An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be imp...An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.展开更多
In this work,microwaves and terahertz waves have performed a dual-frequency combineddiagnosis in high-temperature,large-scale plasma.According to the attenuation and phase shift of electromagnetic waves in the plasma,...In this work,microwaves and terahertz waves have performed a dual-frequency combineddiagnosis in high-temperature,large-scale plasma.According to the attenuation and phase shift of electromagnetic waves in the plasma,the electron density and collision frequency of theplasma can be inversely calculated.However,when the plasma size is large and the electron density is high,the phase shift of the electromagnetic wave is large(multiple times 2πperiod).Due to the limitations of the test equipment,the true phase shift is difficult to test accurately or to recover reality.That is,there is a problem of phase integer ambiguity.In order to obtain a phase shift of less than 180°,a higher electromagnetic wave frequency(terahertz wave with 890 GHz)is used for diagnosis.However,the attenuation of the terahertz wave diagnosis is too small(less than 0.1 d B),only the electron density can be obtained,and the collision frequency cannot be accurately obtained.Therefore,a combined diagnosis was carried out by combining twofrequencies(microwave with 36 GHz,terahertz wave with 890 GHz)to obtain electron density and collision frequency.The diagnosis result shows that the electron density is in the range of(0.65–1.5)×1019m^(-3),the collision frequency is in the range of 0.65–2 GHz,and the diagnostic accuracy is about 60%.展开更多
The ambiguity resolution in the field of GPS is investigated in detail. A new algorithm to resolve the ambiguity is proposed. The algorithm first obtains the floating resolution of the ambiguity aided with triple diff...The ambiguity resolution in the field of GPS is investigated in detail. A new algorithm to resolve the ambiguity is proposed. The algorithm first obtains the floating resolution of the ambiguity aided with triple difference measurement. Decorrelation of searching space is done by reducing the ambiguity covariance matrix＇s dimension to overcome the possible sick factorization of the matrix brought by Z-transformation. In simulation, the proposed algorithm is compared with least-squares ambiguity decorrelation adjustment （LAMBDA）. The result shows that the proposed algorithm is better than LAMBDA because of lesser resolving time, which approximately reduces 20% resolving time. Thus, the proposed algorithm adapts to the high dynamic real-time applications.展开更多
Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate...Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.展开更多
The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application sc...The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.展开更多
A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties ...A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties of square roots and a method for finding Gaussian generators are demonstrated. The generators can be instrumental in constructing other cryptosystems. It is shown how to significantly reduce average complexity of decryption per each block of ciphertext.展开更多
Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on th...Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on the different classes of ambiguity resolution,we still hope to find the relationships among these specific algorithms.In this work,we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates.A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived.Then,we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution(MICAR)to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR(FAR)algorithm instead of BIE.In the experiments,we utilize the simulated data of GPS(Global Positioning System)+BDS(BeiDou Navigation Satellite System)+Galileo(Galileo navigation satellite system)to contrast the effects of MICAR and single candidate estimator,i.e.,FAR.By taking the threshold of 5 cm at 95%confidence level as an example,MICAR accelerates the convergence process by about 3.0 min.When the positioning sequence converges,MICAR reduces the root mean square of the positioning error by 9.8%in horizontal directions and 3.5%in vertical direction,which is attributed to more fixed NL.展开更多
针对传统的RTK中长基线双频非组合定位模型解算精度低问题,该文推导了一种BDS无电离组合中长基线RTK定位算法,并提出了一种新的RTK中长基线定位双差整周模糊度固定策略。利用Matlab编程语言,设计和开发了一种BDS双频数据中长基线RTK定...针对传统的RTK中长基线双频非组合定位模型解算精度低问题,该文推导了一种BDS无电离组合中长基线RTK定位算法,并提出了一种新的RTK中长基线定位双差整周模糊度固定策略。利用Matlab编程语言,设计和开发了一种BDS双频数据中长基线RTK定位分析软件(BDS_MLRTK),用于比较分析BDS双频数据中长基线RTK定位算法性能。实验选取北京某CORS网中3条中长基线(24 km、47 km和67 km)2023年152 d UTC 08:00:00-10:00:00连续2 h BDS-3+BDS-2的B1I/B3I双频数据进行RTK定位算法性能比较分析。结果表明:传统双频非组合模型和无电离层组合模型,利用本文提出的RTK中长基线整周模糊度固定策略获得的模糊度固定成功率基本相当且均在96.5%以上,BDS-3+BDS-2的B1I/B3I双频数据中长基线RTK定位固定解精度均优于对应的浮点解,其中两种模型在BDS-3+BDS-2的B1I/B3I双频数据中长基线RTK浮点解上基本相当但在RTK固定解上无电离层组合模型优于传统双频非组合模型,且无电离层组合模型获得了平面RMS优于2 cm、点位RMS优于5 cm的RTK固定解定位精度,为BDS双频数据中长基线RTK定位提供一种有效的新算法。展开更多
The Precise Point Positioning(PPP)technique uses a single Global Navigation Satellite System(GNSS)receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the p...The Precise Point Positioning(PPP)technique uses a single Global Navigation Satellite System(GNSS)receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided.According to the observations used,there are basically two approaches,namely,the ionosphere-free combination approach and the raw observation approach.The former eliminates the ionosphere effects in the observation domain,while the latter estimates the ionosphere effects using uncombined and undifferenced observations,i.e.,so-called raw observations.These traditional techniques do not fix carrier-phase ambiguities to integers,if the additional corrections of satellite hardware biases are not provided to the users.To derive the corrections of hardware biases in network side,the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies.This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free(or narrow-lane)combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution.The reparameterization and the manipulation of design matrix coefficients are described.A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly.The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions.The proposed method is applied to process the data of a GNSS network covering a large part of China.We produce the satellite biases of BeiDou,GPS and Galileo.The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution.The BeiDou contributions on accuracy and convergence are also assessed.It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined,at least in China's Mainland.The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions.The accuracy in horizontal components is better than 6 mm,and in the height component better than 20 mm(one sigma).The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements.The contribution of BDS is numerically highlighted.展开更多
文摘An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.
基金supported in part by National Natural Science Foundation of China(Nos.61627901,61601353,61801343 and 61901321)。
文摘In this work,microwaves and terahertz waves have performed a dual-frequency combineddiagnosis in high-temperature,large-scale plasma.According to the attenuation and phase shift of electromagnetic waves in the plasma,the electron density and collision frequency of theplasma can be inversely calculated.However,when the plasma size is large and the electron density is high,the phase shift of the electromagnetic wave is large(multiple times 2πperiod).Due to the limitations of the test equipment,the true phase shift is difficult to test accurately or to recover reality.That is,there is a problem of phase integer ambiguity.In order to obtain a phase shift of less than 180°,a higher electromagnetic wave frequency(terahertz wave with 890 GHz)is used for diagnosis.However,the attenuation of the terahertz wave diagnosis is too small(less than 0.1 d B),only the electron density can be obtained,and the collision frequency cannot be accurately obtained.Therefore,a combined diagnosis was carried out by combining twofrequencies(microwave with 36 GHz,terahertz wave with 890 GHz)to obtain electron density and collision frequency.The diagnosis result shows that the electron density is in the range of(0.65–1.5)×1019m^(-3),the collision frequency is in the range of 0.65–2 GHz,and the diagnostic accuracy is about 60%.
文摘The ambiguity resolution in the field of GPS is investigated in detail. A new algorithm to resolve the ambiguity is proposed. The algorithm first obtains the floating resolution of the ambiguity aided with triple difference measurement. Decorrelation of searching space is done by reducing the ambiguity covariance matrix＇s dimension to overcome the possible sick factorization of the matrix brought by Z-transformation. In simulation, the proposed algorithm is compared with least-squares ambiguity decorrelation adjustment （LAMBDA）. The result shows that the proposed algorithm is better than LAMBDA because of lesser resolving time, which approximately reduces 20% resolving time. Thus, the proposed algorithm adapts to the high dynamic real-time applications.
文摘Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.
基金funded by the National Key R&D Program of China(Grant No.2021YFC3000502)the National Natural Science Foundation of China(Grant No.42274034)+2 种基金the Major Program(JD)of Hubei Province(Grant No.2023BAA026)the Special Fund of Hubei Luojia Laboratory(Grant No.2201000038)the Research project of Chongqing Administration for Marktet Regulation,China(Grant No.CQSJKJ2022037).
文摘The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.
文摘A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties of square roots and a method for finding Gaussian generators are demonstrated. The generators can be instrumental in constructing other cryptosystems. It is shown how to significantly reduce average complexity of decryption per each block of ciphertext.
基金National Natural Science Foundation of China,42174029,Shengfeng Gu.
文摘Among all the ambiguity resolution techniques,the Full Ambiguity Resolution(FAR),Partial Ambiguity Resolution(PAR)and Best Integer Equivariant(BIE)estimator are widely used.Although the researches have been done on the different classes of ambiguity resolution,we still hope to find the relationships among these specific algorithms.In this work,we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates.A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived.Then,we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution(MICAR)to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR(FAR)algorithm instead of BIE.In the experiments,we utilize the simulated data of GPS(Global Positioning System)+BDS(BeiDou Navigation Satellite System)+Galileo(Galileo navigation satellite system)to contrast the effects of MICAR and single candidate estimator,i.e.,FAR.By taking the threshold of 5 cm at 95%confidence level as an example,MICAR accelerates the convergence process by about 3.0 min.When the positioning sequence converges,MICAR reduces the root mean square of the positioning error by 9.8%in horizontal directions and 3.5%in vertical direction,which is attributed to more fixed NL.
文摘针对传统的RTK中长基线双频非组合定位模型解算精度低问题,该文推导了一种BDS无电离组合中长基线RTK定位算法,并提出了一种新的RTK中长基线定位双差整周模糊度固定策略。利用Matlab编程语言,设计和开发了一种BDS双频数据中长基线RTK定位分析软件(BDS_MLRTK),用于比较分析BDS双频数据中长基线RTK定位算法性能。实验选取北京某CORS网中3条中长基线(24 km、47 km和67 km)2023年152 d UTC 08:00:00-10:00:00连续2 h BDS-3+BDS-2的B1I/B3I双频数据进行RTK定位算法性能比较分析。结果表明:传统双频非组合模型和无电离层组合模型,利用本文提出的RTK中长基线整周模糊度固定策略获得的模糊度固定成功率基本相当且均在96.5%以上,BDS-3+BDS-2的B1I/B3I双频数据中长基线RTK定位固定解精度均优于对应的浮点解,其中两种模型在BDS-3+BDS-2的B1I/B3I双频数据中长基线RTK浮点解上基本相当但在RTK固定解上无电离层组合模型优于传统双频非组合模型,且无电离层组合模型获得了平面RMS优于2 cm、点位RMS优于5 cm的RTK固定解定位精度,为BDS双频数据中长基线RTK定位提供一种有效的新算法。
基金the National Natural Science Foundation of China(Grant Nos.42030109).The support is gratefully acknowledged.
文摘The Precise Point Positioning(PPP)technique uses a single Global Navigation Satellite System(GNSS)receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided.According to the observations used,there are basically two approaches,namely,the ionosphere-free combination approach and the raw observation approach.The former eliminates the ionosphere effects in the observation domain,while the latter estimates the ionosphere effects using uncombined and undifferenced observations,i.e.,so-called raw observations.These traditional techniques do not fix carrier-phase ambiguities to integers,if the additional corrections of satellite hardware biases are not provided to the users.To derive the corrections of hardware biases in network side,the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies.This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free(or narrow-lane)combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution.The reparameterization and the manipulation of design matrix coefficients are described.A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly.The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions.The proposed method is applied to process the data of a GNSS network covering a large part of China.We produce the satellite biases of BeiDou,GPS and Galileo.The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution.The BeiDou contributions on accuracy and convergence are also assessed.It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined,at least in China's Mainland.The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions.The accuracy in horizontal components is better than 6 mm,and in the height component better than 20 mm(one sigma).The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements.The contribution of BDS is numerically highlighted.
