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
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
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
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
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.
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。
