An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integratio...An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.展开更多
Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on th...Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.展开更多
We present two efficient approaches,namely the epoch-differenced(ED) and satellite-and epoch-differenced(SDED) approaches,for the estimation of IFCBs of the two Block IIF satellites.For the analysis,data from 18 stati...We present two efficient approaches,namely the epoch-differenced(ED) and satellite-and epoch-differenced(SDED) approaches,for the estimation of IFCBs of the two Block IIF satellites.For the analysis,data from 18 stations from the IGS network spanning 96 d is processed.Results show that the IFCBs of PRN25 and PRN01 exhibit periodical signal of one orbit revolution with a magnitude up to 18 cm.The periodical variation of the IFCBs is modeled by a sinusoidal function of the included angle between the sun,earth and the satellite.The presented model enables a consistent use of L1/L2 clock products in L1/L5-based positioning.The algorithm is incorporated into the MGPSS software at SHAO(Shanghai Astronomical Observatory,Chinese Academy of Sciences) and is used to monitor the IFCB variation in near real-time.展开更多
Based on the analysis of the satellite DCB data estimated by our method and the Center for Orbit Determination in Europe(CODE)from 1999 to 2011,the features of the temporal variation of differential code biases(DCB)ar...Based on the analysis of the satellite DCB data estimated by our method and the Center for Orbit Determination in Europe(CODE)from 1999 to 2011,the features of the temporal variation of differential code biases(DCB)are studied.Summarily,there are three types of variations in DCB on different time scales.The first one is the day-to-day variation that exhibits more obviously in solar maximum years.The second one is the variation with about one year periodic variation that behaves more obviously from 1999 to 2004.The last one is the monotonously descending tendency from 1999 to 2010.Considering the basic ionospheric approximation in DCB estimation method,the features of the variability of the ionospheric morphology from 1999to 2010 are also displayed based on the ionospheric characteristic parameters.It can be concluded that the day-to-day and annual variation of the estimated global positioning system(GPS).DCB is related to the ionospheric variability.The variation of DCBs on solar cycle time scale includes the real hardware DCBs and pseudo-DCBs induced by ionospheric variation.No doubt,these kinds of"pseudo"variations of DCB will affect the precision of ionospheric total electron content(TEC)derived from the GPS data.In addition,this study is helpful for evaluating the influence of ionospheric weather on TEC derivation and is also useful for developing one estimation method of DCB with more stability and precision through introducing a more practical ionospheric model.展开更多
基金Project(50875028) supported by the National Natural Science Foundation of China
文摘An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.
基金supported by the National Natural Science Foundation of China under Grant Nos.10571070 and 11001097
文摘Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41204034,41174023 and 11173049)the Opening Project of Shanghai Key Laboratory of Space Navigation and Position Techniques (Grant No. Y224 353002)
文摘We present two efficient approaches,namely the epoch-differenced(ED) and satellite-and epoch-differenced(SDED) approaches,for the estimation of IFCBs of the two Block IIF satellites.For the analysis,data from 18 stations from the IGS network spanning 96 d is processed.Results show that the IFCBs of PRN25 and PRN01 exhibit periodical signal of one orbit revolution with a magnitude up to 18 cm.The periodical variation of the IFCBs is modeled by a sinusoidal function of the included angle between the sun,earth and the satellite.The presented model enables a consistent use of L1/L2 clock products in L1/L5-based positioning.The algorithm is incorporated into the MGPSS software at SHAO(Shanghai Astronomical Observatory,Chinese Academy of Sciences) and is used to monitor the IFCB variation in near real-time.
基金supported by the National Natural Science Foundation of China(41274156 and 41174134)National Important Basic Research Project of China(Grant No.2011CB811405)
文摘Based on the analysis of the satellite DCB data estimated by our method and the Center for Orbit Determination in Europe(CODE)from 1999 to 2011,the features of the temporal variation of differential code biases(DCB)are studied.Summarily,there are three types of variations in DCB on different time scales.The first one is the day-to-day variation that exhibits more obviously in solar maximum years.The second one is the variation with about one year periodic variation that behaves more obviously from 1999 to 2004.The last one is the monotonously descending tendency from 1999 to 2010.Considering the basic ionospheric approximation in DCB estimation method,the features of the variability of the ionospheric morphology from 1999to 2010 are also displayed based on the ionospheric characteristic parameters.It can be concluded that the day-to-day and annual variation of the estimated global positioning system(GPS).DCB is related to the ionospheric variability.The variation of DCBs on solar cycle time scale includes the real hardware DCBs and pseudo-DCBs induced by ionospheric variation.No doubt,these kinds of"pseudo"variations of DCB will affect the precision of ionospheric total electron content(TEC)derived from the GPS data.In addition,this study is helpful for evaluating the influence of ionospheric weather on TEC derivation and is also useful for developing one estimation method of DCB with more stability and precision through introducing a more practical ionospheric model.
