Analytical optimization on GNSS buoy array for underwater positioning
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摘要
Global navigation satellite system(GNSS)/acoustic positioning precision is determined by the positioning geometry and the ranging precision; thus optimizing GNSS buoys array is meaningful to improve the positioning accuracy and reliability. An analytical method is proposed for optimizing the GNSS buoys array with regard to the cutoff angle constraints for underwater acoustic observations. For the practical limitation of coplanarity of GNSS buoys and the cutoff angle, an algorithm is proposed to analytically minimize the position dilution of precision(PDOP). The proposed method is validated to give complete solutions of PDOP minimization with five GNSS buoys. At last, in order to search a best configuration among the PDOP solution set, we propose a search algorithm to get the solution with the smallest geometric dilution of precision(GDOP). It indicates that within a given region, the GDOP minimization at the center of a region is equivalent to the PDOP mean minimization over the region. The relation between the positioning accuracy and the positioning geometry with five known points is illustrated in an experiment performed in South China Sea.
Global navigation satellite system(GNSS)/acoustic positioning precision is determined by the positioning geometry and the ranging precision; thus optimizing GNSS buoys array is meaningful to improve the positioning accuracy and reliability. An analytical method is proposed for optimizing the GNSS buoys array with regard to the cutoff angle constraints for underwater acoustic observations. For the practical limitation of coplanarity of GNSS buoys and the cutoff angle, an algorithm is proposed to analytically minimize the position dilution of precision(PDOP). The proposed method is validated to give complete solutions of PDOP minimization with five GNSS buoys. At last, in order to search a best configuration among the PDOP solution set, we propose a search algorithm to get the solution with the smallest geometric dilution of precision(GDOP). It indicates that within a given region, the GDOP minimization at the center of a region is equivalent to the PDOP mean minimization over the region. The relation between the positioning accuracy and the positioning geometry with five known points is illustrated in an experiment performed in South China Sea.
Global navigation satellite system(GNSS)/acoustic positioning precision is determined by the positioning geometry and the ranging precision; thus optimizing GNSS buoys array is meaningful to improve the positioning accuracy and reliability. An analytical method is proposed for optimizing the GNSS buoys array with regard to the cutoff angle constraints for underwater acoustic observations. For the practical limitation of coplanarity of GNSS buoys and the cutoff angle, an algorithm is proposed to analytically minimize the position dilution of precision(PDOP). The proposed method is validated to give complete solutions of PDOP minimization with five GNSS buoys. At last, in order to search a best configuration among the PDOP solution set, we propose a search algorithm to get the solution with the smallest geometric dilution of precision(GDOP). It indicates that within a given region, the GDOP minimization at the center of a region is equivalent to the PDOP mean minimization over the region. The relation between the positioning accuracy and the positioning geometry with five known points is illustrated in an experiment performed in South China Sea.
引文
Alcocer A,Oliveira P,Pascoal A.2006.Underwater acoustic positioning systems based on buoys with GPS.In:Proceedings of the Eighth European Conference on Underwater Acoustics,1-8
Akyildiz I F,Pompili D,Melodia T.2005.Underwater acoustic sensor networks:research challenges.Ad Hoc Networks,3(3):257-279,doi:10.1016/j.adhoc.2005.01.004
Béchaz C,Boucquaert F.2008.Underwater positioning.Hydro International,2008-01-01,3
Chen Pengyun,Li Ye,Su Yumin,et al.2015.Review of AUV underwater terrain matching navigation.The Journal of Navigation,68(6):1155-1172,doi:10.1017/S0373463315000429
Fujita M,Ishikawa T,Mochizuki M,et al.2006.GPS/Acoustic seafloor geodetic observation:method of data analysis and its application.Earth,Planets and Space,58(3):265-275,doi:10.1186/BF03351923
Fujiwara T,Kodaira S,No T,et al.2011.The 2011 Tohoku-oki earthquake:displacement reaching the trench axis.Science,334(6060):1240,doi:10.1126/science.1211554
Loveless J P,Meade B J.2011.Spatial correlation of interseismic coupling and coseismic rupture extent of the 2011 MW=9.0Tohoku-oki earthquake.Geophysical Research Letters,38(17):L17306
Matsumoto Y,Fujita M,Ishikawa T,et al.2006.Undersea co-seismic crustal movements associated with the 2005 Off Miyagi Prefecture Earthquake detected by GPS/acoustic seafloor geodetic observation.Earth,Planets and Space,58(12):1573-1576,doi:10.1186/BF03352663
Parkinson B W,Enge P,Axelrad P,et al.1996.Global Positioning System:Theory and Applications,Volume II.Reston,VA:AIAA,163
Rummel R,Rothacher M,Beutler G.2005.Integrated global geodetic observing system(IGGOS)-science rationale.Journal of Geodynamics,40(4-5):357-362,doi:10.1016/j.jog.2005.06.003
Sato M,Fujita M,Matsumoto Y,et al.2013.Improvement of GPS/acoustic seafloor positioning precision through controlling the ship’s track line.Journal of Geodesy,87(9):825-842,doi:10.1007/s00190-013-0649-9
Spiess F N,Chadwell C D,Hildebrand J A,et al.1998.Precise GPS/Acoustic positioning of seafloor reference points for tectonic studies.Physics of the Earth and Planetary Interiors,108(2):101-112,doi:10.1016/S0031-9201(98)00089-2
Teunissen P J G.1998.A proof of Nielsen’s conjecture on the GPS dilution of precision.IEEE Transactions on Aerospace and Electronic Systems,34(2):693-695,doi:10.1109/7.670364
Teunissen P J G.1990.Nonlinear least-squares.Manuscripta Geodaetica,15(3):137-150
Wu Lin,Wang Hubiao,Chai Hua,et al.2015.Research on the relative positions-constrained pattern matching method for underwater gravity-aided inertial navigation.Journal of Navigation,68(5):937-950,doi:10.1017/S0373463315000235
Xu Peiliang,Ando M,Tadokoro K.2005.Precise,three-dimensional seafloor geodetic deformation measurements using difference techniques.Earth,Planets and Space,57(9):795-808,doi:10.1186/BF03351859
Xue Shuqiang,Yang Yuanxi.2015.Positioning configurations with the lowest GDOP and their classification.Journal of Geodesy,89(1):49-71,doi:10.1007/s00190-014-0760-6
Xue Shuqiang,Yang Yuanxi.2017a.Understanding GDOP minimization in GNSS positioning:infinite solutions,finite solutions and no solution.Advances in Space Research,59(3):775-785,doi:10.1016/j.asr.2016.10.019
Xue Shuqiang,Yang Yuanxi.2017b.Unbiased nonlinear least squares estimations of short-distance equations.The Journal of Navigation,70(4):810-828,doi:10.1017/S0373463317000030
Xue Shuqiang,Yang Yuanxi,Dang Yamin.2014a.A closed-form of Newton method for solving over-determined pseudo-distance equations.Journal of Geodesy,88(5):441-448,doi:10.1007/s00190-014-0695-y
Xue Shuqiang,Yang Yuanxi,Dang Yamin,et al.2014b.Dynamic positioning configuration and its first-order optimization.Journal of Geodesy,88(2):127-143,doi:10.1007/s00190-013-0683-7
Xue Shuqiang,Yang Yuanxi,Dang Yamin,et al.2015.A conditional equation for minimizing the GDOP of multi-GNSS constellation and its boundary solution with geostationary satellites.In:Proceedings of the IAG Scientific Assembly.Postdam,Germany:Springer,143:681-690
Yan Weisheng,Chen Wei,Cui Rongxin,et al.2015.Optimal distance between mobile buoy and target for moving long baseline positioning system.Journal of Navigation,68(4):809-826,doi:10.1017/S0373463315000077
Yang Yuanxi,Li Jinlong,Tang Junyi,et al.2011.Generalised DOPs with consideration of the influence function of signal-in-space errors.Journal of Navigation,64(S1):S3-S18,doi:10.1017/S0373463311000415
Yang Yuanxi,Xu Junyi.2016.Navigation performance of beidou in polar area.Geomatics and Information Science of Wuhan University(in Chinese),41(1):15-20
Yang Yuanxi,Xu Tianhe,Xue Shuqiang.2017.Progresses and prospects in developing marine geodetic datum and marine navigation of China.Acta Geodaetica et Cartographica Sinica(in Chinese),46(1):1-8
Yarlagadda R,Ali I,Al-Dhahir N,et al.2000.GPS GDOP metric.IEEProceedings-Radar,Sonar and Navigation,147(5):259-264,doi:10.1049/ip-rsn:20000554
Yokota Y,Ishikawa T,Sato M,et al.2015.Heterogeneous interplate coupling along the Nankai Trough,Japan,detected by GPS-acoustic seafloor geodetic observation.Progress in Earth and Planetary Science,2:10,doi:10.1186/s40645-015-0040-y
Zhao Jianhu,Zou Yajing,Zhang Hongmei,et al.2016.A new method for absolute datum transfer in seafloor control network measurement.Journal of Marine Science and Technology,21(2):216-226,doi:10.1007/s00773-015-0344-z
Zou Yajing,Wang Chisheng,Zhu Jiasong,et al.2017.Optimal sensor configuration for positioning seafloor geodetic node.Ocean Engineering,142:1-9,doi:10.1016/j.oceaneng.2017.06.033
Akyildiz I F,Pompili D,Melodia T.2005.Underwater acoustic sensor networks:research challenges.Ad Hoc Networks,3(3):257-279,doi:10.1016/j.adhoc.2005.01.004
Béchaz C,Boucquaert F.2008.Underwater positioning.Hydro International,2008-01-01,3
Chen Pengyun,Li Ye,Su Yumin,et al.2015.Review of AUV underwater terrain matching navigation.The Journal of Navigation,68(6):1155-1172,doi:10.1017/S0373463315000429
Fujita M,Ishikawa T,Mochizuki M,et al.2006.GPS/Acoustic seafloor geodetic observation:method of data analysis and its application.Earth,Planets and Space,58(3):265-275,doi:10.1186/BF03351923
Fujiwara T,Kodaira S,No T,et al.2011.The 2011 Tohoku-oki earthquake:displacement reaching the trench axis.Science,334(6060):1240,doi:10.1126/science.1211554
Loveless J P,Meade B J.2011.Spatial correlation of interseismic coupling and coseismic rupture extent of the 2011 MW=9.0Tohoku-oki earthquake.Geophysical Research Letters,38(17):L17306
Matsumoto Y,Fujita M,Ishikawa T,et al.2006.Undersea co-seismic crustal movements associated with the 2005 Off Miyagi Prefecture Earthquake detected by GPS/acoustic seafloor geodetic observation.Earth,Planets and Space,58(12):1573-1576,doi:10.1186/BF03352663
Parkinson B W,Enge P,Axelrad P,et al.1996.Global Positioning System:Theory and Applications,Volume II.Reston,VA:AIAA,163
Rummel R,Rothacher M,Beutler G.2005.Integrated global geodetic observing system(IGGOS)-science rationale.Journal of Geodynamics,40(4-5):357-362,doi:10.1016/j.jog.2005.06.003
Sato M,Fujita M,Matsumoto Y,et al.2013.Improvement of GPS/acoustic seafloor positioning precision through controlling the ship’s track line.Journal of Geodesy,87(9):825-842,doi:10.1007/s00190-013-0649-9
Spiess F N,Chadwell C D,Hildebrand J A,et al.1998.Precise GPS/Acoustic positioning of seafloor reference points for tectonic studies.Physics of the Earth and Planetary Interiors,108(2):101-112,doi:10.1016/S0031-9201(98)00089-2
Teunissen P J G.1998.A proof of Nielsen’s conjecture on the GPS dilution of precision.IEEE Transactions on Aerospace and Electronic Systems,34(2):693-695,doi:10.1109/7.670364
Teunissen P J G.1990.Nonlinear least-squares.Manuscripta Geodaetica,15(3):137-150
Wu Lin,Wang Hubiao,Chai Hua,et al.2015.Research on the relative positions-constrained pattern matching method for underwater gravity-aided inertial navigation.Journal of Navigation,68(5):937-950,doi:10.1017/S0373463315000235
Xu Peiliang,Ando M,Tadokoro K.2005.Precise,three-dimensional seafloor geodetic deformation measurements using difference techniques.Earth,Planets and Space,57(9):795-808,doi:10.1186/BF03351859
Xue Shuqiang,Yang Yuanxi.2015.Positioning configurations with the lowest GDOP and their classification.Journal of Geodesy,89(1):49-71,doi:10.1007/s00190-014-0760-6
Xue Shuqiang,Yang Yuanxi.2017a.Understanding GDOP minimization in GNSS positioning:infinite solutions,finite solutions and no solution.Advances in Space Research,59(3):775-785,doi:10.1016/j.asr.2016.10.019
Xue Shuqiang,Yang Yuanxi.2017b.Unbiased nonlinear least squares estimations of short-distance equations.The Journal of Navigation,70(4):810-828,doi:10.1017/S0373463317000030
Xue Shuqiang,Yang Yuanxi,Dang Yamin.2014a.A closed-form of Newton method for solving over-determined pseudo-distance equations.Journal of Geodesy,88(5):441-448,doi:10.1007/s00190-014-0695-y
Xue Shuqiang,Yang Yuanxi,Dang Yamin,et al.2014b.Dynamic positioning configuration and its first-order optimization.Journal of Geodesy,88(2):127-143,doi:10.1007/s00190-013-0683-7
Xue Shuqiang,Yang Yuanxi,Dang Yamin,et al.2015.A conditional equation for minimizing the GDOP of multi-GNSS constellation and its boundary solution with geostationary satellites.In:Proceedings of the IAG Scientific Assembly.Postdam,Germany:Springer,143:681-690
Yan Weisheng,Chen Wei,Cui Rongxin,et al.2015.Optimal distance between mobile buoy and target for moving long baseline positioning system.Journal of Navigation,68(4):809-826,doi:10.1017/S0373463315000077
Yang Yuanxi,Li Jinlong,Tang Junyi,et al.2011.Generalised DOPs with consideration of the influence function of signal-in-space errors.Journal of Navigation,64(S1):S3-S18,doi:10.1017/S0373463311000415
Yang Yuanxi,Xu Junyi.2016.Navigation performance of beidou in polar area.Geomatics and Information Science of Wuhan University(in Chinese),41(1):15-20
Yang Yuanxi,Xu Tianhe,Xue Shuqiang.2017.Progresses and prospects in developing marine geodetic datum and marine navigation of China.Acta Geodaetica et Cartographica Sinica(in Chinese),46(1):1-8
Yarlagadda R,Ali I,Al-Dhahir N,et al.2000.GPS GDOP metric.IEEProceedings-Radar,Sonar and Navigation,147(5):259-264,doi:10.1049/ip-rsn:20000554
Yokota Y,Ishikawa T,Sato M,et al.2015.Heterogeneous interplate coupling along the Nankai Trough,Japan,detected by GPS-acoustic seafloor geodetic observation.Progress in Earth and Planetary Science,2:10,doi:10.1186/s40645-015-0040-y
Zhao Jianhu,Zou Yajing,Zhang Hongmei,et al.2016.A new method for absolute datum transfer in seafloor control network measurement.Journal of Marine Science and Technology,21(2):216-226,doi:10.1007/s00773-015-0344-z
Zou Yajing,Wang Chisheng,Zhu Jiasong,et al.2017.Optimal sensor configuration for positioning seafloor geodetic node.Ocean Engineering,142:1-9,doi:10.1016/j.oceaneng.2017.06.033