GPS/INS组合导航数据处理算法拓展研究
|
摘要
本文对GPS/INS组合导航数据处理的算法进行了较系统研究，内容涵盖GPS/INS组合导航的基本原理、Kalman滤波先验随机模型误差的影响分析、组合导航中观测异常及动力学模型异常影响控制、非差精密单点定位与INS组合导航以及载波相位时间差分改善GPS/INS紧组合速度估计精度等方面的研究，论文的主要工作和创新点概括如下：
1、总结了GPS/INS组合导航数据处理的基本原理，分别介绍了GPS和INS导航数据处理方法，并简单介绍INS导航常用的坐标系以及不同坐标系之间的转换，详细给出INS的地固系中的解算过程和GPS/INS组合导航的滤波模型。
2、简单介绍Kalman滤波以及抗差自适应Kalman滤波的基本原理，着重分析了先验随机模型误差对Kalman滤波解的影响，分别对先验状态噪声协方差阵、先验观测噪声协方差阵以及先验状态参数协方差阵以及上述矩阵中部分元素存在误差情况进行了分析。计算结果表明，Kalman滤波的先验随机模型在滤波过程中有一个平衡点，只要在这个平衡点上或是在平衡点附近，动力学模型提供的先验状态信息和当前观测信息对Kalman滤波解的贡献都能达到或是接近理想水平，从而获取较可靠的滤波结果；若动力学模型本身精度较差，则增大相应预测状态协方差矩阵，能够提高参数估计值的精度。
3、由于组合导航中观测信息冗余较少，观测异常误差的影响无法通过抗差估计的方法进行处理。为了控制观测值异常对组合导航精度的影响，本文提出基于交互多模型的组合导航观测数据异常影响控制算法，即建立观测正常和异常的多模型集，滤波过程中各个模型并行进行计算，各模型间通过马尔克夫模型概率进行切换，当观测值正常时，正常模型起作用；观测值异常时，故障模型起作用，滤波结果为各个模型滤波结果的加权融合。该算法能较好地抑制观测信息异常对滤波解的影响。其中，模型概率的计算很重要，它影响模型的选择。若预测残差过大会造成模型概率过小，再有舍入误差，就无法进行模型的选择。文中简化了模型概率的计算公式，可以避免上述问题。
4、在动态导航计算中，标准Kalman滤波不具备抵制粗差的能力，易受系统状态异常扰动或观测异常等因素的影响，导致滤波结果往往远远偏离真值。在动力学模型可靠的情况下，为避免观测异常对滤波结果的影响，建立处理观测异常的观测模型集合，以观测模型集合中系数矩阵的期望来代替观测方程的系数矩阵，利用随机系数矩阵Kalman滤波算法来控制观测信息异常的影响。计算结果表明，该算法同样可有效地控制观测值异常对滤波结果的影响。
5、在GPS/INS组合导航中，对于观测异常的控制，可以建立相应的观测异常处理模型集合，通过交互多模型或基于随机系数矩阵的Kalman滤波算法来进行控制；而对于状态异常扰动误差的影响，同样也可利用上述两种算法进行控制，前提需建立相应的动力学模型异常扰动误差的模型集。但是，组合系统主要依赖于INS的力学编排提供载体的状态信息，建立其相应的动力学模型异常扰动误差的模型集并不容易，鉴于此，提出一种基于随机系数矩阵的自适应Kalman滤波算法，即利用自适应因子控制来动力学模型异常误差的影响，用随机系数矩阵的Kalman滤波控制观测异常误差的影响。
6、GPS/INS紧组合利用GPS原始的观测值与INS进行组合，没有充分利用GPS的运动信息，本文提出一种顾及GPS运动信息的GPS/INS紧组合融合算法。该算法利用GPS常速度模型来预测载体的位置和速度误差，为组合系统位置和速度误差状态的预报值增加了冗余，从而增强了组合系统部分先验预测状态的可靠性，进一步改善了整体导航精度。
7、利用载波相位时间差分提高GPS/INS紧组合导航速度参数的估计精度。分别采用两种不同的方法进行速度估计，1、基于阈值的自适应载波相位时间差分观测值与Doppler观测值估计速度；2、基于部分状态参数的抗差估计，将载波相位时间差分观测值作为附加的虚拟Doppler观测值扩充至组合观测方程中，再通过部分状态参数不符值进行速度参数的抗差估计。实测计算结果表明，上述两种方法都能有效地提高紧组合导航速度参数估计的精度。
This dissertation mainly focuses on algorithms of data processing in GPS/INS integratednavigation which includes the principles of GPS/INS integrated navigation. After analyzing ofthe influence of the prior covariance errors in standard Kalman filter, the influence ofobservation outliers and the dynamic model errors in GPS/INS navigation is discussed. Theprecise point positioning (PPP)/INS integration and use of time differencing carrier phase(TDCP) in improving the velocity estimation are also studied. The main works andcontributions are summarized as follows:
1. The principles of GPS/INS integrated navigation are summarized including the principlesof INS navigation and GPS navigation. An overview on the common reference frames andtransformations in inertial navigation is provided. The data processing of INS in EarthCentered Earth Fixed (ECEF) frame and the filter models of GPS/INS integration are alsoprovided.
2. The principles of Kalman filter and adaptively robust filter are summarized. The influenceof the prior covariance errors to the standard dynamic Kalman filtering is discussed. Theinfluence expressions of the prior covariance matrix errors including the covariance matrix ofstate parameters, dynamical model errors and measurement noises are deduced. The resultshows that there is a balance between the prior covariance matrixes, which guarantee theKalman filter to achieve an optimal result. The more precise of the measurement, the smallerof the covariance matrix of measurement noise is. If the dynamical model is low precise, thefilter result can be improved from augmenting the covariance matrix of the predicted states.
3. Generally there are not enough redundant observations to estimate all the state parametersin GPS/INS navigation, thus if the measurements exist errors, it’s not proper to control theirinfluences by using robust filter. In order to eliminate or depress the influences of themeasurement errors, an interacting multiple model algorithm is proposed. A model set,including both normal and exceptional observational models, is established. The Markovtransition probabilities are used to switch one model to another. When observations arenormal, the normal observation model is used chiefly, otherwise the exceptional observationmodel works. The navigation result is weighted fusion of all the outputs in the model set. The Markov transition probabilities take important part in the algorithm for model choosing. It isdifficult to choose which model works if the probabilities are too small, which are calculatedby the predicted residuals. So a simple formulation is given for probability calculation, whichcan avoid the confusion about the model choosing.
4. Kalman filter is widely used in the area of kinematic positioning and navigation. However,it does not have the ability to resist the influence of measurement outliers. Hence itsperformance is easy impacted by the observation outliers or kinematic state disturbing. Inorder to guarantee the reliability of the navigation with precise dynamic model, a model set,which contains many different observation models, is established. An improved Kalmanfiltering, in which the design matrix of the observational model is substituted by itsexpectation is proposed to control the influences of the measurement outliers. An integratedGPS/INS navigation example is given to show that the modified Kalman filtering algorithmworks well.
5. In GPS/INS integrated navigation, the IMM algorithm and Kalman filtering with randomparameter matrices are proposed to depress the influence of measurement outliers. Similarly,the both algorithms also can be used to get rid of the dynamical model errors if thecorresponding model set is established properly. However, the state prediction is mainly relyon the mechanization equations of initial navigation system, and it is not easy to establish areliable dynamical model set. So an adaptively Kalman filtering with random parametermatrices is proposed, in which the adaptive factor and random parameter matrices are used tocontrol the influence of the dynamical model errors and measurement outliers respectively.
6. In the tightly coupled GPS/INS integrated navigation, the information of the GPSmeasurements are not using sufficiently. Actually the carrier’s dynamical information can beextraction from GPS observations. A novel tightly coupled GPS/INS integration consideringthe GPS dynamical information is proposed. This algorithm can increase the redundant in thepredicted states of position and velocity from GPS CV model, and also can enhance thereliability of the prior predicted states.
7. An improved time differencing carrier phase (TDCP) velocity estimation algorithm in thetightly coupled GPS/INS integration has been proposed. Velocity is estimated using twodifferent methods. One employs the Doppler measurements and the derived Doppler measurements from TDCP to improve the velocity estimation; and the other one takes use ofthe derived Doppler measurements as virtual measurements in observation model. Then thepartial state discrepancy is used to estimate the velocity by using robust estimation.Experimental results shown that the precision of the velocity from both methods can beimproved effectively.
1、总结了GPS/INS组合导航数据处理的基本原理，分别介绍了GPS和INS导航数据处理方法，并简单介绍INS导航常用的坐标系以及不同坐标系之间的转换，详细给出INS的地固系中的解算过程和GPS/INS组合导航的滤波模型。
2、简单介绍Kalman滤波以及抗差自适应Kalman滤波的基本原理，着重分析了先验随机模型误差对Kalman滤波解的影响，分别对先验状态噪声协方差阵、先验观测噪声协方差阵以及先验状态参数协方差阵以及上述矩阵中部分元素存在误差情况进行了分析。计算结果表明，Kalman滤波的先验随机模型在滤波过程中有一个平衡点，只要在这个平衡点上或是在平衡点附近，动力学模型提供的先验状态信息和当前观测信息对Kalman滤波解的贡献都能达到或是接近理想水平，从而获取较可靠的滤波结果；若动力学模型本身精度较差，则增大相应预测状态协方差矩阵，能够提高参数估计值的精度。
3、由于组合导航中观测信息冗余较少，观测异常误差的影响无法通过抗差估计的方法进行处理。为了控制观测值异常对组合导航精度的影响，本文提出基于交互多模型的组合导航观测数据异常影响控制算法，即建立观测正常和异常的多模型集，滤波过程中各个模型并行进行计算，各模型间通过马尔克夫模型概率进行切换，当观测值正常时，正常模型起作用；观测值异常时，故障模型起作用，滤波结果为各个模型滤波结果的加权融合。该算法能较好地抑制观测信息异常对滤波解的影响。其中，模型概率的计算很重要，它影响模型的选择。若预测残差过大会造成模型概率过小，再有舍入误差，就无法进行模型的选择。文中简化了模型概率的计算公式，可以避免上述问题。
4、在动态导航计算中，标准Kalman滤波不具备抵制粗差的能力，易受系统状态异常扰动或观测异常等因素的影响，导致滤波结果往往远远偏离真值。在动力学模型可靠的情况下，为避免观测异常对滤波结果的影响，建立处理观测异常的观测模型集合，以观测模型集合中系数矩阵的期望来代替观测方程的系数矩阵，利用随机系数矩阵Kalman滤波算法来控制观测信息异常的影响。计算结果表明，该算法同样可有效地控制观测值异常对滤波结果的影响。
5、在GPS/INS组合导航中，对于观测异常的控制，可以建立相应的观测异常处理模型集合，通过交互多模型或基于随机系数矩阵的Kalman滤波算法来进行控制；而对于状态异常扰动误差的影响，同样也可利用上述两种算法进行控制，前提需建立相应的动力学模型异常扰动误差的模型集。但是，组合系统主要依赖于INS的力学编排提供载体的状态信息，建立其相应的动力学模型异常扰动误差的模型集并不容易，鉴于此，提出一种基于随机系数矩阵的自适应Kalman滤波算法，即利用自适应因子控制来动力学模型异常误差的影响，用随机系数矩阵的Kalman滤波控制观测异常误差的影响。
6、GPS/INS紧组合利用GPS原始的观测值与INS进行组合，没有充分利用GPS的运动信息，本文提出一种顾及GPS运动信息的GPS/INS紧组合融合算法。该算法利用GPS常速度模型来预测载体的位置和速度误差，为组合系统位置和速度误差状态的预报值增加了冗余，从而增强了组合系统部分先验预测状态的可靠性，进一步改善了整体导航精度。
7、利用载波相位时间差分提高GPS/INS紧组合导航速度参数的估计精度。分别采用两种不同的方法进行速度估计，1、基于阈值的自适应载波相位时间差分观测值与Doppler观测值估计速度；2、基于部分状态参数的抗差估计，将载波相位时间差分观测值作为附加的虚拟Doppler观测值扩充至组合观测方程中，再通过部分状态参数不符值进行速度参数的抗差估计。实测计算结果表明，上述两种方法都能有效地提高紧组合导航速度参数估计的精度。
This dissertation mainly focuses on algorithms of data processing in GPS/INS integratednavigation which includes the principles of GPS/INS integrated navigation. After analyzing ofthe influence of the prior covariance errors in standard Kalman filter, the influence ofobservation outliers and the dynamic model errors in GPS/INS navigation is discussed. Theprecise point positioning (PPP)/INS integration and use of time differencing carrier phase(TDCP) in improving the velocity estimation are also studied. The main works andcontributions are summarized as follows:
1. The principles of GPS/INS integrated navigation are summarized including the principlesof INS navigation and GPS navigation. An overview on the common reference frames andtransformations in inertial navigation is provided. The data processing of INS in EarthCentered Earth Fixed (ECEF) frame and the filter models of GPS/INS integration are alsoprovided.
2. The principles of Kalman filter and adaptively robust filter are summarized. The influenceof the prior covariance errors to the standard dynamic Kalman filtering is discussed. Theinfluence expressions of the prior covariance matrix errors including the covariance matrix ofstate parameters, dynamical model errors and measurement noises are deduced. The resultshows that there is a balance between the prior covariance matrixes, which guarantee theKalman filter to achieve an optimal result. The more precise of the measurement, the smallerof the covariance matrix of measurement noise is. If the dynamical model is low precise, thefilter result can be improved from augmenting the covariance matrix of the predicted states.
3. Generally there are not enough redundant observations to estimate all the state parametersin GPS/INS navigation, thus if the measurements exist errors, it’s not proper to control theirinfluences by using robust filter. In order to eliminate or depress the influences of themeasurement errors, an interacting multiple model algorithm is proposed. A model set,including both normal and exceptional observational models, is established. The Markovtransition probabilities are used to switch one model to another. When observations arenormal, the normal observation model is used chiefly, otherwise the exceptional observationmodel works. The navigation result is weighted fusion of all the outputs in the model set. The Markov transition probabilities take important part in the algorithm for model choosing. It isdifficult to choose which model works if the probabilities are too small, which are calculatedby the predicted residuals. So a simple formulation is given for probability calculation, whichcan avoid the confusion about the model choosing.
4. Kalman filter is widely used in the area of kinematic positioning and navigation. However,it does not have the ability to resist the influence of measurement outliers. Hence itsperformance is easy impacted by the observation outliers or kinematic state disturbing. Inorder to guarantee the reliability of the navigation with precise dynamic model, a model set,which contains many different observation models, is established. An improved Kalmanfiltering, in which the design matrix of the observational model is substituted by itsexpectation is proposed to control the influences of the measurement outliers. An integratedGPS/INS navigation example is given to show that the modified Kalman filtering algorithmworks well.
5. In GPS/INS integrated navigation, the IMM algorithm and Kalman filtering with randomparameter matrices are proposed to depress the influence of measurement outliers. Similarly,the both algorithms also can be used to get rid of the dynamical model errors if thecorresponding model set is established properly. However, the state prediction is mainly relyon the mechanization equations of initial navigation system, and it is not easy to establish areliable dynamical model set. So an adaptively Kalman filtering with random parametermatrices is proposed, in which the adaptive factor and random parameter matrices are used tocontrol the influence of the dynamical model errors and measurement outliers respectively.
6. In the tightly coupled GPS/INS integrated navigation, the information of the GPSmeasurements are not using sufficiently. Actually the carrier’s dynamical information can beextraction from GPS observations. A novel tightly coupled GPS/INS integration consideringthe GPS dynamical information is proposed. This algorithm can increase the redundant in thepredicted states of position and velocity from GPS CV model, and also can enhance thereliability of the prior predicted states.
7. An improved time differencing carrier phase (TDCP) velocity estimation algorithm in thetightly coupled GPS/INS integration has been proposed. Velocity is estimated using twodifferent methods. One employs the Doppler measurements and the derived Doppler measurements from TDCP to improve the velocity estimation; and the other one takes use ofthe derived Doppler measurements as virtual measurements in observation model. Then thepartial state discrepancy is used to estimate the velocity by using robust estimation.Experimental results shown that the precision of the velocity from both methods can beimproved effectively.
引文
[1] Abdel-salam, M. A. t. Precise Point Positioning Using Un-Differenced Code andCarrier Phase Observations [D]. PhD. Thesis. UCGE Report No.20229, Departmentof Geomatics Engineering, University of Calgary, Canada,2005.
[2] Alexander S.T. Fast adaptive filters: a geometrical approach[C]. IEEE ASSP Mag.,1986,18-28.
[3] Antonio Angrisano. GNSS/INS Integration Methods [D]. PhD. Thesis, Department ofGeomatics Engineering, University of Calgary, Canada,2010.
[4] Ben K. H. Soon, Steve Scheding, Hyung-Kuen Lee, An approach to aid INS usingtime-differenced GPS carrier phase (TDCP) measurements [J]. GPS Solution,2008,12:261-271.
[5] Bisnath, S. B. and R. B. Langley. Precise Orbit Determination of Low Earth Orbiterswith GPS Point Positioning [C]. ION National Technical Meeting, The Institute ofNavigation. Long Beach,California,2001:725-733.
[6] Bisnath, S.B. and R.B. Langley. A New Approach to an Old Problem: Carrier PhaseCycle Slips [J]. GPS World.2001, Vol.12(5):46-51.
[7] Blom H A P, Bar-Shalom Y. The interacting multiple model algorithm for systemswith Markovian switching coefficients [J]. IEEE Transactions on Automatic Control,1988,33(8):780-783.
[8] Bock H. Efficient Methods for Determining Precise Orbits of Low Earth OrbitersUsing the Global Positioning System [D]. PhD. Thesis. Astronomical InstituteUniversity of Berne, Switzerland,2003.
[9] Brenner, M. Integrated GPS/Inertial Fault Detection Availability [C]. In Proceedingsof ION GPS, September, Palm Spring CA, pp.1949-1958, U.S. Institute of Navigation,Fairfax VA,1995.
[10] Carvalho H., Moral P. D.. Optimal nonlinear filtering in GPS/INS integration[J]. IEEETrans on AES,1997,33(3),835-849.
[11] Christopher Hide, Terry Moore and Martin Smith. Adaptive Kalman Filtering forLow-cost INS/GPS [J]. Journal of Navigation.2003,156,143-152.
[12] De Koning W L. Optimal estimation of linear discrete-time systems with stochasticparameters [J]. Automatica,1984,20:113-115.
[13] Ding W, Wang J and Rizos C. Improving Adaptive Kalman Estimation in GPS/INSIntegration [J]. The Journal of Navigation,2007,60,517~529.
[14] Du S. Integration of Precise Point Positioning and Low Cost MEMS IMU [D]. MasterThesis, UCGE Report No.20319, Department of Geomatics Engineering, Universityof Calgary, Canada,2010.
[15] El-Sheimy, N. Inertial techniques and INS/DGPS integration [D]. PhD. Thesis, ENGO623Course Notes, Department of Geomatics Engineering, University of Calgary,Canada,2004.
[16] Eun-Hwan Shin. Accuracy Improvement of Low Cost INS/GPS for Land Applications
[D].Calgary,Alberta,Canada:The University of Calgary,2001.
[17] Fagin S L. Recursive linear regression theory, optimal filter theory and error analysisof optimal system [J]. IEEE Int. Convent,1964, Record,12:216-240.
[18] Friedland B. Treatment of bias in recursive filtering[J]. IEEE Trans. AC,1969,14(4):359-367.
[19] Gao, Y. and X. Shen. A New Method of Carrier Phase Based Precise Point Positioning[J]. Journal of the Institute of Navigation,2002, Vol.49(2):109-116.
[20] Gao, Y. and X. Shen. Improving Ambiguity Convergence in Carrier Phase-BasedPrecise Point Positioning [C]. Proceeding of ION GPS2001, Salt Lake City,US,2001.
[21] Gautier, J., B. Parkinson. Using the GPS/INS Generalized Evaluation Tool (GIGET)for the Comparison of Loosely Coupled, Tightly Coupled and Ultra-Tightly CoupledIntegrated Navigation Systems [J]. ION,2003,65-67.
[22] Godha S. Performance Evaluation of Low Cost MEMS-Based IMU Integrated WithGPS for Land Vehicle Navigation Application [D]. PhD Thesis, UCGE Report No.20239, Department of Geomatics Engineering, University of Calgary, Canada,2006.
[23] Han Songlai, Wang Jinling. Land Vehicle Navigation with the Integration of GPS andReduced INS: Performance Improvement with Velocity Aiding [J]. The Journal ofNavigation,2010,63:153-166.
[24] Hatch R．The synergism of GPS code and carrier measurements[C]. Proceedings ofthe3rd International Geodetic Symposium on Satellite Doppler Positioning.1982，2：1213-1231.
[25] Huang Dongliang, Henry Leung. EM-IMM Based Land-Vehicle Navigation withGPS/INS [C]. IEEE Intelligent Transportation Systems Conference,2004:624-629.
[26] Hwang P.Y.C., Mcgraw G. A., Bader J R. Enhanced differential GPS carrier smoothedcode processing using dual-frequency measurements [J]. Journal of the Institute ofNavigation,1999,46(2):127-137.
[27] Kleusberg, A. and P. J. G. Teunissen. GPS for Geodesy [Ed]. Berlin,Germany:Springer-Verlag,1996:407.
[28] Jazwinski A H. Stochastic Processes and Filtering Theory[C]. Mathematics in Scienceand Engineering. Academic Press,1970, New York.
[29] Koch K R and Yang Y. Robust Kalman filter for rank deficient observation model [J].Journal of Geodesy,1998,72(8):436-441.
[30] Koch KR. Parameter Estimation and Hypothesis Testing in Linear Models (SecondEdition), Springer,1999, Berlin.
[31] Kouba, J. and P. Heroux. Precise Point Positioning Using IGS Orbit and ClockProducts [J]. GPS Solutions,2001,5(2):12-28.
[32] Li X.R. Survey of Maneuvering Target Tracking Part V: Multiple-Model Methods [J].IEEE Trans on Aerospace and Electronic Systems.2005,41(4):1255-1321.
[33] Li X.R., Bar-Shalom Y. Performance Prediction of the IMM Algorithms [J]. IEEETrans.1993,29(3):755-770.
[34] Luo, D.D., Zhu, Y.M. Application of random parameter matrices Kalman filtering inuncertain observation and multi-model systems [C]. In Proceedings of theInternational Federation of the Automatic Control, Seoul, Korea,2008,7:6-11.
[35] Luo, Y.T., Zhu, Y.M., Luo, D.D. et al. Globally optimal multisensor distributedrandom parameter matrices Kalman filtering fusion with application[J]. Sensors2008,8(12):8086-8103.
[36] Mathur, N. G. Feasibility of Using a Low-Cost Inertial Measurement Unit withCentimeter Accuracy Differential Global Positioning System, PhD Thesis, OhioUniversity, USA, UMI No.9975068,1999.
[37] Mazor E, Averbuch A, Bar-Shalom Y, et al. Interacting Multiple Model Methods inTarget Tracking [J]. IEEE Transactions on Aerospace and Electronic Systems,1998,34(1):103-123.
[38] Moafipoor, S., Gejner-Brzezinska, D.A. and Toth, C.K. Tightly coupled GPS/INSintegration based on GPS carrier phase velocity update [J]. ION NTM2004, SanDiego, pp1094-1102.
[39] Mohamed A.H., Schwarz K.P. Adaptive Kalman Filtering for INS/GPS [J]. Journal ofGeodesy,1999,73(4):193-203.
[40] Nassar S. Improving the Inertial Navigation System (INS) Error Model for INS andINS/DGPS Applications [D]. PhD Thesis, UCGE Report No.20183, Department ofGeomatics Engineering, University of Calgary, Canada,2003.
[41] Numajima T., Kihara M., Kubo Y., Sugimoto S. and Seki T. INS/DGPS/VMSIntegration for In-Motion Alignment [J]. ION GPS2002,556-564.
[42] Park B., Kee C. Optimal Hatch filter with a flexible smoothing window width [J].Journal of the Institute Navigation,2008,61(3):435-454.
[43] Petovello M.G. Real-Time Integration of a Tactical-Grade IMU and GPS forHigh-Accuracy Positioning and Navigation [D]. Ph.D. Thesis, Department ofGeomatics Engineering, University of Calgary, Canada, UCGE Report No.20173,2003.
[44] Petovello, M.G., D. Sun, G. Lachapelle and M.E. Cannon. Performance Analysis of anUltra-Tightly Integrated GPS and Reduced IMU System [J]. ION GNSS2007,602-609.
[45] Rogers R.M. Applied Mathematics in Integrated Navigation Systems. AmericanInstitute of Aeronautics and Astronautics, Inc., Reston, VA, USA.
[46] Ryan S., Lachapelle G. and Cannon M. E.(1997), DGPS Kinematic Carrier PhaseSignal Simulation Analysis in the Velocity Domain. Proceedings of ION GPS97,Kansas City, Missouri, September16-19,1997.
[47] Sage A.P., Husa G.W. Adaptive Filtering with Unknown Prior Statistics [C]. JointAmerican Control Conference,1969:769-774.
[48] Salytcheva A.O. Medium Accuracy INS/GPS Integration in Various GPSEnvironments [D]. M.S. Thesis, Department of Geomatics Engineering, University ofCalgary, Canada, UCGE Report No.20200,2004.
[49] Schwarz, K. P. and M. Wei. Modeling INS/GPS for Attitude and Gravity Applications
[C]. Proceedings of the3thInternational Workshop of High Precision Navigation,Stuttgart, Germany, April3-6,1995.
[50] Sorenson H.W. and Sacks J.E. Recursive fading memory filtering [J]. Inform, SCI,1971,3,101-119.
[51] Sorenson H. W. Kalman filtering: Theory and application [M]. New York: IEEE Press,1985.
[52] Szarmes M, Ryan S and Lachapelle G.(1997), DGPS High Accuracy Aircraft VelocityDetermination Using Doppler Measurements. Proceedings of the InternationalSymposium on Kinematic Systems (KIS), Banff, AB, Canada, June3-6,1997
[53] Upadhyay T.N., Cotterill S., Deaton A.W.. Autonomous GPS/INS navigationexperiment for Space transfer vehicle [J] IEEE, Transactions on Aerospace andElectronic Systems,1993,29(3):772-785.
[54] Van Grass, F.&Soloviev, A. Precise velocity estimation using a stand-alone GPSreceiver [J]. Journal of the Institute of Navigation,2004,51:283-292.
[55] Wang Qianxin, Xu Tianhe. Combining GPS carrier phase and Doppler observationsfor precise velocity determination [J]. Science China,2011,54(6):1022-1028.
[56] Wei M., Schwarz K.P. A Strapdown Inertial Algorithm Using an Earth-Fixed CartesianFrame [J]. Journal of the Institute of Navigation.1990,37(2):153-167.
[57] Weidong Ding, Jinling Wang. Precise Velocity Estimation with Stand-Alone GPSReceiver [J]. The Journal of Navigation,2011,64(2):311-325.
[58] Wendel J, Meister O, Mo¨nikes R, Trommer GF (2006) Time-differenced carrier phasemeasurements for tightly coupled GPS/INS integration [J]. In: Proceedings of instituteof navigation (ION)/IEEE position, location, and navigation symposium (PLANS)2006, San Diego, pp54–60.
[59] X. Rong LI, Vesselin P. JILKOV. Survey of Maneuvering Target Tracking. Part V:Multiple-Model Methods[J]. IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1255-1321.
[60] Xu G., GPS Theory, Algorithms and Applications [M]. Berlin, Heidelberg: Springer,2007
[61] Yang Y, Gao W2005: Comparison of adaptive factors in Kalman filters on navigationresults, The Journal of Navigation,58,471-478.
[62] Yang Y, Gao W. A New Learning Statistic for Adaptive Filter Based on PredictedResiduals [J]. Progress in Natural Science,2006,16(8):833~837.
[63] Yang Y, Gao W. An Optimal Adaptive Kalman Filter [J]. Journal of Geodesy,2006,80:177~183.
[64] Yang Y, Gao W. Comparison of Two Fading Filters and Adaptively Robust Filter [J].Geo-Spatial Information Science,2007,10(3):200~203.
[65] Yang Yuanxi, Xu Tian-he and He Haibo. On Adaptively Kinematic Filtering[J],Selected Papers for English of Acta Geodetica et Cartographica Sinica,2001a,25-32.
[66] Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodeticpositioning, Journal of Geodesy,2001b,75(2/3):109-116.
[67] Yang Y, Song L and Xu T. Robust estimator for correlated observations based onbifactor equivalent weights,2002, Journal of Geodesy, Vol.76(6-7):353-358.
[68] Yang Y. Tightly Coupled MEMS INS/GPS Integration with INS Aided ReceiverTracking Loops [D]. PhD Thesis, UCGE Report No.20270, Department of GeomaticsEngineering, University of Calgary, Canada,2008.
[69] Yang Yuan-xi and Xu Tian-he. An Adaptive Kalman Filter Based on Sage WindowingWeights and Variance Components [J]. The Journal of Navigation,2003,56(2):231-240.
[70] Yang Yuanxi. Robust Estimation for Dependent Observation [J]. ManuscriptaGeodeatica,1994,19:10-17.
[71] Yoshimura T. and Sueda T. A technique for compenating the filter performance by afictitious noise [J], Trans. ASME,1978,100(2):154-156.
[72] Zhang H. Performance Comparison of Kinematic GPS Integrated with DifferentTactical Grade IMUs [D]. PhD Thesis, UCGE Report No.20237, Department ofGeomatics Engineering, University of Calgary, Canada,2006.
[73] Zhang Yufeng and Gao Yang. Integration of INS and un-differenced GPSmeasurements for precise position and attitude determination [J]. The Journal ofNavigation,2008,61,87-97.
[74] Zhang Yufeng and Gao Yang. Performance comparison between point and differentialGPS/INS Systems [C]. ION GNSS18thInternational technical meeting of the satellitedivision,13-16September2005, Long Beach, CA.2504-2509.
[75] Zhang Yufeng GaoYang. Design and analysis of a tightly coupled Kalman filter forpoint GPS/INS system: preliminary results [C]. Proceedings of2004InternationalSymposium on GPS/INS. Sydney. Australia. November6-8.2004.
[76] Zumbeger, J. F, M. B Heflin, D. C. Jefferson, et al．Precise point positioning forefficient and robust analysis of GPS data from large networks[J]．Journal ofGeophysical Research,1997,102:5005~5017．
[77]曹梦龙，崔平远.多模型高精度组合导航算法研究[J].系统工程与电子技术，2008，30（7）：1304-1307.
[78]柴艳菊，欧吉坤. Kalman滤波质量控制的一种改进算法[J].自然科学进展，2004，14（8）：904-909.
[79]柴艳菊.挖掘信息提高GPS/INS导航精度的理论与方法研究[D].武汉：中国科学院测量与地球物理研究所，2008.
[80]陈俊勇，党亚民.全球导航卫星系统的进展及建设CORS的思考[J].地理空间信息，2009，7（3）：1-3.
[81]陈俊勇.全球导航卫星系统进展及其对导航定位的改善[J].大地测量与地球动力学，2009，29（2）：1-3.
[82]陈勖，李尔园. GPS空间段的发展过程及其前景[J].全球定位系统，2011，1：58-61.
[83]程向红，郑梅.捷联惯导系统初始对准中Kalman参数优化方法[J].中国惯性技术学报.2006，14（4）：12-17.
[84]董绪荣，张守信，华仲春. GPS/INS组合导航定位及其应用[M].国防科技大学出版社,长沙,1998.
[85]范龙，翟国君，白鸽.基于抗差最小二乘估计的载体速度计算方法[J].测绘学报，2011，40（增刊）：95-99.
[86]房建成.最优估计理论与方法在组合导航中的应用研究[D]。博士论文，东南大学，1998.
[87]付梦印，邓志红，闫莉萍. Kalman滤波理论及其在导航系统中的应用（第二版）
[M].北京：科学出版社，2010.
[88]干国强，邱致和.导航与定位-现代战争的北斗星[M].国防工业出版社，北京，2000.
[89]高为广. GPS/INS自适应组合导航算法研究[D].郑州：解放军信息工程大学，2008.
[90]郭建锋，欧吉坤，袁运斌，王海涛.双频GPS数据的最优相位平滑伪距算法研究[J].自然科学进展，2008，18(2)：221~224.
[91]韩崇昭，朱洪艳，段站胜.多源信息融合[M].北京：清华大学出版社，2006.
[92]郝明.加速GPS精密单点定位收敛的方法研究[D].武汉：中国科学院测量与地球物理研究所，2007.
[93]何海波，杨元喜，孙中苗，马煦. GPS多普勒频移测量速度模型与误差分析[J].测绘学院学报.2003，20（2）：79-82.
[94]何海波，杨元喜，孙中苗.几种GPS测速方法的比较分析[J].测绘学报，2002，31（3）：217-221.
[95]何海波，郭海荣，李保利.广域差分参考站两种伪距平滑算法的再评估[J].测绘学院学报，2005，22(3)：157~159.
[96]何正斌，聂建亮，吴富梅.基于交互多模型的组合导航观测异常影响控制[J].大地测量与地球动力学，2011，31（3）：102-105.
[97]何正斌，吴富梅，聂建亮.先验协方差阵误差对动态Kalman滤波解的影响[J].武汉大学学报·信息科学版.2011,36(1):34-38.
[98]胡丛玮，刘大杰.基于方差分量估计原理的自适应卡尔曼滤波及其应用[J].测绘学院学报.2002，19（1）：15-18.
[99]胡国荣，欧吉坤.改进的高动态GPS定位自适应卡尔曼滤波方法[J].测绘学报，1999，28（4）：290-294.
[100]黄维彬.近代平差理论及其应用[M].解放军出版社，1990.
[101]贾彩娟，祝小平，周洲.交互多模型算法的无人机控制系统故障诊断[J].火力与指挥控制，2006，31（7）：8-10.
[102]孔金生，翟弦.车辆导航中的交互多模卡尔曼滤波跟踪方法[J].计算机工程与应用,2009,45(14):198-200.
[103]梁彦，谭伟，潘泉等.两级交互多模型算法[J].自动化学报，2001，27（5）：651-656.
[104]林瑜滢，阮仁桂，黄健，刘勇.动态精密单点定位传统模型与UofC模型的比较[J].测绘科学技术学报，2010，27（1）：31-34.
[105]刘基余. GPS卫星导航定位原理与方法[M].北京：科学出版社，2003.
[106]刘基余. GPS信号的新近发展及其应用思考[J].遥测遥控，2011，32（6）：7-13.
[107]罗丹丹，朱允民.随机系数矩阵卡尔曼滤波[J].四川大学学报(自然科学版)，2008，45（6）：1309-1312.
[108]马谦伟，杨艳霞.基于状态噪声协方差矩阵自适应的一种卡尔曼滤波方法[J].中国雷达.2008，第3期：53-56.
[109]马昕，于海田，袁信.组合导航系统故障检测问题研究[J].东南大学学报，1999，29（3）：78-82.
[110]聂建亮、吴富梅、何正斌、张双成.利用交互多模型的动态精密单点定位故障诊断算法.武汉大学学报·信息科学版.2011,36(6):644-647.
[111]欧吉坤，柴艳菊，袁运斌.自适应选权滤波[M].大地测量与地球动力学进展，武汉：湖北科学技术出版社，2004，816-823.
[112]潘寒尽，邱学军. GPS发展现状及其军事应用[J].导航天地应用服务，2011，2：64-66.
[113]庞晨鹏，刘藻珍.基于自适应航迹融合算法的GPS/INS紧组合导航系统研究[J].系统仿真学报，2008，20（19）：5136-5140.
[114]彭冬亮，文成林，薛安克.多传感器多源信息融合理论及应用[M].北京：科学出版社，2010.
[115]秦永元.惯性导航[M].北京：科学出版社，2006.
[116]尚捷. MIMU及其与GPS组合系统设计与实验研究[D].北京：清华大学，2005.
[117]孙红星.差分GPS/INS组合定位定姿及其在MMS中的应用[D].武汉：武汉大学，2004.
[118]唐浩. GPS现代化技术发展综述[C].第七届中国通信学会学术年会论文集，南宁，2010：182-188.
[119]唐卫明，刘智敏. GPS载波相位平滑伪距精度分析与应用探讨[J].测绘信息与工程，2005，30（3）：37-39.
[120]陶本藻.测量数据处理的统计理论和方法[M].北京：测绘出版社，2007.
[121]陶本藻.卡尔曼滤波模型误差的识别[J].地壳形变与地震.1999，19（4）：15-20.
[122]涂锐. GPS单频精密单点定位与区域电离层模型研究[D].西安：长安大学，2011.
[123]万德钧，房建成，王庆.惯性导航初始对准[M].南京：东南大学出版社，1998.
[124]王海涛，欧吉坤，郭建锋. GPS相位平滑伪距严密定权以及在卫星编队飞行相对定位中的应用[J].宇航学报，2007，28(2)：282~286.
[125]王惠南. GPS导航原理与应用[M].北京：科学出版社，2003.
[126]王杰华.国外卫星导航定位系统最新进展及发展趋势[J].2008.
[127]魏子卿，葛茂荣.GPS相对定位的数学模型[M].北京:测绘出版社，1998.
[128]吴富梅，秦显平，唐颖哲.低成本车载GPS/INS组合导航速度更新算法[J].测绘科学技术学报,2010,27(4):243-246.
[129]吴富梅，唐颖哲.基于载波相位平滑伪距技术的GPS/INS组合导航[J].大地测量与地球动力学，2010，30（1）：130-135.
[130]吴富梅，肖云.利用伪距差分法进行GPS测速[J].武汉大学学报·信息科学版，2010，35（9）：1034-1038.
[131]吴富梅，杨元喜，崔先强.利用部分状态不符值构造的自适应因子在GPS/INS紧组合导航中的应用[J].武汉大学学报·信息科学版.2010，35（2）：156-159.
[132]吴富梅. GNSS/INS组合导航误差补偿与自适应滤波理论的拓展[D].郑州：解放军信息工程大学，2010.
[133]吴江飞，黄珹. GPS精密单点定位模型及其应用分析[J].大地测量与地球动力学，2008，28（1）：96-100.
[134]夏启军，孙优贤，周春晖。渐消卡尔曼滤波器的最佳自适应算法及其应用[J]。自动化学报，1990，16(3)：210-216。
[135]肖乾.多模型估计理论[J].舰船科学技术，2005，27（2）：63-67.
[136]肖云，夏哲仁.利用相位率和多普勒确定载体速度的比较[J].武汉大学学报·信息科学版，2003，28（5）：581-584.
[137]徐景硕，周胜明，蒋华君.惯性导航系统的发展及其关键技术综述[J].科技信息，2009，35：865-866.
[138]徐天河，杨元喜.改进的Sage自适应滤波方法[J].测绘科学.2000，25（3）：22-24.
[139]徐田来，崔平远，崔祜涛.组合导航自适应交互多模型算法研究[J].系统工程与电子技术，2008，30（11）；2070-2074.
[140]许国昌，李强，刘广军等. GPS理论、算法与应用（第二版）[M].北京：清华大学出版社，2011.
[141]杨旭东，何平，胡恒章.离散卡尔曼滤波器滤波精度与噪声统计模型准确度的关系[J].电机与控制学报.1999，3（2）：69-72.
[142]杨元喜,何海波,徐天河.论动态自适应滤波[J].测绘学报，2001,30（4）：293~298.
[143]杨元喜，徐天河.基于移动开窗法协方差估计和方差分量估计的自适应滤波[J].武汉大学学报·信息科学版.2003，28（6）：714-718.
[144]杨元喜，高为广。基于方差分量估计的自适应融合导航[J]。测绘学报，2004a，33(1)：22-26.
[145]杨元喜，高为广。基于多传感器观测信息抗差估计的自适应融合导航[J]。武大学报信息科学版，2004b，29(10)：885-888。
[146]杨元喜、高为广.两种渐消滤波与自适应抗差滤波的综合比较分析[J].武大学报.信息科学版，2006,31(11):980~982，1026.
[147]杨元喜.动态Kalman滤波模型误差的影响[J].测绘科学.2006，31（1）：17-18.
[148]杨元喜.动态定位自适应滤波解的性质[J].测绘学报.2003，32（3）：189-192.
[149]杨元喜.动态系统的抗差Kalman滤波[J].解放军测绘学院学报.1997，14（2）：79-84.
[150]杨元喜.抗差估计理论及其应用[M].北京：八一出版社，1993.
[151]杨元喜.自适应动态导航定位[M].北京：测绘出版社，2006.
[152]叶世榕. GPS非差相位精密单点定位理论与实现[D].武汉：武汉大学，2002.
[153]袁俊.美军GPS系统及其技术发展[J].航空科学技术，2007，（3）10-13.
[154]张勤，李家权. GPS测量原理及应用[M].北京：科学出版社，2005.
[155]张双成，杨元喜，张勤.一种基于抗差自校正Kalman滤波的GPS导航算法[J].武汉大学学报·信息科学版.2005，30（10）：881-884.
[156]张炎华，王立瑞，战兴群，翟传润.惯性导航技术的新进展及发展趋势[J].中国造船，2008，49增刊（183）：134-144.
[157]赵玉霞.捷联惯导系统仿真算法的研究及其实现[D].大连：大连理工大学，2005.
[158]周江文，黄幼才，杨元喜，欧吉坤。抗差最小二乘法[M]。武汉：华中理工大学出版社，1997.
[159]周徐昌，沈建森.惯性导航技术的发展及其应用[J].自动测量与控制，2006，25（9）：55-59.
[160]周泽波，沈云中，李博峰.基于相位平滑伪距与多普勒数据的GPS动态定位[J].大地测量与地球动力学，2008，28（3）：59-63.
[2] Alexander S.T. Fast adaptive filters: a geometrical approach[C]. IEEE ASSP Mag.,1986,18-28.
[3] Antonio Angrisano. GNSS/INS Integration Methods [D]. PhD. Thesis, Department ofGeomatics Engineering, University of Calgary, Canada,2010.
[4] Ben K. H. Soon, Steve Scheding, Hyung-Kuen Lee, An approach to aid INS usingtime-differenced GPS carrier phase (TDCP) measurements [J]. GPS Solution,2008,12:261-271.
[5] Bisnath, S. B. and R. B. Langley. Precise Orbit Determination of Low Earth Orbiterswith GPS Point Positioning [C]. ION National Technical Meeting, The Institute ofNavigation. Long Beach,California,2001:725-733.
[6] Bisnath, S.B. and R.B. Langley. A New Approach to an Old Problem: Carrier PhaseCycle Slips [J]. GPS World.2001, Vol.12(5):46-51.
[7] Blom H A P, Bar-Shalom Y. The interacting multiple model algorithm for systemswith Markovian switching coefficients [J]. IEEE Transactions on Automatic Control,1988,33(8):780-783.
[8] Bock H. Efficient Methods for Determining Precise Orbits of Low Earth OrbitersUsing the Global Positioning System [D]. PhD. Thesis. Astronomical InstituteUniversity of Berne, Switzerland,2003.
[9] Brenner, M. Integrated GPS/Inertial Fault Detection Availability [C]. In Proceedingsof ION GPS, September, Palm Spring CA, pp.1949-1958, U.S. Institute of Navigation,Fairfax VA,1995.
[10] Carvalho H., Moral P. D.. Optimal nonlinear filtering in GPS/INS integration[J]. IEEETrans on AES,1997,33(3),835-849.
[11] Christopher Hide, Terry Moore and Martin Smith. Adaptive Kalman Filtering forLow-cost INS/GPS [J]. Journal of Navigation.2003,156,143-152.
[12] De Koning W L. Optimal estimation of linear discrete-time systems with stochasticparameters [J]. Automatica,1984,20:113-115.
[13] Ding W, Wang J and Rizos C. Improving Adaptive Kalman Estimation in GPS/INSIntegration [J]. The Journal of Navigation,2007,60,517~529.
[14] Du S. Integration of Precise Point Positioning and Low Cost MEMS IMU [D]. MasterThesis, UCGE Report No.20319, Department of Geomatics Engineering, Universityof Calgary, Canada,2010.
[15] El-Sheimy, N. Inertial techniques and INS/DGPS integration [D]. PhD. Thesis, ENGO623Course Notes, Department of Geomatics Engineering, University of Calgary,Canada,2004.
[16] Eun-Hwan Shin. Accuracy Improvement of Low Cost INS/GPS for Land Applications
[D].Calgary,Alberta,Canada:The University of Calgary,2001.
[17] Fagin S L. Recursive linear regression theory, optimal filter theory and error analysisof optimal system [J]. IEEE Int. Convent,1964, Record,12:216-240.
[18] Friedland B. Treatment of bias in recursive filtering[J]. IEEE Trans. AC,1969,14(4):359-367.
[19] Gao, Y. and X. Shen. A New Method of Carrier Phase Based Precise Point Positioning[J]. Journal of the Institute of Navigation,2002, Vol.49(2):109-116.
[20] Gao, Y. and X. Shen. Improving Ambiguity Convergence in Carrier Phase-BasedPrecise Point Positioning [C]. Proceeding of ION GPS2001, Salt Lake City,US,2001.
[21] Gautier, J., B. Parkinson. Using the GPS/INS Generalized Evaluation Tool (GIGET)for the Comparison of Loosely Coupled, Tightly Coupled and Ultra-Tightly CoupledIntegrated Navigation Systems [J]. ION,2003,65-67.
[22] Godha S. Performance Evaluation of Low Cost MEMS-Based IMU Integrated WithGPS for Land Vehicle Navigation Application [D]. PhD Thesis, UCGE Report No.20239, Department of Geomatics Engineering, University of Calgary, Canada,2006.
[23] Han Songlai, Wang Jinling. Land Vehicle Navigation with the Integration of GPS andReduced INS: Performance Improvement with Velocity Aiding [J]. The Journal ofNavigation,2010,63:153-166.
[24] Hatch R．The synergism of GPS code and carrier measurements[C]. Proceedings ofthe3rd International Geodetic Symposium on Satellite Doppler Positioning.1982，2：1213-1231.
[25] Huang Dongliang, Henry Leung. EM-IMM Based Land-Vehicle Navigation withGPS/INS [C]. IEEE Intelligent Transportation Systems Conference,2004:624-629.
[26] Hwang P.Y.C., Mcgraw G. A., Bader J R. Enhanced differential GPS carrier smoothedcode processing using dual-frequency measurements [J]. Journal of the Institute ofNavigation,1999,46(2):127-137.
[27] Kleusberg, A. and P. J. G. Teunissen. GPS for Geodesy [Ed]. Berlin,Germany:Springer-Verlag,1996:407.
[28] Jazwinski A H. Stochastic Processes and Filtering Theory[C]. Mathematics in Scienceand Engineering. Academic Press,1970, New York.
[29] Koch K R and Yang Y. Robust Kalman filter for rank deficient observation model [J].Journal of Geodesy,1998,72(8):436-441.
[30] Koch KR. Parameter Estimation and Hypothesis Testing in Linear Models (SecondEdition), Springer,1999, Berlin.
[31] Kouba, J. and P. Heroux. Precise Point Positioning Using IGS Orbit and ClockProducts [J]. GPS Solutions,2001,5(2):12-28.
[32] Li X.R. Survey of Maneuvering Target Tracking Part V: Multiple-Model Methods [J].IEEE Trans on Aerospace and Electronic Systems.2005,41(4):1255-1321.
[33] Li X.R., Bar-Shalom Y. Performance Prediction of the IMM Algorithms [J]. IEEETrans.1993,29(3):755-770.
[34] Luo, D.D., Zhu, Y.M. Application of random parameter matrices Kalman filtering inuncertain observation and multi-model systems [C]. In Proceedings of theInternational Federation of the Automatic Control, Seoul, Korea,2008,7:6-11.
[35] Luo, Y.T., Zhu, Y.M., Luo, D.D. et al. Globally optimal multisensor distributedrandom parameter matrices Kalman filtering fusion with application[J]. Sensors2008,8(12):8086-8103.
[36] Mathur, N. G. Feasibility of Using a Low-Cost Inertial Measurement Unit withCentimeter Accuracy Differential Global Positioning System, PhD Thesis, OhioUniversity, USA, UMI No.9975068,1999.
[37] Mazor E, Averbuch A, Bar-Shalom Y, et al. Interacting Multiple Model Methods inTarget Tracking [J]. IEEE Transactions on Aerospace and Electronic Systems,1998,34(1):103-123.
[38] Moafipoor, S., Gejner-Brzezinska, D.A. and Toth, C.K. Tightly coupled GPS/INSintegration based on GPS carrier phase velocity update [J]. ION NTM2004, SanDiego, pp1094-1102.
[39] Mohamed A.H., Schwarz K.P. Adaptive Kalman Filtering for INS/GPS [J]. Journal ofGeodesy,1999,73(4):193-203.
[40] Nassar S. Improving the Inertial Navigation System (INS) Error Model for INS andINS/DGPS Applications [D]. PhD Thesis, UCGE Report No.20183, Department ofGeomatics Engineering, University of Calgary, Canada,2003.
[41] Numajima T., Kihara M., Kubo Y., Sugimoto S. and Seki T. INS/DGPS/VMSIntegration for In-Motion Alignment [J]. ION GPS2002,556-564.
[42] Park B., Kee C. Optimal Hatch filter with a flexible smoothing window width [J].Journal of the Institute Navigation,2008,61(3):435-454.
[43] Petovello M.G. Real-Time Integration of a Tactical-Grade IMU and GPS forHigh-Accuracy Positioning and Navigation [D]. Ph.D. Thesis, Department ofGeomatics Engineering, University of Calgary, Canada, UCGE Report No.20173,2003.
[44] Petovello, M.G., D. Sun, G. Lachapelle and M.E. Cannon. Performance Analysis of anUltra-Tightly Integrated GPS and Reduced IMU System [J]. ION GNSS2007,602-609.
[45] Rogers R.M. Applied Mathematics in Integrated Navigation Systems. AmericanInstitute of Aeronautics and Astronautics, Inc., Reston, VA, USA.
[46] Ryan S., Lachapelle G. and Cannon M. E.(1997), DGPS Kinematic Carrier PhaseSignal Simulation Analysis in the Velocity Domain. Proceedings of ION GPS97,Kansas City, Missouri, September16-19,1997.
[47] Sage A.P., Husa G.W. Adaptive Filtering with Unknown Prior Statistics [C]. JointAmerican Control Conference,1969:769-774.
[48] Salytcheva A.O. Medium Accuracy INS/GPS Integration in Various GPSEnvironments [D]. M.S. Thesis, Department of Geomatics Engineering, University ofCalgary, Canada, UCGE Report No.20200,2004.
[49] Schwarz, K. P. and M. Wei. Modeling INS/GPS for Attitude and Gravity Applications
[C]. Proceedings of the3thInternational Workshop of High Precision Navigation,Stuttgart, Germany, April3-6,1995.
[50] Sorenson H.W. and Sacks J.E. Recursive fading memory filtering [J]. Inform, SCI,1971,3,101-119.
[51] Sorenson H. W. Kalman filtering: Theory and application [M]. New York: IEEE Press,1985.
[52] Szarmes M, Ryan S and Lachapelle G.(1997), DGPS High Accuracy Aircraft VelocityDetermination Using Doppler Measurements. Proceedings of the InternationalSymposium on Kinematic Systems (KIS), Banff, AB, Canada, June3-6,1997
[53] Upadhyay T.N., Cotterill S., Deaton A.W.. Autonomous GPS/INS navigationexperiment for Space transfer vehicle [J] IEEE, Transactions on Aerospace andElectronic Systems,1993,29(3):772-785.
[54] Van Grass, F.&Soloviev, A. Precise velocity estimation using a stand-alone GPSreceiver [J]. Journal of the Institute of Navigation,2004,51:283-292.
[55] Wang Qianxin, Xu Tianhe. Combining GPS carrier phase and Doppler observationsfor precise velocity determination [J]. Science China,2011,54(6):1022-1028.
[56] Wei M., Schwarz K.P. A Strapdown Inertial Algorithm Using an Earth-Fixed CartesianFrame [J]. Journal of the Institute of Navigation.1990,37(2):153-167.
[57] Weidong Ding, Jinling Wang. Precise Velocity Estimation with Stand-Alone GPSReceiver [J]. The Journal of Navigation,2011,64(2):311-325.
[58] Wendel J, Meister O, Mo¨nikes R, Trommer GF (2006) Time-differenced carrier phasemeasurements for tightly coupled GPS/INS integration [J]. In: Proceedings of instituteof navigation (ION)/IEEE position, location, and navigation symposium (PLANS)2006, San Diego, pp54–60.
[59] X. Rong LI, Vesselin P. JILKOV. Survey of Maneuvering Target Tracking. Part V:Multiple-Model Methods[J]. IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1255-1321.
[60] Xu G., GPS Theory, Algorithms and Applications [M]. Berlin, Heidelberg: Springer,2007
[61] Yang Y, Gao W2005: Comparison of adaptive factors in Kalman filters on navigationresults, The Journal of Navigation,58,471-478.
[62] Yang Y, Gao W. A New Learning Statistic for Adaptive Filter Based on PredictedResiduals [J]. Progress in Natural Science,2006,16(8):833~837.
[63] Yang Y, Gao W. An Optimal Adaptive Kalman Filter [J]. Journal of Geodesy,2006,80:177~183.
[64] Yang Y, Gao W. Comparison of Two Fading Filters and Adaptively Robust Filter [J].Geo-Spatial Information Science,2007,10(3):200~203.
[65] Yang Yuanxi, Xu Tian-he and He Haibo. On Adaptively Kinematic Filtering[J],Selected Papers for English of Acta Geodetica et Cartographica Sinica,2001a,25-32.
[66] Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodeticpositioning, Journal of Geodesy,2001b,75(2/3):109-116.
[67] Yang Y, Song L and Xu T. Robust estimator for correlated observations based onbifactor equivalent weights,2002, Journal of Geodesy, Vol.76(6-7):353-358.
[68] Yang Y. Tightly Coupled MEMS INS/GPS Integration with INS Aided ReceiverTracking Loops [D]. PhD Thesis, UCGE Report No.20270, Department of GeomaticsEngineering, University of Calgary, Canada,2008.
[69] Yang Yuan-xi and Xu Tian-he. An Adaptive Kalman Filter Based on Sage WindowingWeights and Variance Components [J]. The Journal of Navigation,2003,56(2):231-240.
[70] Yang Yuanxi. Robust Estimation for Dependent Observation [J]. ManuscriptaGeodeatica,1994,19:10-17.
[71] Yoshimura T. and Sueda T. A technique for compenating the filter performance by afictitious noise [J], Trans. ASME,1978,100(2):154-156.
[72] Zhang H. Performance Comparison of Kinematic GPS Integrated with DifferentTactical Grade IMUs [D]. PhD Thesis, UCGE Report No.20237, Department ofGeomatics Engineering, University of Calgary, Canada,2006.
[73] Zhang Yufeng and Gao Yang. Integration of INS and un-differenced GPSmeasurements for precise position and attitude determination [J]. The Journal ofNavigation,2008,61,87-97.
[74] Zhang Yufeng and Gao Yang. Performance comparison between point and differentialGPS/INS Systems [C]. ION GNSS18thInternational technical meeting of the satellitedivision,13-16September2005, Long Beach, CA.2504-2509.
[75] Zhang Yufeng GaoYang. Design and analysis of a tightly coupled Kalman filter forpoint GPS/INS system: preliminary results [C]. Proceedings of2004InternationalSymposium on GPS/INS. Sydney. Australia. November6-8.2004.
[76] Zumbeger, J. F, M. B Heflin, D. C. Jefferson, et al．Precise point positioning forefficient and robust analysis of GPS data from large networks[J]．Journal ofGeophysical Research,1997,102:5005~5017．
[77]曹梦龙，崔平远.多模型高精度组合导航算法研究[J].系统工程与电子技术，2008，30（7）：1304-1307.
[78]柴艳菊，欧吉坤. Kalman滤波质量控制的一种改进算法[J].自然科学进展，2004，14（8）：904-909.
[79]柴艳菊.挖掘信息提高GPS/INS导航精度的理论与方法研究[D].武汉：中国科学院测量与地球物理研究所，2008.
[80]陈俊勇，党亚民.全球导航卫星系统的进展及建设CORS的思考[J].地理空间信息，2009，7（3）：1-3.
[81]陈俊勇.全球导航卫星系统进展及其对导航定位的改善[J].大地测量与地球动力学，2009，29（2）：1-3.
[82]陈勖，李尔园. GPS空间段的发展过程及其前景[J].全球定位系统，2011，1：58-61.
[83]程向红，郑梅.捷联惯导系统初始对准中Kalman参数优化方法[J].中国惯性技术学报.2006，14（4）：12-17.
[84]董绪荣，张守信，华仲春. GPS/INS组合导航定位及其应用[M].国防科技大学出版社,长沙,1998.
[85]范龙，翟国君，白鸽.基于抗差最小二乘估计的载体速度计算方法[J].测绘学报，2011，40（增刊）：95-99.
[86]房建成.最优估计理论与方法在组合导航中的应用研究[D]。博士论文，东南大学，1998.
[87]付梦印，邓志红，闫莉萍. Kalman滤波理论及其在导航系统中的应用（第二版）
[M].北京：科学出版社，2010.
[88]干国强，邱致和.导航与定位-现代战争的北斗星[M].国防工业出版社，北京，2000.
[89]高为广. GPS/INS自适应组合导航算法研究[D].郑州：解放军信息工程大学，2008.
[90]郭建锋，欧吉坤，袁运斌，王海涛.双频GPS数据的最优相位平滑伪距算法研究[J].自然科学进展，2008，18(2)：221~224.
[91]韩崇昭，朱洪艳，段站胜.多源信息融合[M].北京：清华大学出版社，2006.
[92]郝明.加速GPS精密单点定位收敛的方法研究[D].武汉：中国科学院测量与地球物理研究所，2007.
[93]何海波，杨元喜，孙中苗，马煦. GPS多普勒频移测量速度模型与误差分析[J].测绘学院学报.2003，20（2）：79-82.
[94]何海波，杨元喜，孙中苗.几种GPS测速方法的比较分析[J].测绘学报，2002，31（3）：217-221.
[95]何海波，郭海荣，李保利.广域差分参考站两种伪距平滑算法的再评估[J].测绘学院学报，2005，22(3)：157~159.
[96]何正斌，聂建亮，吴富梅.基于交互多模型的组合导航观测异常影响控制[J].大地测量与地球动力学，2011，31（3）：102-105.
[97]何正斌，吴富梅，聂建亮.先验协方差阵误差对动态Kalman滤波解的影响[J].武汉大学学报·信息科学版.2011,36(1):34-38.
[98]胡丛玮，刘大杰.基于方差分量估计原理的自适应卡尔曼滤波及其应用[J].测绘学院学报.2002，19（1）：15-18.
[99]胡国荣，欧吉坤.改进的高动态GPS定位自适应卡尔曼滤波方法[J].测绘学报，1999，28（4）：290-294.
[100]黄维彬.近代平差理论及其应用[M].解放军出版社，1990.
[101]贾彩娟，祝小平，周洲.交互多模型算法的无人机控制系统故障诊断[J].火力与指挥控制，2006，31（7）：8-10.
[102]孔金生，翟弦.车辆导航中的交互多模卡尔曼滤波跟踪方法[J].计算机工程与应用,2009,45(14):198-200.
[103]梁彦，谭伟，潘泉等.两级交互多模型算法[J].自动化学报，2001，27（5）：651-656.
[104]林瑜滢，阮仁桂，黄健，刘勇.动态精密单点定位传统模型与UofC模型的比较[J].测绘科学技术学报，2010，27（1）：31-34.
[105]刘基余. GPS卫星导航定位原理与方法[M].北京：科学出版社，2003.
[106]刘基余. GPS信号的新近发展及其应用思考[J].遥测遥控，2011，32（6）：7-13.
[107]罗丹丹，朱允民.随机系数矩阵卡尔曼滤波[J].四川大学学报(自然科学版)，2008，45（6）：1309-1312.
[108]马谦伟，杨艳霞.基于状态噪声协方差矩阵自适应的一种卡尔曼滤波方法[J].中国雷达.2008，第3期：53-56.
[109]马昕，于海田，袁信.组合导航系统故障检测问题研究[J].东南大学学报，1999，29（3）：78-82.
[110]聂建亮、吴富梅、何正斌、张双成.利用交互多模型的动态精密单点定位故障诊断算法.武汉大学学报·信息科学版.2011,36(6):644-647.
[111]欧吉坤，柴艳菊，袁运斌.自适应选权滤波[M].大地测量与地球动力学进展，武汉：湖北科学技术出版社，2004，816-823.
[112]潘寒尽，邱学军. GPS发展现状及其军事应用[J].导航天地应用服务，2011，2：64-66.
[113]庞晨鹏，刘藻珍.基于自适应航迹融合算法的GPS/INS紧组合导航系统研究[J].系统仿真学报，2008，20（19）：5136-5140.
[114]彭冬亮，文成林，薛安克.多传感器多源信息融合理论及应用[M].北京：科学出版社，2010.
[115]秦永元.惯性导航[M].北京：科学出版社，2006.
[116]尚捷. MIMU及其与GPS组合系统设计与实验研究[D].北京：清华大学，2005.
[117]孙红星.差分GPS/INS组合定位定姿及其在MMS中的应用[D].武汉：武汉大学，2004.
[118]唐浩. GPS现代化技术发展综述[C].第七届中国通信学会学术年会论文集，南宁，2010：182-188.
[119]唐卫明，刘智敏. GPS载波相位平滑伪距精度分析与应用探讨[J].测绘信息与工程，2005，30（3）：37-39.
[120]陶本藻.测量数据处理的统计理论和方法[M].北京：测绘出版社，2007.
[121]陶本藻.卡尔曼滤波模型误差的识别[J].地壳形变与地震.1999，19（4）：15-20.
[122]涂锐. GPS单频精密单点定位与区域电离层模型研究[D].西安：长安大学，2011.
[123]万德钧，房建成，王庆.惯性导航初始对准[M].南京：东南大学出版社，1998.
[124]王海涛，欧吉坤，郭建锋. GPS相位平滑伪距严密定权以及在卫星编队飞行相对定位中的应用[J].宇航学报，2007，28(2)：282~286.
[125]王惠南. GPS导航原理与应用[M].北京：科学出版社，2003.
[126]王杰华.国外卫星导航定位系统最新进展及发展趋势[J].2008.
[127]魏子卿，葛茂荣.GPS相对定位的数学模型[M].北京:测绘出版社，1998.
[128]吴富梅，秦显平，唐颖哲.低成本车载GPS/INS组合导航速度更新算法[J].测绘科学技术学报,2010,27(4):243-246.
[129]吴富梅，唐颖哲.基于载波相位平滑伪距技术的GPS/INS组合导航[J].大地测量与地球动力学，2010，30（1）：130-135.
[130]吴富梅，肖云.利用伪距差分法进行GPS测速[J].武汉大学学报·信息科学版，2010，35（9）：1034-1038.
[131]吴富梅，杨元喜，崔先强.利用部分状态不符值构造的自适应因子在GPS/INS紧组合导航中的应用[J].武汉大学学报·信息科学版.2010，35（2）：156-159.
[132]吴富梅. GNSS/INS组合导航误差补偿与自适应滤波理论的拓展[D].郑州：解放军信息工程大学，2010.
[133]吴江飞，黄珹. GPS精密单点定位模型及其应用分析[J].大地测量与地球动力学，2008，28（1）：96-100.
[134]夏启军，孙优贤，周春晖。渐消卡尔曼滤波器的最佳自适应算法及其应用[J]。自动化学报，1990，16(3)：210-216。
[135]肖乾.多模型估计理论[J].舰船科学技术，2005，27（2）：63-67.
[136]肖云，夏哲仁.利用相位率和多普勒确定载体速度的比较[J].武汉大学学报·信息科学版，2003，28（5）：581-584.
[137]徐景硕，周胜明，蒋华君.惯性导航系统的发展及其关键技术综述[J].科技信息，2009，35：865-866.
[138]徐天河，杨元喜.改进的Sage自适应滤波方法[J].测绘科学.2000，25（3）：22-24.
[139]徐田来，崔平远，崔祜涛.组合导航自适应交互多模型算法研究[J].系统工程与电子技术，2008，30（11）；2070-2074.
[140]许国昌，李强，刘广军等. GPS理论、算法与应用（第二版）[M].北京：清华大学出版社，2011.
[141]杨旭东，何平，胡恒章.离散卡尔曼滤波器滤波精度与噪声统计模型准确度的关系[J].电机与控制学报.1999，3（2）：69-72.
[142]杨元喜,何海波,徐天河.论动态自适应滤波[J].测绘学报，2001,30（4）：293~298.
[143]杨元喜，徐天河.基于移动开窗法协方差估计和方差分量估计的自适应滤波[J].武汉大学学报·信息科学版.2003，28（6）：714-718.
[144]杨元喜，高为广。基于方差分量估计的自适应融合导航[J]。测绘学报，2004a，33(1)：22-26.
[145]杨元喜，高为广。基于多传感器观测信息抗差估计的自适应融合导航[J]。武大学报信息科学版，2004b，29(10)：885-888。
[146]杨元喜、高为广.两种渐消滤波与自适应抗差滤波的综合比较分析[J].武大学报.信息科学版，2006,31(11):980~982，1026.
[147]杨元喜.动态Kalman滤波模型误差的影响[J].测绘科学.2006，31（1）：17-18.
[148]杨元喜.动态定位自适应滤波解的性质[J].测绘学报.2003，32（3）：189-192.
[149]杨元喜.动态系统的抗差Kalman滤波[J].解放军测绘学院学报.1997，14（2）：79-84.
[150]杨元喜.抗差估计理论及其应用[M].北京：八一出版社，1993.
[151]杨元喜.自适应动态导航定位[M].北京：测绘出版社，2006.
[152]叶世榕. GPS非差相位精密单点定位理论与实现[D].武汉：武汉大学，2002.
[153]袁俊.美军GPS系统及其技术发展[J].航空科学技术，2007，（3）10-13.
[154]张勤，李家权. GPS测量原理及应用[M].北京：科学出版社，2005.
[155]张双成，杨元喜，张勤.一种基于抗差自校正Kalman滤波的GPS导航算法[J].武汉大学学报·信息科学版.2005，30（10）：881-884.
[156]张炎华，王立瑞，战兴群，翟传润.惯性导航技术的新进展及发展趋势[J].中国造船，2008，49增刊（183）：134-144.
[157]赵玉霞.捷联惯导系统仿真算法的研究及其实现[D].大连：大连理工大学，2005.
[158]周江文，黄幼才，杨元喜，欧吉坤。抗差最小二乘法[M]。武汉：华中理工大学出版社，1997.
[159]周徐昌，沈建森.惯性导航技术的发展及其应用[J].自动测量与控制，2006，25（9）：55-59.
[160]周泽波，沈云中，李博峰.基于相位平滑伪距与多普勒数据的GPS动态定位[J].大地测量与地球动力学，2008，28（3）：59-63.