estimated covariance matrix.Then,we made use of them to investigate the inconsistency issue.We showed that the measurement noise and the observation times can drive the EKF SLAM out of consistency.Moreover,we demonstrated the explicit effects of measurement noise and observation times on inconsistency of the EKF SLAM.Our simulation experiments verified the results.展开更多
We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. U...We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.展开更多
The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint ...The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.展开更多
The national benchmarks on islands were mostly established by trigonometric leveling in Korea. This method results in inaccuracy, which is a serious problem in Geoga Grand Bridge construction work that tried to link t...The national benchmarks on islands were mostly established by trigonometric leveling in Korea. This method results in inaccuracy, which is a serious problem in Geoga Grand Bridge construction work that tried to link the mainland and the islands. The Geoga Grand Bridge （Pusan-Geoje fixed link project） was selected as the study area, a huge construction work in Korea that will connect the mainland （Pnsan） and an island （Gecje island）. However, the orthometric heights issued at benchmarks （JINH and GOFJ） were not consistent, because they did not refer to the same zero point, which would make the linking of the sections problematic. This paper introduces the precise local geoidas a vertical datum for the construction area in order to establish a consistent height system. To determine the precise local geoid for the construction area, we firstly developed a precise gravimetric geoid for Korea and its adjoining seas as a whole. This gravimetric geoid was developed by use of all available gravity data, including surface and satellite data on land and on the ocean. The gravimetrie gecid was computed by spherical fast fourier transform with modified Stokes＇ kernels. The remove-restore technique was used to eliminate the terrain effects by use of the RTM reduction and to determine the residual geoid by combining the GGM02S/EGM96 geopotential model, free-air gravity anomalies and high-resolutinn DEM data. Finally, the gravimetric model was fitted to the geoid heights obtained from GPS and tide observations （Ncps/Tiae） by least square coUocatian, to provide the final GPS-consistent local precise geoid model. The post-fit error （std. dev. ） of the final geoid to the NetS/Tide derived from GPS and tide observations was ± 2.2 cm for the construction area. We solved the height inconsistency problem by calculating the orthometric height of the benchmarks and the cnntrol points using the final geoid model. Also, the highly accurate orthometric height was estimated through the GPS/leveling technique by applying the developed local precise geoid. Therefore, the precise local geoid is expected to improve the quality of the construction procedure of the Geoga Grand Bridge.展开更多
In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved un...In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.展开更多
文摘Inconsistency is a fundamental problem in simultaneous localization and mapping(SLAM).Previous works from predecessors have studied the inconsistent problem of extended Kalman filter(EKF)SLAM algorithm focusing on the linearization errors.In this paper,we studied the inconsistency issue of EKF SLAM in theory based on measurement noise and observation time.In a simplified situation,we deduced some useful theorems of estimated covariance matrix.Then,we made use of them to investigate the inconsistency issue.We showed that the measurement noise and the observation times can drive the EKF SLAM out of consistency.Moreover,we demonstrated the explicit effects of measurement noise and observation times on inconsistency of the EKF SLAM.Our simulation experiments verified the results.
基金supported by FAU Start-up funding at the C. E. Schmidt Collegeof Science
文摘We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.
基金National Nature Science Foundation of China(No.60974030)the Chinese Universities Scientific Fund(No.CUSF-DH-D-2014059)
文摘The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.
文摘The national benchmarks on islands were mostly established by trigonometric leveling in Korea. This method results in inaccuracy, which is a serious problem in Geoga Grand Bridge construction work that tried to link the mainland and the islands. The Geoga Grand Bridge （Pusan-Geoje fixed link project） was selected as the study area, a huge construction work in Korea that will connect the mainland （Pnsan） and an island （Gecje island）. However, the orthometric heights issued at benchmarks （JINH and GOFJ） were not consistent, because they did not refer to the same zero point, which would make the linking of the sections problematic. This paper introduces the precise local geoidas a vertical datum for the construction area in order to establish a consistent height system. To determine the precise local geoid for the construction area, we firstly developed a precise gravimetric geoid for Korea and its adjoining seas as a whole. This gravimetric geoid was developed by use of all available gravity data, including surface and satellite data on land and on the ocean. The gravimetrie gecid was computed by spherical fast fourier transform with modified Stokes＇ kernels. The remove-restore technique was used to eliminate the terrain effects by use of the RTM reduction and to determine the residual geoid by combining the GGM02S/EGM96 geopotential model, free-air gravity anomalies and high-resolutinn DEM data. Finally, the gravimetric model was fitted to the geoid heights obtained from GPS and tide observations （Ncps/Tiae） by least square coUocatian, to provide the final GPS-consistent local precise geoid model. The post-fit error （std. dev. ） of the final geoid to the NetS/Tide derived from GPS and tide observations was ± 2.2 cm for the construction area. We solved the height inconsistency problem by calculating the orthometric height of the benchmarks and the cnntrol points using the final geoid model. Also, the highly accurate orthometric height was estimated through the GPS/leveling technique by applying the developed local precise geoid. Therefore, the precise local geoid is expected to improve the quality of the construction procedure of the Geoga Grand Bridge.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19631040) .
文摘In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.
