A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formu...A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.展开更多
An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances ...An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...展开更多
Allan variance(AV)stochastic process identification method for inertial sensors has successfully combined the wavelet transform denoising scheme.However,the latter usually employs a traditional hard threshold or soft ...Allan variance(AV)stochastic process identification method for inertial sensors has successfully combined the wavelet transform denoising scheme.However,the latter usually employs a traditional hard threshold or soft threshold that presents some mathematical problems.An adaptive dual threshold for discrete wavelet transform(DWT)denoising function overcomes the disadvantages of traditional approaches.Assume that two thresholds for noise and signal and special fuzzy evaluation function for the signal with range between the two thresholds assure continuity and overcome previous difficulties.On the basis of AV,an application for strap-down inertial navigation system(SINS)stochastic model extraction assures more efficient tuning of the augmented 21-state improved exact modeling Kalman filter(IEMKF)states.The experimental results show that the proposed algorithm is superior in denoising performance.Furthermore,the improved filter estimation of navigation solution is better than that of conventional Kalman filter(CKF).展开更多
A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan ...A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan variance method and each error coefficient is identified. Furthermore, a random drift error model for IFOG is built by the method of time series analysis. The conclusion provides supports for improving IFOG design and compensating for errors of IFOG in practice.展开更多
In Electronic Warfare, and more specifically in the domain of passive localization, accurate time synchronization between platforms is decisive, especially on systems relying on TDOA （time difference of arrival） and...In Electronic Warfare, and more specifically in the domain of passive localization, accurate time synchronization between platforms is decisive, especially on systems relying on TDOA （time difference of arrival） and FDOA （frequency difference of arrival）. This paper investigates this issue by presenting an analysis in terms of final localization performance of an experimental passive localization system based on off-the-shelf components. This system is detailed, as well as the methodology used to carry out the acquisition of real data. This experiment has been realized with two different kinds of clock. The results are analyzed by calculating the Allan deviation and time deviation. The choice of these metrics is explained and their properties are discussed in the scope of an airborne bi-platform passive localization context. Conclusions are drawn regarding the overall localization performance of the system.展开更多
This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generali...This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.展开更多
Optically levitated oscillators in high vacuum have excellent environmental isolation and low mass compared with conventional solid-state sensors,which makes them suitable for ultrasensitive force detection.The force ...Optically levitated oscillators in high vacuum have excellent environmental isolation and low mass compared with conventional solid-state sensors,which makes them suitable for ultrasensitive force detection.The force resolution usually scales with the measurement bandwidth,which represents the ultimate detection capability of the system under ideal conditions if sufficient time is provided for measurement.However,considering the stability of a real system,a method based on the Allan variance is more reliable to evaluate the actual force detection performance.In this study,a levitated optomechanical system with a force detection sensitivity of 6.33±1.62 zN/Hz^(1/2)was demonstrated.And for the first time,the Allan variance was introduced to evaluate the system stability due to the force sensitivity fluctuations.The force detection resolution of 166.40±55.48 yN was reached at the optimal measurement time of 2751 s.The system demonstrated in this work has the best force detection performance in both sensitivity and resolution that have been reported so far for optically levitated particles.The reported high-sensitivity force detection system is an excellent candidate for the exploration of new physics such as fifth force searching,high-frequency gravitational waves detection,dark matter research and so on.展开更多
A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method w...A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.展开更多
As a rule,stability calculation of atomic clock requires observations with equivalent sampling interval.Apart from atomic clocks in laboratory,orbital atomic clock stability calculations are impacted of raw data sampl...As a rule,stability calculation of atomic clock requires observations with equivalent sampling interval.Apart from atomic clocks in laboratory,orbital atomic clock stability calculations are impacted of raw data sampling intervals,noncontinuous time series,non-data segment,frequency drift,and other factors.So,the calculated stability results are not so exact.In this article,the impacts of kinds of error sources on Allan and Hadamard variances are analyzed using global positioning system satellite precise clock offset data.And the laws of variety are summarized.展开更多
Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is o...Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is one method of determining INS stochastic errors.However,it is known that INS errors can vary depending on a vehicle’s motion and environment,and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic.In order to overcome this limitation,this paper proposes the use of Dynamic Allan Variance(DAV).The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV.The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV,applied on a kinematic dataset compared to the AV,applied on a static laboratory dataset.展开更多
文摘A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.
基金National Basic Research Program of China (JW132006093)
文摘An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...
文摘Allan variance(AV)stochastic process identification method for inertial sensors has successfully combined the wavelet transform denoising scheme.However,the latter usually employs a traditional hard threshold or soft threshold that presents some mathematical problems.An adaptive dual threshold for discrete wavelet transform(DWT)denoising function overcomes the disadvantages of traditional approaches.Assume that two thresholds for noise and signal and special fuzzy evaluation function for the signal with range between the two thresholds assure continuity and overcome previous difficulties.On the basis of AV,an application for strap-down inertial navigation system(SINS)stochastic model extraction assures more efficient tuning of the augmented 21-state improved exact modeling Kalman filter(IEMKF)states.The experimental results show that the proposed algorithm is superior in denoising performance.Furthermore,the improved filter estimation of navigation solution is better than that of conventional Kalman filter(CKF).
文摘A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan variance method and each error coefficient is identified. Furthermore, a random drift error model for IFOG is built by the method of time series analysis. The conclusion provides supports for improving IFOG design and compensating for errors of IFOG in practice.
文摘In Electronic Warfare, and more specifically in the domain of passive localization, accurate time synchronization between platforms is decisive, especially on systems relying on TDOA （time difference of arrival） and FDOA （frequency difference of arrival）. This paper investigates this issue by presenting an analysis in terms of final localization performance of an experimental passive localization system based on off-the-shelf components. This system is detailed, as well as the methodology used to carry out the acquisition of real data. This experiment has been realized with two different kinds of clock. The results are analyzed by calculating the Allan deviation and time deviation. The choice of these metrics is explained and their properties are discussed in the scope of an airborne bi-platform passive localization context. Conclusions are drawn regarding the overall localization performance of the system.
基金supported by the National Science Foundation of China(Nos.42274037,41874034)the Beijing Natural Science Foundation(No.4202041)the National Key Research and Development Program of China(No.2020YFB0505804).
文摘This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.
基金supported by grants from the National Natural Science Foundation of China(62005248,62075193)Major Project of Natural Science Foundation of Zhejiang Province(LD22F050002)+2 种基金Major Scientific Research Project of Zhejiang Lab(2019MB0AD01,2021MB0AL02,2022MB0AL02)the Fundamental Research Funds for the Central Universities,China(2016XZZX00401 and 2018FZA5002)the National Program for Special Support of Top-Notch Young Professionals(W02070390),China.
文摘Optically levitated oscillators in high vacuum have excellent environmental isolation and low mass compared with conventional solid-state sensors,which makes them suitable for ultrasensitive force detection.The force resolution usually scales with the measurement bandwidth,which represents the ultimate detection capability of the system under ideal conditions if sufficient time is provided for measurement.However,considering the stability of a real system,a method based on the Allan variance is more reliable to evaluate the actual force detection performance.In this study,a levitated optomechanical system with a force detection sensitivity of 6.33±1.62 zN/Hz^(1/2)was demonstrated.And for the first time,the Allan variance was introduced to evaluate the system stability due to the force sensitivity fluctuations.The force detection resolution of 166.40±55.48 yN was reached at the optimal measurement time of 2751 s.The system demonstrated in this work has the best force detection performance in both sensitivity and resolution that have been reported so far for optically levitated particles.The reported high-sensitivity force detection system is an excellent candidate for the exploration of new physics such as fifth force searching,high-frequency gravitational waves detection,dark matter research and so on.
基金supported by the National Natural Sciences Foundation of China(Grant No.41574029)Youth Innovation Promotion Association CAS(Grant No.2016242)
文摘A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.
基金This work was supported by the National Natural Science Foundation of China(No.41074020).
文摘As a rule,stability calculation of atomic clock requires observations with equivalent sampling interval.Apart from atomic clocks in laboratory,orbital atomic clock stability calculations are impacted of raw data sampling intervals,noncontinuous time series,non-data segment,frequency drift,and other factors.So,the calculated stability results are not so exact.In this article,the impacts of kinds of error sources on Allan and Hadamard variances are analyzed using global positioning system satellite precise clock offset data.And the laws of variety are summarized.
文摘Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is one method of determining INS stochastic errors.However,it is known that INS errors can vary depending on a vehicle’s motion and environment,and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic.In order to overcome this limitation,this paper proposes the use of Dynamic Allan Variance(DAV).The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV.The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV,applied on a kinematic dataset compared to the AV,applied on a static laboratory dataset.
