Abstract
A theoretical performance analysis of Kalman Filters for Global Navigation Satellite System GNSS-based space vehicle position estimation in varying Position Dilution of Precision (PDOP) conditions is presented. The PDOP indicates the possible accuracy of GNSS measurements using Least Square Estimation (LSE). The Kalman Filter combines the knowledge of the vehicle motion with the GNSS measurements and then provides better accuracy than the LSE. For the same nonlinear vehicular motion and PDOP condition, the ratio of average position error and noise standard deviation varies depending on the type of Kalman Filter used. The presented theoretical analysis explains and characterizes this behavior for four Kalman Filters, which are the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF) and two newly developed Unscented Type Kalman Filters. The experiment shows that for highly nonlinear space vehicle motion, the performance of the UKF is better than the EKF in high PDOP conditions and all the filters perform similarly for low PDOP conditions. For a space vehicle with lower nonlinearity in the motion, the performances of all the filters are indistinguishable for any PDOP condition.
Similar content being viewed by others
References
Bar-shalom Y, Li X, Kirubarajan T (2004) Estimation with applications to tracking and navigation: theory algorithms and software. Wiley, New York
Biswas SK, Qiao L, Dempster A (2015) Application of a fast unscented Kalman Filtering method to satellite position estimation using a space-borne multi-GNSS receiver. In: Proceedings of ION GNSS+ 2016, Institute of Navigation, Tampa, Florida, September 2015, pp 2625–2631
Biswas SK, Qiao L, Dempster AG (2016a) A novel a priori state computation strategy for the unscented Kalman filter to improve computational efficiency. IEEE Trans Autom Control. doi:10.1109/TAC.2016.2599291
Biswas SK, Qiao L, Dempster AG (2016b) Computationally efficient unscented Kalman Filtering techniques for launch vehicle navigation using a space-borne GPS receiver. In: Proceedings of ION GNSS+ 2016, Institute of Navigation, Portland, Oregon, September 2016, pp 186–194
Braun B, Markgraf M, Montenbruck O (2016) Performance analysis of IMU-augmented GNSS tracking systems for space launch vehicles. Ceas Space J 8:117. doi:10.1007/s12567-016-0113-9
Choi EJ, Yoon JC, Lee BS, Park SY, Choi KH (2010) Onboard orbit determination using GPS observations based on the unscented Kalman filter. Adv Space Res 46(11):1440–1450
Curtis HD (2010) Orbital mechanics for engineering students. Butterworth-Heinemann, Oxford
Doong SH (2009) A closed-form formula for GPS GDOP computation. GPS Solut 13(3):183–190
Julier S, Uhlmann J (1997). A new extension of the Kalman filter to nonlinear systems. In: Proceedings of signal processing, sensor fusion, and target recognition VI, Orlando, Florida, April 1997, pp 182–193
Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422
Julier S, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45(3):477–482
Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME J Basic Eng 82((Series D)):35–45
Kaplan ED, Hegarty CJ (eds) (2005) Understanding GPS: principles and applications. In: Understanding GPS: principles and applications. Artech house, Boston
Misra P, Enge P (2006) Global positioning system: signals, measurements and performance. Ganga-Jamuna Press, Lincoln
Montenbruck O, Gill E (2012) Satellite orbits: models, methods and applications. Springer, Berlin
Montenbruck O, Ramos-Bosch P (2008) Precision real-time navigation of LEO satellites using global positioning system measurements. GPS Solut 12(3):187–198
Montenbruck O, Hauschild A, Andres Y, Engeln A, Marquardt C (2012) (Near-)real-time orbit determination for GNSS radio occultation processing. GPS Solut 17(2):199–209
Nadarajah N, Teunissen PJG, Buist PJ (2012) Attitude determination of LEO satellites using an array of GNSS sensors. In: Proceedings of 15th international conference on information fusion (FUSION), Singapore 2012, pp 1066–1072
NASA (2014) SpaceX CRS-5 fifth commercial resupply services flight to the international space station
Parkinson KJ, Mumford PJ, Glennon EP, Shivaramaiah NC, Dempster AG, Rizos C (2011) A low cost Namuru V3 receiver for Spacecraft operations. In: Proceedings of IGNSS symposium 2011, pp 15–17
Qiao L, Samsung L, Rizos C (2009) A multiple GNSS-based orbit determination algorithm for geostationary satellites. In: Proceedings of IGNSS symposium 2009
SpaceX (2009). Falcon 9 launch vehicle payload user’s guide revision 1
Vallado DA (2001) Fundamentals of astrodynamics and applications. Springer, Berlin
Yunck TP (1993) Coping with the atmosphere and ionosphere in precise satellite and ground positioning. Washington DC American Geophysical Union Geophysical Monograph Series, 73, pp 1–16
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Biswas, S.K., Qiao, L. & Dempster, A.G. Effect of PDOP on performance of Kalman Filters for GNSS-based space vehicle position estimation. GPS Solut 21, 1379–1387 (2017). https://doi.org/10.1007/s10291-017-0621-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10291-017-0621-x