Abstract: To overcome the shortcomings of the traditional measurement error calibration methods for spaceflight telemetry, tracking and command (TT&C) systems, an online error calibration method based on low Earth orbit satellite-to-ground double- differential GPS (LEO-ground DDGPS) is proposed in this study. A fixed-interval smoother combined with a pair of forward and backward adaptive robust Kalman filters (ARKFs) is adopted to solve the LEO-ground baseline, and the ant colony optimization (ACO) algorithm is used to deal with the ambiguity resolution problem. The precise baseline solution of DDGPS is then used as a comparative reference to calibrate the systematic errors in the TT&C measurements, in which the parameters of the range error model are solved by a batch least squares algorithm. To validate the performance of the new online error calibration method, a hardware-in-the-loop simulation platform is constructed with independently developed spaceborne dual-frequency GPS receivers and a Spirent GPS signal generator. The simulation results show that with the fixed-interval smoother, a baseline estimation accuracy (RMS, single axis) of better than 10 cm is achieved. Using this DDGPS solution as the reference, the systematic error of the TT&C ranging system is effectively calibrated, and the residual systematic error is less than 5 cm.

基于星地差分GPS的航天测控系统在线误差标校方法研究

[1]Blewitt G, 1989. Carrier phase ambiguity resolution for the Global Positioning System applied to geodetic baselines up to 2000 km. J Geophys Res Sol Earth, 94(B8): 10187-10203.

[2]Boehm J, Niell A, Tregoning P, et al., 2006. Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett, 33(7):L07304.

[3]Box GEP, Muller ME, 1958. A note on the generation of random normal deviates. Ann Math Stat, 29(2):610-611.

[4]Dorigo M, Maniezzo V, Colorni A, 1996. Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern, 26(1):29-41.

[5]Gelb A, 1974. Applied Optimal Estimation. MIT Press, Cambridge, the UK.

[6]Jazaeri S, Amiri-Simkooei AR, Sharifi MA, 2013. Fast GNSS ambiguity resolution by ant colony optimisation. Surv Rev, 45(330):190-196.

[7]Kommuri SK, Defoort M, Karimi HR, et al., 2016. A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans Ind Electron, 63(12):7671- 7681.

[8]Langer JV, Feess WA, Hanington KM, et al., 1994. RADCAL: precision orbit determination with a commercial grade GPS receiver. Proc National Technical Meeting of the Institute of Navigation, p.421-431.

[9]Li XB, Mo SF, Zhou KM, 2010. Fault detection for linear discrete time-varying systems. 49^th IEEE Conf on Decision and Control, p.762-767.

[10]Li ZS, Liu M, Karimi HR, et al., 2013. Sampled-data control of spacecraft rendezvous with discontinuous Lyapunov approach. Math Probl Eng, 2013:814271.

[11]Lin SG, 2015. Assisted adaptive extended Kalman filter for low-cost single-frequency GPS/SBAS kinematic positioning. GPS Sol, 19(2):215-223.

[12]Liu DL, 2015. The Research on Methods and Key Technologies of Ship-Board Radar Detection Accuracy Calibration. PhD Thesis, Dalian Maritime University, Dalian (in Chinese).

[13]Liu H, Nassar S, El-Sheimy N, 2010. Two-filter smoothing for accurate INS/GPS land-vehicle navigation in urban centers. IEEE Trans Veh Technol, 59(9):4256-4267.

[14]Martin LK, Fisher NG, Jones WH, et al., 2011. Ho‘oponopono: a radar calibration CubeSat. 25^th Annual AIAA/USU Conf on Small Satellites.

[15]Matias B, Oliveira H, Almeida J, et al., 2015. High-accuracy low-cost RTK-GPS for an unmanned surface vehicle. OCEANS-Genova, p.1-4.

[16]Niell AE, 1996. Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res Sol Earth, 101(B2):3227-3246.

[17]Reimann M, Doerner K, Hartl RF, 2004. D-ants: savings based ants divide and conquer the vehicle routing problem. Comput Oper Res, 31(4):563-591.

[18]Saastamoinen J, 1972. Atmospheric correction for troposphere and stratosphere in radio ranging of satellites. 3^rd Int Symp on the Use of Artificial Satellites for Geodesy.

[19]Socha K, Dorigo M, 2008. Ant colony optimization for continuous domains. Eur J Oper Res, 185(3):1155-1173.

[20]Švehla D, Rothacher M, 2003. CHAMP double-difference kinematic POD with ambiguity resolution. In: Reigber C, Lühr H, Schwintzer P (Eds.), First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies. Springer Berlin Heidelberg, p.70-77.

[21]Takasu T, Yasuda A, 2008. Evaluation of RTK-GPS performance with low-cost single-frequency GPS receivers. Proc Int Symp on GPS/GNSS, p.852-861.

[22]Takasu T, Yasuda A, 2009. Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB. Int Symp on GPS/GNSS.

[23]Teunissen P, Joosten P, Tiberius C, 2003. A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution. Proc 15^th Int Technical Meeting of the Satellite Division of the Institute of Navigation.

[24]Teunissen PJG, de Jonge PJ, Tiberius CCJM, 1997. Performance of the LAMBDA method for fast GPS ambiguity resolution. Navigation, 44(3):373-383.

[25]Verhagen S, Li BF, Teunissen PJG, 2013. Ps-LAMBDA: ambiguity success rate evaluation software for interferometric applications. Comput Geosci, 54:361-376.

[26]Wan N, Liu M, Karimi HR, 2014. Observer-based robust control for spacecraft rendezvous with thrust saturation. Abstr Appl Anal, 2014:710850.

[27]Xu GC, Xu Y, 2016. GPS: Theory, Algorithms and Applications (3^rd Ed.). Springer, New York, USA.

[28]Yang YX, Gao WG, 2006. An optimal adaptive Kalman filter. J Geod, 80(4):177-183.

[29]Zhang HP, Ping JS, Zhu WY, et al., 2006. Brief review of the ionospheric delay models. Progr Astron, 24(1):16-26 (in Chinese).