gyroscopyГироскопия и навигацияGiroskopiya i Navigatsiya0869-70352075-0927AO «Концерн «ЦНИИ «Электроприбор»10.17285/0869-7035.2015.23.1.003-017gyroscopy-385Research ArticleСтатьиСильносвязанное комплексирование приращений фазовых GPS-измерений и данных бюджетного инерциального МЭМС-блокаЧжаоИ.

Чжао Инвэй

БеккерМ.

Беккер Матиас

БеккерД.ЛяйненС.

Ляйнен Стефан

Технический университет Дармштадт, факультет физической и спутниковой геодезии Института геодезииGermany201518122025231317Copyright © Чжао И., Беккер М., Беккер Д., Ляйнен С., 20252025Чжао И., Беккер М., Беккер Д., Ляйнен С.Чжао И., Беккер М., Беккер Д., Ляйнен С.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.gyroscopy.ru/jour/article/view/385

Рассматривается сильносвязанная инерциально-спутниковая система, в которой помимо данных инерциального модуля в обработке участвуют временные приращения фазовых GPS-измерений в обычном (недифференциальном) режиме. Предлагается модифицированный метод комплексирования инерциальных и спутниковых данных, в котором при формировании матрицы наблюдения учитывается изменчивость матрицы динамики ошибок ИНС. В алгоритме комплексирования используется кубатурный фильтр Калмана (КФК), позволяющий учесть нелинейный характер уравнения, описывающего погрешности ИНС на этапе выставки. Приводятся результаты автомобильных испытаний. Сравниваются результаты, полученные тремя фильтрами: обобщенным ФК, модифицированным (в части вычисления матрицы наблюдения) обобщенным ФК, модифицированным КФК. Установлено преимущество последнего фильтра.

 

To avoid the difficulties in fixing the carrier phase ambiguities, the time difference carrier phase approach is applied to a GPS/IMU tightly-coupled navigation system to eliminate the ambiguity between two successive GPS epochs, which can provide high velocity estimation accuracy. The carrier phases are carefully corrected before use. A modified method is proposed by using the system matrix in each time up-date to calculate the integration of the velocity errors in the measurement update equation. A Cubature Kalman Filter (CKF) is applied to the integrated navigation system to improve the attitude estimation accuracy. The navigation result and comparison show the accuracy improvement after applying the carrier phase corrections, modified measurement update method and the CKF.

Приращения фазы несущейинерциальный измерительный модульсильносвязанное комплексированиекубатурный фильтр Калмана.Time difference carrier phaseIMUCubature Kalman FilterMeasurement update equationReferencesKnight, D.T., Rapid development of tightly-coupled GPS/INS systems, in Position Location and Navigation Symposium, 1996, IEEE 1996, pp. 300–305. IEEE, 1996.Knight, D.T., Rapid development of tightly-coupled GPS/INS systems, in Position Location and Navigation Symposium, 1996, IEEE 1996, pp. 300–305. IEEE, 1996.Miller, I., Schimpf, B., Campbell, M., and Leyssens, J., Tightly-Coupled GPS/INS system design for autonomous urban navigation, in Position, Location and Navigation Symposium, 2008 IEEE/ION, pp. 1297–1310, IEEE, 2008.Miller, I., Schimpf, B., Campbell, M., and Leyssens, J., Tightly-Coupled GPS/INS system design for autonomous urban navigation, in Position, Location and Navigation Symposium, 2008 IEEE/ION, pp. 1297–1310, IEEE, 2008.Wendel, J. and Trommer, G.F., Tightly coupled GPS/INS integration for missile applications, Aerospace Science and Technology, 2004, no. 8(7), pp. 627–634.Wendel, J. and Trommer, G.F., Tightly coupled GPS/INS integration for missile applications, Aerospace Science and Technology, 2004, no. 8(7), pp. 627–634.Wendel, J., Metzger, J., Moenikes, R., Maier, A., and Trommer, G.F., A performance comparison of tightly coupled GPS/INS navigation systems based on extended and sigma point Kalman filters, Navigation, 2006, no. 53(1), pp. 21–31.Wendel, J., Metzger, J., Moenikes, R., Maier, A., and Trommer, G.F., A performance comparison of tightly coupled GPS/INS navigation systems based on extended and sigma point Kalman filters, Navigation, 2006, no. 53(1), pp. 21–31.Ding, W. and Wang, J., Precise velocity estimation with a stand-alone GPS receiver, Journal of Navigation, 2011, no. 64(02), pp. 311–325.Ding, W. and Wang, J., Precise velocity estimation with a stand-alone GPS receiver, Journal of Navigation, 2011, no. 64(02), pp. 311–325.Serrano, L., Kim, D., Langley, R.B., Itani, K., and Ueno, M., A GPS velocity sensor: how accurate can it be? A first look, ION NTM, 2004, pp. 875–885.Serrano, L., Kim, D., Langley, R.B., Itani, K., and Ueno, M., A GPS velocity sensor: how accurate can it be? A first look, ION NTM, 2004, pp. 875–885.Soon, B.K.H., Scheding, S., Lee, H.-K., Lee, H.-K., and Durrant-Whyte, H., An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements, GPS Solutions, 2008, no. 12(4), pp. 261–271.Soon, B.K.H., Scheding, S., Lee, H.-K., Lee, H.-K., and Durrant-Whyte, H., An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements, GPS Solutions, 2008, no. 12(4), pp. 261–271.Moafipoor, S., Grejner-Brzezinska, D.A., and Toth, C.K., Tightly coupled GPS/INS integration based on GPS carrier phase velocity update, ION NTM, 2004.Moafipoor, S., Grejner-Brzezinska, D.A., and Toth, C.K., Tightly coupled GPS/INS integration based on GPS carrier phase velocity update, ION NTM, 2004.Ding, W., Integration of MEMS INS with GPS carrier phase derived velocity: A new approach, Proceedings of ION GNSS 2007, 2007, pp. 2085–2093.Ding, W., Integration of MEMS INS with GPS carrier phase derived velocity: A new approach, Proceedings of ION GNSS 2007, 2007, pp. 2085–2093.Tang, Y., Lian, J., Wu, M., and Shen, L., Reduced Kalman filter for RDSS/INS integration based on time differenced carrier phase, Industrial Electronics and Applications, 2007. ICIEA 2007. 2nd IEEE Conference on, pp. 11–14.Tang, Y., Lian, J., Wu, M., and Shen, L., Reduced Kalman filter for RDSS/INS integration based on time differenced carrier phase, Industrial Electronics and Applications, 2007. ICIEA 2007. 2nd IEEE Conference on, pp. 11–14.Han, S. and Wang, J., Integrated GPS/INS navigation system with dual-rate Kalman filter, GPS solutions, 2012, no. 16(3), pp. 389–404.Han, S. and Wang, J., Integrated GPS/INS navigation system with dual-rate Kalman filter, GPS solutions, 2012, no. 16(3), pp. 389–404.Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, 2013.Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, 2013.Farrell, J., Aided Navigation: GPS with High Rate Sensors, New York: McGraw-Hill, 2008.Farrell, J., Aided Navigation: GPS with High Rate Sensors, New York: McGraw-Hill, 2008.Ali, J. and Rasheeq Ullah Baig Mirza, M., Initial orientation of inertial navigation system realized through nonlinear modeling and filtering, Measurement, 2011, no. 44(5), pp. 793–801.Ali, J. and Rasheeq Ullah Baig Mirza, M., Initial orientation of inertial navigation system realized through nonlinear modeling and filtering, Measurement, 2011, no. 44(5), pp. 793–801.Yi, Y. and Grejner-Brzezinska, D.A., Tightly-coupled GPS/INS integration using unscented Kalman filter and particle filter, Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), 2006, pp. 2182–2191.Yi, Y. and Grejner-Brzezinska, D.A., Tightly-coupled GPS/INS integration using unscented Kalman filter and particle filter, Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), 2006, pp. 2182–2191.Zhou, J., Edwan, E., Knedlik, S., and Loffeld, O., Low-cost INS/GPS with nonlinear filtering methods, 13th IEEE Conference on Information Fusion (FUSION), 2010, pp. 1–8.Zhou, J., Edwan, E., Knedlik, S., and Loffeld, O., Low-cost INS/GPS with nonlinear filtering methods, 13th IEEE Conference on Information Fusion (FUSION), 2010, pp. 1–8.Arasaratnam, I. and Haykin, S., Cubature Kalman filters, IEEE Transactions on Automatic Control, 2009, no. 54(6), pp. 1254–1269.Arasaratnam, I. and Haykin, S., Cubature Kalman filters, IEEE Transactions on Automatic Control, 2009, no. 54(6), pp. 1254–1269.Jiang, L., Bai-gen, C., Tao, T., and Jian, W., A CKF based GNSS/INSS train integrated positioning method, IEEE International Conference on Mechatronics and Automation (ICMA), 2010, pp. 1686–1689.Jiang, L., Bai-gen, C., Tao, T., and Jian, W., A CKF based GNSS/INSS train integrated positioning method, IEEE International Conference on Mechatronics and Automation (ICMA), 2010, pp. 1686–1689.Li, W. and Jia, Y., Location of mobile station with maneuvers using an IMM-based cubature Kalman filter, IEEE Transactions on Industrial Electronics, 2012, no. 59(11), 4338–4348.Li, W. and Jia, Y., Location of mobile station with maneuvers using an IMM-based cubature Kalman filter, IEEE Transactions on Industrial Electronics, 2012, no. 59(11), 4338–4348.Tang, X., Wei, J., and Chen, K., Square-root adaptive cubature Kalman filter with application to spacecraft attitude estimation, 15th IEEE International Conference on Information Fusion (FUSION), 2012, pp. 1406–1412.Tang, X., Wei, J., and Chen, K., Square-root adaptive cubature Kalman filter with application to spacecraft attitude estimation, 15th IEEE International Conference on Information Fusion (FUSION), 2012, pp. 1406–1412.Kong, X., Nebot, E.M., and Durrant-Whyte, H., Development of a nonlinear psi-angle model for large misalignment errors and its application in INS alignment and calibration, IEEE International Conference on Robotics and Automation, 1999, vol. 2, pp. 1430–1435.Kong, X., Nebot, E.M., and Durrant-Whyte, H., Development of a nonlinear psi-angle model for large misalignment errors and its application in INS alignment and calibration, IEEE International Conference on Robotics and Automation, 1999, vol. 2, pp. 1430–1435.Wang, Q., Li, Y., Rizos, C., and Li, S., The UKF and CDKF for low-cost SDINS/GPS in-motion alignment, Proceedings of International Symposium on GPS/GNSS, 2008, pp. 441–448.Wang, Q., Li, Y., Rizos, C., and Li, S., The UKF and CDKF for low-cost SDINS/GPS in-motion alignment, Proceedings of International Symposium on GPS/GNSS, 2008, pp. 441–448.Li, W., Wang, J., Lu, L., and Wu, W., A novel scheme for DVL-aided SINS in-motion alignment using UKF techniques, Sensors, 2013, no. 13(1), pp. 1046–1063.Li, W., Wang, J., Lu, L., and Wu, W., A novel scheme for DVL-aided SINS in-motion alignment using UKF techniques, Sensors, 2013, no. 13(1), pp. 1046–1063.Georgy, J., Noureldin, A., Korenberg, M.J., and Bayoumi, M.M., Low-cost three-dimensional navigation solution for RISS/GPS integration using mixture particle filter, IEEE Transactions on Vehicular Technology, 2010, no. 59(2), pp. 599–615.Georgy, J., Noureldin, A., Korenberg, M.J., and Bayoumi, M.M., Low-cost three-dimensional navigation solution for RISS/GPS integration using mixture particle filter, IEEE Transactions on Vehicular Technology, 2010, no. 59(2), pp. 599–615.Yi, Y., On improving the accuracy and reliability of GPS/INS-based direct sensor georeferencing, PhD thesis, The Ohio State University, 2007.Yi, Y., On improving the accuracy and reliability of GPS/INS-based direct sensor georeferencing, PhD thesis, The Ohio State University, 2007.Hong, S., Lee, M.H., Chun, H.-H., Kwon, S.-H., and Speyer, J.L., Observability of error states in GPS/INS integration, IEEE Transactions on Vehicular Technology, 2005, no. 54(2), pp. 731–743.Hong, S., Lee, M.H., Chun, H.-H., Kwon, S.-H., and Speyer, J.L., Observability of error states in GPS/INS integration, IEEE Transactions on Vehicular Technology, 2005, no. 54(2), pp. 731–743.Rhee, I., Abdel-Hafez, M.F., and Speyer, J.L., Observability of an integrated GPS/INS during maneuvers, IEEE Transactions on Aerospace and Electronic Systems, 2004, no. 40(2), pp. 526–535.Rhee, I., Abdel-Hafez, M.F., and Speyer, J.L., Observability of an integrated GPS/INS during maneuvers, IEEE Transactions on Aerospace and Electronic Systems, 2004, no. 40(2), pp. 526–535.Tang, Y., Wu, Y., Wu, M., Wu, W., Hu, X., and Shen, L., INS/GPS integration: global observability analysis, IEEE Transactions on Vehicular Technology, 2009., no. 58(3), pp. 1129–1142.Tang, Y., Wu, Y., Wu, M., Wu, W., Hu, X., and Shen, L., INS/GPS integration: global observability analysis, IEEE Transactions on Vehicular Technology, 2009., no. 58(3), pp. 1129–1142.Madgwick, S.O.H., Harrison, A.J.L., and Vaidyanathan, R., Estimation of IMU and MARG orientation using a gradient descent algorithm, IEEE International Conference on Rehabilitation Robotics (ICORR), 2011, pp. 1–7.Madgwick, S.O.H., Harrison, A.J.L., and Vaidyanathan, R., Estimation of IMU and MARG orientation using a gradient descent algorithm, IEEE International Conference on Rehabilitation Robotics (ICORR), 2011, pp. 1–7.

The authors declare that there are no conflicts of interest present.