GPS快速定姿技术研究
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摘要
全球定位系统(Global Positioning System)的应用是飞行器导航、制导和控制(GNC)领域的一场革命。应用GPS载波相位测量技术来确定载体的姿态，因具有精度高、不受美国P码(Y码)保密的限制等特点而日益成为导航领域研究的热点。
通过对安装在载体上的多个GPS天线测得的载波相位信息进行差分处理，就可以实时确定载体的姿态。本论文从理论和试验两个方面对GPS快速定姿技术进行了研究。
理论上从GPS载波相位观测方程入手，对单差方程、双差方程和误差源进行了分析；接着，给出由基线矢量确定姿态的方法，重点讲述了基于最小二乘的姿态估计法和姿态的直接计算法，并对误差进行了分析；最后针对本课题技术要求的实际特点，提出一种适合于单历元姿态求解的基于空间几何关系模糊度搜索算法，能有效地解决模糊度搜索速度；为了提高成功率，提出了一种基于姿态角约束金字塔算法，并编写了相应的软件。
试验方面，利用低价CMC ALLSTAR的GPS接收设备进行了大量的试验。试验结果表明，在静态实时定姿试验中，1m长的基线航向角能获得优于0.3度(均方差)的精度，4m长的基线航向角能获得优于0.1(均方差)的精度。在动态实时定姿中，通过各种环境的试验验证算法的可性有效性。通过试验，该测姿系统在实时性、精度、可靠性等方面能满足中、低动态实时定姿要求，可用姿态测量的应用，是实现动基座惯性导航系统快速初始对准的重要手段之一。
The Global Positioning System (GPS) is poised to revolutionize flight vehicle Guidance, navigation, and Control. The technology of determining attitude of carrier by GPS carrier phase measurements is becoming a particle of navigation fields because of its high precision and its freedom from the constraints of Precise Code (or Y code) by the U.S.
Real-time attitude determination is derived from extremely precise differential carrier phase measurements among multiple GPS antennas mounted on a flight vehicle. This dissertation describes the application of GPS attitude determination system in theory as well as experiments.
With the help of phase observation equations, single differential, double differential observations and their error sources are analyzed at first. Then methods of attitude determination derived from baseline vectors are proposed, especially, a least squares attitude estimation procedure and a direct computation method for attitude are discussed in details, and error analysis of the estimated attitude parameters is performed. Last but not least, directed at the practical features of the task, a new ambiguity estimation searching based on space geometry conditions is analyzed. In order to improve reliability of attitude determination, a pyramid algorithm based on attitude constraints is presented.
As far as experiment is concerned, an attitude system using GPS is composed by some low-cost CMC ALLSTAR receivers. Methods presented in this paper were tested on the static and dynamic condition. On the static real-time condition, an accuracy better than 0.1 degrees for heading for 4m long baseline has been achieved, and an accuracy better than 0.3 degrees for heading for 1m long baseline has been achieved. On the dynamic condition, the correction of algorithm has been demonstrated. Such a performance of multiple GPS sensors attitude systems demonstrate an alternative means to provide real-time, cost-effective, accurate and reliable attitude information for attitude surveys, and a key means to realize INS alignment on a moving platform.
通过对安装在载体上的多个GPS天线测得的载波相位信息进行差分处理，就可以实时确定载体的姿态。本论文从理论和试验两个方面对GPS快速定姿技术进行了研究。
理论上从GPS载波相位观测方程入手，对单差方程、双差方程和误差源进行了分析；接着，给出由基线矢量确定姿态的方法，重点讲述了基于最小二乘的姿态估计法和姿态的直接计算法，并对误差进行了分析；最后针对本课题技术要求的实际特点，提出一种适合于单历元姿态求解的基于空间几何关系模糊度搜索算法，能有效地解决模糊度搜索速度；为了提高成功率，提出了一种基于姿态角约束金字塔算法，并编写了相应的软件。
试验方面，利用低价CMC ALLSTAR的GPS接收设备进行了大量的试验。试验结果表明，在静态实时定姿试验中，1m长的基线航向角能获得优于0.3度(均方差)的精度，4m长的基线航向角能获得优于0.1(均方差)的精度。在动态实时定姿中，通过各种环境的试验验证算法的可性有效性。通过试验，该测姿系统在实时性、精度、可靠性等方面能满足中、低动态实时定姿要求，可用姿态测量的应用，是实现动基座惯性导航系统快速初始对准的重要手段之一。
The Global Positioning System (GPS) is poised to revolutionize flight vehicle Guidance, navigation, and Control. The technology of determining attitude of carrier by GPS carrier phase measurements is becoming a particle of navigation fields because of its high precision and its freedom from the constraints of Precise Code (or Y code) by the U.S.
Real-time attitude determination is derived from extremely precise differential carrier phase measurements among multiple GPS antennas mounted on a flight vehicle. This dissertation describes the application of GPS attitude determination system in theory as well as experiments.
With the help of phase observation equations, single differential, double differential observations and their error sources are analyzed at first. Then methods of attitude determination derived from baseline vectors are proposed, especially, a least squares attitude estimation procedure and a direct computation method for attitude are discussed in details, and error analysis of the estimated attitude parameters is performed. Last but not least, directed at the practical features of the task, a new ambiguity estimation searching based on space geometry conditions is analyzed. In order to improve reliability of attitude determination, a pyramid algorithm based on attitude constraints is presented.
As far as experiment is concerned, an attitude system using GPS is composed by some low-cost CMC ALLSTAR receivers. Methods presented in this paper were tested on the static and dynamic condition. On the static real-time condition, an accuracy better than 0.1 degrees for heading for 4m long baseline has been achieved, and an accuracy better than 0.3 degrees for heading for 1m long baseline has been achieved. On the dynamic condition, the correction of algorithm has been demonstrated. Such a performance of multiple GPS sensors attitude systems demonstrate an alternative means to provide real-time, cost-effective, accurate and reliable attitude information for attitude surveys, and a key means to realize INS alignment on a moving platform.
引文
[1] 潘科炎，航天器的自主导航技术，航天控制，1994年第2期，pp.18-27。
[2] Richard D. Jurgens, Charles E. Rodgers, GPS方位确定系统设计，导航，1993年3月第1期, pp. 23-28。
[3] John B. Schleppe, Development of a Real-Time Attitude System Using a Quaternion Parameterization and Non-Dedicated GPS Receivers, UCGE Reports, JULY 1996, pp. 3．
[4] Lightsey, E.G., Cohen C. E., Fees W. A., Parkinson, B. W., Analysis for Spacecraft Attitude Measurement Using Onboard GPS, AAS Guidance and Control Conf., Keystone, Co, Feb. 94, pp. 521-532．
[5] Graas F V, Braasch M S. GPS interferometric attitude and heading determination: flight test results. Navigation, 1991,38(4) , pp.183-191．
[6] Cohen C E, Parkinson B W, Mcnally B D. Flight tests of attitude determination using GPS compared against an inertial navigaion unit. Navigation,1994, 41(1) , pp. 83-97 .
[7] Q. P. Chu, P. Th. L. M. van Woerkom, T. Zwartbol, Attitude Estimation for low-cost Spacecraft Equipped with GPS, PB97-194989/XAB.
[8] Lachapelle, G., M. E. Cannon, G. Lu (1992) : High-Precision GPS Navigation with Emphasis on Carrier-Phase Ambiguity Resolution, Marine Geodesy, Vol. 15, pp. 253-269．
[9] Tranquilla, J. M. and B. G. Colpitts (1989) : GPS Antenna Design Characteristics For HighPrecision Applications, Journal of Surveying Engineering, ASCE, Vol. 115, No. I.February 1989．
[10] Penina Axelrad, Peter F.MacDoran, Christopher J. Comp, A Study of GPS Measurement Errors due to Noise and Multipath Interference for CGADS, NASA-CR-200249, Jan. 1996．
[11] Wahba, G. (1965) : A Least Squares Estimate of Spacecraft Attitude, SUM Review Vol. 7, No. 3, July 1965, p. 409．
[12] Markley, F. L. (1988) : Attitude Determination Using Vector Observations and the Singular Value Decomposition, The Journal of the Astronautical Sciences, Vol. 36, No. 3, July-September 1988, pp. 245-258．
[13] Shuster, M. D. and S. D. Oh (1981) : Three-Axis Attitude Determination from Vector bservations, Journal of Guidance and Control, Vol. 4,No. 1, 1981, pp. 70-77．
[14] Gang Lu, Development of a GPS Multi-Antenna System for Attitude Determination, UCGE Reports ,Number 20073, January 1995
[15] Krakiwsky, E. J. (Ed.) (1987) : Papers For The CISM Adjustment and Analysis Seminars, Second Edtion, The Canadian Institute of Surveying and Mapping, Box 5378, Station F, Ottawa, Ont. Canada.
[16] Cohen, C. E., H. S. Cobb and B. W. Parkinson (1992) : Two Studies of High
Performance Attitude Determination Using GPS: Generalizing Wahba's Problem or High Output Rates and Evaluation of Static Accuracy Using A Theodolite, Proceedings of the Fifth International Technical Meeting of the Satellite Division of the ION, GPS-92, Albuquerque, N. M. 16-18 September 1992.
[17] Comp, C. (1993): Optimal Antenna Configuration for GPS Based Attitude Determination, Proceedings of the sixth International Technical Meeting of the Satellite Division of the ION, GPS-93, Salt Lake City, Utah, 22-24 September 1993.
[18] P.J.G. reunissen, A new method for fast carrier phase ambiguity estimation. Proceedings of IEEE PLANS'94, Las Vegas, NV, April 11-15, pp. 562-573
[19] Chen, D., G. Lachapelle, A Comparison of the Fast and Least-Squares Search Algorithms for On-The-Fly Ambiguity Resolution, Journal of The Institute of Navigation, Vol. 42, No. 2, Summer, 1995, pp. 371-390.
[20] Chen, D. S. and G. Lachapelle (1994): A Comparison of the FASF and Least Squares Search Algorithms for Ambiguity Resolution On The Fly, Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada, August 30-September 2, 1994.
[21] Hatch, R. (1991): Instantaneous Ambiguity Resolution, Proceedings of IAG Symposium No. 107 on Kinematic Systems in Geodesy, Surveying and Remote Sensing, Springer Verlag, New York.
[22] Remondi, B.W., Performing Centimeter-level Surveys in Seconds with GPS Carrier Phase: Initial Results, Journal of The Institute of Navigation, Vol. 32, No. 4, Winter, 1985, pp. 386-400.
[23] Patrick Y.C. Hwang, Kinematic GPS for Differential Positioning: Resolving Integer Ambiguities on the Fly, Navigation: Journal of The Institute of Navigation, Vol. 38, No.1, Spring 1991, pp. 1-15.
[24] Benjamin W. Remondi, Pseudo-Kinematic GPS Results Using the Ambiguity Function Method, Navigation: Journal of The Institute of Navigation, Vol. 38, No.1, Spring 1991, pp.17-36.
[25] Paul de Jonge, Christian Tiberius, The LAMBDA method for integer ambiguity estimation: implementation aspects, LGR-series, No. 12, August 1996, Delft Geodetic Computing Center.
[26] Hatch, R., H.-J. Euler, Comparison of Several AROF Kinematic Techniques, Proceedings of ION GPS-94, Salt Lake City, USA, September 20-23, pp. 363-370.
[27] 张守信，GPS卫星测量定位理论与应用，北京：国防科技大学出版社，1996，pp．91-92．
[28] 赵健康．《关于GPS定姿研究的技术报告》，内部资料，1997．
[29] Koch, K. R. (1988): Parameter Estimation and Hypothesis Testing in Linear Models, Springer-Verlag, Berlin Heidelberg 1988.
[30] 朱淼良，计算机视觉，浙江大学出版社，1997，pp．137-140．
[31] 张系国(著)，吴健康(译)，图像信息系统设计原理，科学出版社，1990．
[32] 逯亮清，GPS快速定向技术研究，工学硕士论文，2001．
[2] Richard D. Jurgens, Charles E. Rodgers, GPS方位确定系统设计，导航，1993年3月第1期, pp. 23-28。
[3] John B. Schleppe, Development of a Real-Time Attitude System Using a Quaternion Parameterization and Non-Dedicated GPS Receivers, UCGE Reports, JULY 1996, pp. 3．
[4] Lightsey, E.G., Cohen C. E., Fees W. A., Parkinson, B. W., Analysis for Spacecraft Attitude Measurement Using Onboard GPS, AAS Guidance and Control Conf., Keystone, Co, Feb. 94, pp. 521-532．
[5] Graas F V, Braasch M S. GPS interferometric attitude and heading determination: flight test results. Navigation, 1991,38(4) , pp.183-191．
[6] Cohen C E, Parkinson B W, Mcnally B D. Flight tests of attitude determination using GPS compared against an inertial navigaion unit. Navigation,1994, 41(1) , pp. 83-97 .
[7] Q. P. Chu, P. Th. L. M. van Woerkom, T. Zwartbol, Attitude Estimation for low-cost Spacecraft Equipped with GPS, PB97-194989/XAB.
[8] Lachapelle, G., M. E. Cannon, G. Lu (1992) : High-Precision GPS Navigation with Emphasis on Carrier-Phase Ambiguity Resolution, Marine Geodesy, Vol. 15, pp. 253-269．
[9] Tranquilla, J. M. and B. G. Colpitts (1989) : GPS Antenna Design Characteristics For HighPrecision Applications, Journal of Surveying Engineering, ASCE, Vol. 115, No. I.February 1989．
[10] Penina Axelrad, Peter F.MacDoran, Christopher J. Comp, A Study of GPS Measurement Errors due to Noise and Multipath Interference for CGADS, NASA-CR-200249, Jan. 1996．
[11] Wahba, G. (1965) : A Least Squares Estimate of Spacecraft Attitude, SUM Review Vol. 7, No. 3, July 1965, p. 409．
[12] Markley, F. L. (1988) : Attitude Determination Using Vector Observations and the Singular Value Decomposition, The Journal of the Astronautical Sciences, Vol. 36, No. 3, July-September 1988, pp. 245-258．
[13] Shuster, M. D. and S. D. Oh (1981) : Three-Axis Attitude Determination from Vector bservations, Journal of Guidance and Control, Vol. 4,No. 1, 1981, pp. 70-77．
[14] Gang Lu, Development of a GPS Multi-Antenna System for Attitude Determination, UCGE Reports ,Number 20073, January 1995
[15] Krakiwsky, E. J. (Ed.) (1987) : Papers For The CISM Adjustment and Analysis Seminars, Second Edtion, The Canadian Institute of Surveying and Mapping, Box 5378, Station F, Ottawa, Ont. Canada.
[16] Cohen, C. E., H. S. Cobb and B. W. Parkinson (1992) : Two Studies of High
Performance Attitude Determination Using GPS: Generalizing Wahba's Problem or High Output Rates and Evaluation of Static Accuracy Using A Theodolite, Proceedings of the Fifth International Technical Meeting of the Satellite Division of the ION, GPS-92, Albuquerque, N. M. 16-18 September 1992.
[17] Comp, C. (1993): Optimal Antenna Configuration for GPS Based Attitude Determination, Proceedings of the sixth International Technical Meeting of the Satellite Division of the ION, GPS-93, Salt Lake City, Utah, 22-24 September 1993.
[18] P.J.G. reunissen, A new method for fast carrier phase ambiguity estimation. Proceedings of IEEE PLANS'94, Las Vegas, NV, April 11-15, pp. 562-573
[19] Chen, D., G. Lachapelle, A Comparison of the Fast and Least-Squares Search Algorithms for On-The-Fly Ambiguity Resolution, Journal of The Institute of Navigation, Vol. 42, No. 2, Summer, 1995, pp. 371-390.
[20] Chen, D. S. and G. Lachapelle (1994): A Comparison of the FASF and Least Squares Search Algorithms for Ambiguity Resolution On The Fly, Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada, August 30-September 2, 1994.
[21] Hatch, R. (1991): Instantaneous Ambiguity Resolution, Proceedings of IAG Symposium No. 107 on Kinematic Systems in Geodesy, Surveying and Remote Sensing, Springer Verlag, New York.
[22] Remondi, B.W., Performing Centimeter-level Surveys in Seconds with GPS Carrier Phase: Initial Results, Journal of The Institute of Navigation, Vol. 32, No. 4, Winter, 1985, pp. 386-400.
[23] Patrick Y.C. Hwang, Kinematic GPS for Differential Positioning: Resolving Integer Ambiguities on the Fly, Navigation: Journal of The Institute of Navigation, Vol. 38, No.1, Spring 1991, pp. 1-15.
[24] Benjamin W. Remondi, Pseudo-Kinematic GPS Results Using the Ambiguity Function Method, Navigation: Journal of The Institute of Navigation, Vol. 38, No.1, Spring 1991, pp.17-36.
[25] Paul de Jonge, Christian Tiberius, The LAMBDA method for integer ambiguity estimation: implementation aspects, LGR-series, No. 12, August 1996, Delft Geodetic Computing Center.
[26] Hatch, R., H.-J. Euler, Comparison of Several AROF Kinematic Techniques, Proceedings of ION GPS-94, Salt Lake City, USA, September 20-23, pp. 363-370.
[27] 张守信，GPS卫星测量定位理论与应用，北京：国防科技大学出版社，1996，pp．91-92．
[28] 赵健康．《关于GPS定姿研究的技术报告》，内部资料，1997．
[29] Koch, K. R. (1988): Parameter Estimation and Hypothesis Testing in Linear Models, Springer-Verlag, Berlin Heidelberg 1988.
[30] 朱淼良，计算机视觉，浙江大学出版社，1997，pp．137-140．
[31] 张系国(著)，吴健康(译)，图像信息系统设计原理，科学出版社，1990．
[32] 逯亮清，GPS快速定向技术研究，工学硕士论文，2001．
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