The Impact of Vehicle Maneuvers on the Attitude Estimation of GNSS / INS for Mobile Mapping
-
You Li
,
Xiaoji Niu
Abstract
Integrated Global Navigation Satellite Systems (GNSS) and Inertial Navigation Systems (INS) are the core of georeferencing Mobile Mapping Systems (MMS) data. Divergence of attitude errors is a dominant issue when an INS has to work as a stand-alone system for extended periods. This issue can be mitigated by taking specific vehicle maneuvers to make attitude errors observable. Since MMS applications are time consuming and costly, it is preferable to design the trajectory and motion of the mapping vehicles in advance, to guarantee the accuracy of the attitude estimation and minimize the cost. This article investigates the estimation accuracy of attitude under different vehicle maneuvers theoretically through the observability analysis method. Both theoretical analysis and tests show that the attitude estimation is significantly related with the type of vehicle maneuvers and motion parameters such as velocity, acceleration, and angular velocity. The motion with varying angular velocities is the most efficient motion to enhance the estimation of all attitude angles; the motion with varying accelerations can improve the yaw and pitch but has no effect on enhancing the roll. The uniform circular motion can improve the roll and pitch but has slight or no impact on enhancing the yaw (depending on the forward accelerometer error, the forward velocity, and the vertical angular velocity); the linear motion with a constant acceleration can improve the yaw (depending on the cross-track accelerometer error and the forward acceleration) and weakly improve the pitch but cannot improve the roll. The physical interpretations of these properties are also provided. The “S”-shaped motion with varying angular velocities is suggested for efficient attitude estimation; however, the circle, or “8”-shaped motion with uniform angular velocity, is not efficient for MMS applications.
Acknowledgments
The authors would like to thank Dr. Kai-wei Chiang from NCKU for providing valuable suggestions. This work was supported in part by the National Natural Science Foundation of China (41174028), the Key Laboratory Development Fund from the Ministry of Education of China (618-277176), the LIESMARS Special Research Fund, the Research Start-up Fund from Wuhan University (618-273438), and the Fund from China Scholarship Council (201306270139).
Appendix
A.1 Observability properties under linear motion
When the vehicle moves straightforward, the angular velocity of the vehicle is zero, that is,
where λ is the latitude and ψ is the yaw angle. The symbol (·×) and diag(·) denote the skew symmetric matrix and the diagonal matrix form of a vector, respectively.
Since ψ is constant,
Neglecting the second-order term small quantities, more terms become zero:
Then, the matrix Θ in (15) becomes
A.2 Observability properties under uniform linear motion
In this case, fb = [ 0 0 –g ]T. Consequently, (8) equals to
The items –gΦy + bax and gΦx + bay have only zero solutions and thus are observable. Therefore, the unobservable parts of the roll and pitch errors are Φxu = –bayu / g and Φyu = baxu / g, respectively. These equations mean that the roll and pitch errors can be bounded to the same level with the y- and x-axis accelerometer biases divided by the gravity, respectively.
Assuming the vehicle is moving horizontally, then
The last two equations in (a.5) can be changed as
where ωe is the value of the Earth’s rotation angular velocity. Thus, the yaw error is related with the east gyro bias, and its unobservable component is Φzu = –bgEu / (ωe cos λ). However, the yaw error will be several orders of magnitude larger than the east gyro bias because ωe cos λ is only with a 10–5 order.
Neglecting the weakly observable items caused by ωe, the observable items are
A.3 Observability properties under linear motion with a constant acceleration
In this case,
Then, (8) can be written as
Neglecting the weakly observable items caused by ωe, the observable items are
A.4 Observability properties under linear motions with varying accelerations
When the vehicle moves straight forward with changing accelerations,
Then, Θzu = 0 equals to
When j ≥ 4, the coefficients
Substitute (a.14) into
Thus, the observable items are
B.1 Observability properties under uniform circular motion
In this case,
Therefore, the Θ matrix in (15) becomes
with
Hence, Θzu = 0 equals to
When the vehicle is turning,
Therefore, the observable items are
B.2 Observability properties under motions with varying angular velocities
Put
The complexity of vehicle maneuvers makes the third and the followed equations much more complicated. Considering that the effect of third and the followed equations are reducing because they are less direct to the GNSS / INS equations, we neglect them in this analysis. Actually, the neglected equations will further improve the estimations of the states by narrowing the scopes of the nonzero solutions of Θzu=0.
Neglecting ωie, (a.22) equals to
The observable items are
References
[1] Bayoud, F. and Skaloud, J., Vision-aided inertial navigation system for robotic mobile mapping. Journal of Applied Geodesy, 2008. 2(1): 39–52.10.1515/JAG.2008.005Search in Google Scholar
[2] Rieger, P., Studnicka, N., Pfennigbauer, M., and Zach, G., Boresight alignment method for mobile laser scanning systems. Journal of Applied Geodesy, 2010. 4(1): 13–21.10.1515/jag.2010.002Search in Google Scholar
[3] El-Sheimy, N., An overview of mobile mapping systems. FIG Working Week. 2005.Search in Google Scholar
[4] Titterton, D.H. and Weston, J.L., Strapdown inertial navigation technology – 2nd ed. 2004: The Institution of Electrical Engineers, London, United Kingdom.10.1049/PBRA017ESearch in Google Scholar
[5] Li, X., An exact formula for the tilt correction in scalar airborne gravimetry. Journal of Applied Geodesy, 2011. 5(2): 81–85.10.1515/jag.2011.007Search in Google Scholar
[6] Rabiain, A.H., Kealy, A., and Morelande, M., Tightly coupled MEMS based INS / GNSS performance evaluation during extended GNSS outages. Journal of Applied Geodesy, 2013. 7(4): 291–298.10.1515/jag-2013-0056Search in Google Scholar
[7] Nagai, M., Chen, T., Shibasaki, R., and Kumagai, H., UAV-borne 3-D mapping system by multisensor integration. Geoscience and Remote Sensing, IEEE Transactions, 2009. 47(3): 701–708.10.1109/TGRS.2008.2010314Search in Google Scholar
[8] Suzuki, T., Amano, Y., and Hashizume, T., Vision based localization of a small UAV for generating a large mosaic image. SICE Annual Conference 2010, Proceedings of IEEE. 2010.Search in Google Scholar
[9] Gross, J., Gu, Y., Rhudy, M., Gururajab, S., and Napolitano, M., Flight-Test Evaluation of Sensor Fusion Algorithms for Attitude Estimation. Aerospace and Electronic Systems, IEEE Transactions, 2012. 48(3): 2128–2139.10.1109/TAES.2012.6237583Search in Google Scholar
[10] Porat, B. and Bar-Itzhack, I.Y., Effect of acceleration switching during INS in-flight alignment. Journal of Guidance, Control, and Dynamics, 1981. 4(4): 385–389.10.2514/3.19744Search in Google Scholar
[11] Klingbeil, L., Eling, C., Zimmermann, F., and Kuhlmann, H., Magnetic field sensor calibration for attitude determination. Journal of Applied Geodesy, 2014. 8(2): 97–108.10.1515/jag-2014-0003Search in Google Scholar
[12] Li, Y., Georgy, J., Niu, X., Li, Q., and El-Sheimy, N., Autonomous Calibration of MEMS Gyros in Consumer Portable Devices. 2015. 15(7): 4062–4072.10.1109/JSEN.2015.2410756Search in Google Scholar
[13] Dusha, D., Mejias, L., and Walker, R., Fixed‐wing attitude estimation using temporal tracking of the horizon and optical flow. Journal of Field Robotics, 2011. 28(3): 355–372.10.1002/rob.20387Search in Google Scholar
[14] Nadarajah, N., Teunissen, P.J.G., and Raziq, N., Instantaneous BeiDou – GPS attitude determination: A performance analysis. Advances in Space Research, 2013.10.1016/j.asr.2013.08.030Search in Google Scholar
[15] Teunissen, P.J.G., Giorgi, G., and Buist, P.J., Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments. GPS Solutions, 2010. 15(1): 15–28.10.1007/s10291-010-0164-xSearch in Google Scholar
[16] Crassidis, J.L., Markley, F.L., and Cheng, Y., Survey of nonlinear attitude estimation methods. Journal of Guidance, Control, and Dynamics, 2007. 30(1): 12–28.10.2514/1.22452Search in Google Scholar
[17] Chiang, K.-W. and Chang, H.-W., Intelligent Sensor Positioning and Orientation Through Constructive Neural Network-Embedded INS / GPS Integration Algorithms. Sensors, 2010. 10(10): 9252–9285.10.3390/s101009252Search in Google Scholar PubMed PubMed Central
[18] Li, Y., Niu, X., Zhang, Q., Zhang, H., and Shi, C., An in situ hand calibration method using a pseudo-observation scheme for low-end inertial measurement units. Measurement Science and Technology, 2012. 23(10): 1–10.10.1088/0957-0233/23/10/105104Search in Google Scholar
[19] Nassar, S. and El-Sheimy, N., Wavelet analysis for improving INS and INS / DGPS navigation accuracy. Journal of Navigation, 2005. 58(01): 119–134.10.1017/S0373463304003005Search in Google Scholar
[20] Dissanayake, G., Sukkarieh, S., Nebot, E., and Durrant-Whyte, H., The aiding of a low-cost strapdown inertial measurement unit using vehicle model constraints for land vehicle applications. Robotics and Automation, IEEE Transactions, 2001. 17(5): 731–747.10.1109/70.964672Search in Google Scholar
[21] Niu, X., Li, Y., Zhang, Q., Cheng, Y., and Shi, C., Observability Analysis of Non-Holonomic Constraints for Land-Vehicle Navigation Systems. Journal of Global Positioning Systems, 2012. 11(1): 80–88.10.5081/jgps.11.1.80Search in Google Scholar
[22] Wang, J., Lee, H., Hewitson, S., and Lee, H., Influence of dynamics and trajectory on integrated GPS / INS navigation performance. Journal of Global Positioning Systems, 2003. 2(2): 109–116.10.5081/jgps.2.2.109Search in Google Scholar
[23] Hong, S., Lee, M., Chun, H., Kwon, S., and Speyer, J., Observability of error states in GPS / INS integration. Vehicular Technology, IEEE Transactions,, 2005. 54(2): 731–743.10.1109/TVT.2004.841540Search in Google Scholar
[24] Li, Y., Chen, Q., Niu, X., and Shi, C., Simulation Analysis for the Influences of Vehicle Maneuvers to the Attitude Estimations of GNSS / INS Navigation Systems. China Satellite Navigation Conference (CSNC) 2012. 2012. Guangzhou: Springer.10.1007/978-3-642-29187-6_67Search in Google Scholar
[25] Godha, S., Performance Evaluation of Low Cost MEMS-Based IMU Integrated with GPS for Land Vehicle Navigation Application, in Department of Geomatics Engineeing 2006, University of Calgary: Calgary, Canada.Search in Google Scholar
[26] Park, M. and Gao, Y., Error and performance analysis of MEMS-based inertial sensors with a low-cost GPS receiver. Sensors, 2008. 8(4): 2240–2261.10.3390/s8042240Search in Google Scholar PubMed PubMed Central
[27] Liu, C.-Y., The performance evaluation of real-time MEMS INS / GPS integration with ZUPT / ZIHR / NHC for land navigation. ION GNSS 2012. 2012. Nashville, Tennessee.Search in Google Scholar
[28] Petovello, M., Cannon, M., and Lachapelle, G., Quantifying Improvements from the Integration of GPS and a Tactical Grade INS in High Accuracy Navigation Applications. Proceedings of ION NTM. 2003.Search in Google Scholar
[29] Abbott, H. and Powell, D., Land-vehicle navigation using GPS. Proceedings of the IEEE, 1999. 87(1): 145–162.10.1109/5.736347Search in Google Scholar
[30] El-Sheimy, N., Lecture note 623 – Inertial Techniques and INS / DGPS Integration, Department of Geomatics Engineering, University of Calgary. 2014.Search in Google Scholar
[31] Ham, F.M. and Brown, R.G., Observability, eigenvalues, and Kalman filtering. Aerospace and Electronic Systems, IEEE Transactions, 1983(2): 269–273.10.1109/TAES.1983.309446Search in Google Scholar
[32] Bar-Itzhack, I.Y. and Berman, N., Control theoretic approach to inertial navigation systems. Journal of Guidance, Control, and Dynamics, 1988. 11(3):237–245.10.2514/3.20299Search in Google Scholar
[33] Goshen-Meskin, D. and Bar-Itzhack, I.Y., Observability analysis of piece-wise constant systems. I. Theory. Aerospace and Electronic Systems, IEEE Transactions, 1992. 28(4): 1056–1067.10.1109/7.165367Search in Google Scholar
[34] Jiang, Y.F. and Lin, Y.P., Error estimation of INS ground alignment through observability analysis. Aerospace and Electronic Systems, IEEE Transactions, 1992. 28(1): 92–97.10.1109/7.135435Search in Google Scholar
[35] Rhee, I., Abdel-Hafez, M.F., and Speyer, J.L., Observability of an integrated GPS / INS during maneuvers. Aerospace and Electronic Systems, IEEE Transactions, 2004. 40(2): 526–535.10.1109/TAES.2004.1310002Search in Google Scholar
[36] Han, S. and Wang, J., Monitoring degree of observability in GPS / INS integration. Int. Symp. on GPS / GNSS, Yokohama, Japan. 2008.Search in Google Scholar
[37] Tang, Y., Wu, Y., Wu, M., Wu, W., Hu, X., and Shen, L., INS / GPS integration: global observability analysis. Vehicular Technology, IEEE Transactions, 2009. 58(3): 1129–1142.10.1109/TVT.2008.926213Search in Google Scholar
[38] Wu, Y., Zhang, H., Wu, M., Hu, X., and Hu, D., Observability of Strapdown INS Alignment: A Global Perspective. Aerospace and Electronic Systems, IEEE Transactions, 2012. 48(1): 78–102.10.1109/TAES.2012.6129622Search in Google Scholar
[39] Shin, E.-H., Estimation techniques for low-cost inertial navigation, Department of Geomatics Engineering. 2005, University of Calgary: Calgary, Canada.Search in Google Scholar
[40] Wei, M. and Schwarz, K., A strapdown inertial algorithm using an Earth-fixed cartesian frame. Navigation, 1990. 37: 153–167.10.1002/j.2161-4296.1990.tb01544.xSearch in Google Scholar
[41] Maybeck, P.S., Stochastic models, estimation, and control. Vol. 3. 1982: Access Online via Elsevier.Search in Google Scholar
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- Monitoring of Civil Engineering Structures using a State-of-the-art Image Assisted Total Station
- The Impact of Vehicle Maneuvers on the Attitude Estimation of GNSS / INS for Mobile Mapping
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Articles in the same Issue
- Frontmatter
- Research Articles
- A constraint-based parameterization technique for B-spline surfaces
- Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems
- Monitoring of Civil Engineering Structures using a State-of-the-art Image Assisted Total Station
- The Impact of Vehicle Maneuvers on the Attitude Estimation of GNSS / INS for Mobile Mapping
- InKoPoMoVer – Cooperative Positioning for Real-time User Assistance and Guidance at Multi-modal Public Transit Junctions
