SCIENCE CHINA Information Sciences, Volume 62, Issue 9: 192204(2019) https://doi.org/10.1007/s11432-018-9765-y

Adaptive two-filter smoothing based on second-order divided difference filter for distributed position and orientation system

More info
  • ReceivedAug 8, 2018
  • AcceptedDec 12, 2018
  • PublishedJul 25, 2019


The distributed position and orientation system (POS) uses transfer alignment to accurately measure multi-node time-spatial reference information, which is necessary for compensating the motion error of imaging sensors used in aerial surveys. Lever-arm deformation in transfer alignment will result in time-varying covariance of measurement noise, which decreases the estimation accuracy. To address this problem, a second-order adaptive divided difference two-filter smoother (ADDTFS) is proposed for transfer alignment. The second-order adaptive divided difference filter (ADDF2) severs as the forward filter to address nonlinearity in the system. The ADDF2 can estimate the measurement noise covariance in real time based on adaptive estimation using innovation information. The weighted statistical linear regression formulation is used in the backward filter to independently estimate the states and error covariance matrices. Then the forward and backward results are combined, to obtain high-precision estimation results in post-processing. Finally, the vehicle experiment results show that the proposed method can improve the attitude precision of transfer alignment in a distributed POS by 27.84%, which has been successfully applied to motion compensation of airborne interferometric synthetic aperture radar (InSAR).


The work was supported by National Natural Science Foundation of China (Grant Nos. 61722103, 61571030, 61721091) and in part by International (Regional) Cooperation and Communication Project (Grant No. 61661136 007).


[1] Li L C, Li D J, Pan Z H. Compressed sensing application in interferometric synthetic aperture radar. Sci China Inf Sci, 2017, 60: 102305 CrossRef Google Scholar

[2] Irwin K, Beaulne D, Braun A. Fusion of SAR, Optical Imagery and Airborne LiDAR for Surface Water Detection. Remote Sens, 2017, 9: 890 CrossRef ADS Google Scholar

[3] Li J L, Fang J C, Ge S S. Kinetics and Design of a Mechanically Dithered Ring Laser Gyroscope Position and Orientation System. IEEE Trans Instrum Meas, 2013, 62: 210-220 CrossRef Google Scholar

[4] Si F, Zhao Y, Lin Y H. A new transfer alignment of airborne weapons based on relative navigation. Measurement, 2018, 122: 27-39 CrossRef Google Scholar

[5] Ye W, Li J L, Li L C. Design and Development of a Real-Time Multi-DSPs and FPGA-Based DPOS for InSAR Applications. IEEE Senss J, 2018, 18: 3419-3425 CrossRef ADS Google Scholar

[6] Gong X L, Chen L J, Fang J C. A transfer alignment method for airborne distributed POS with three-dimensional aircraft flexure angles. Sci China Inf Sci, 2018, 61: 092204 CrossRef Google Scholar

[7] Lü X F, Cheng C Q, Gong J Y. Review of data storage and management technologies for massive remote sensing data. Sci China Technol Sci, 2011, 54: 3220-3232 CrossRef Google Scholar

[8] Huang Y L, Zhang Y G, Li N. A Robust Gaussian Approximate Fixed-Interval Smoother for Nonlinear Systems With Heavy-Tailed Process and Measurement Noises. IEEE Signal Process Lett, 2016, 23: 468-472 CrossRef ADS Google Scholar

[9] Zhao H, Cui P, Wang W. $H_{\infty}$ Fixed-Interval Smoothing Estimation for Time-Delay Systems. IEEE Trans Signal Process, 2013, 61: 316-326 CrossRef ADS Google Scholar

[10] Gong X L, Zhang J X, Fang J C. A Modified Nonlinear Two-Filter Smoothing for High-Precision Airborne Integrated GPS and Inertial Navigation. IEEE Trans Instrum Meas, 2015, 64: 3315-3322 CrossRef Google Scholar

[11] Liu H, Nassar S, El-Sheimy N. Two-Filter Smoothing for Accurate INS/GPS Land-Vehicle Navigation in Urban Centers. IEEE Trans Veh Technol, 2010, 59: 4256-4267 CrossRef Google Scholar

[12] Han S, Kwon W H. A Note on Two-Filter Smoothing Formulas. IEEE Trans Automat Contr, 2008, 53: 849-854 CrossRef Google Scholar

[13] Lu Z X, Li J L, Fang J C. Adaptive Unscented Two-Filter Smoother Applied to Transfer Alignment for ADPOS. IEEE Senss J, 2018, 18: 3410-3418 CrossRef ADS Google Scholar

[14] Yu J, Lee J G, Park C G. An off-line navigation of a geometry PIG using a modified nonlinear fixed-interval smoothing filter. Control Eng Practice, 2005, 13: 1403-1411 CrossRef Google Scholar

[15] Wang X M, He X K, Bao Y. Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm. Sci China Inf Sci, 2018, 61: 042202 CrossRef Google Scholar

[16] Malleswaran M, Vaidehi V, Irwin S. IMM-UKF-TFS Model-based Approach for Intelligent Navigation. J Navigation, 2013, 66: 859-877 CrossRef Google Scholar

[17] Ning X L, Li Z, Wu W R. Recursive adaptive filter using current innovation for celestial navigation during the Mars approach phase. Sci China Inf Sci, 2017, 60: 032205 CrossRef Google Scholar

[18] Norgaard M, Poulsen N K, Ravn O. New developments in state estimation for nonlinear systems. Automatica, 2000, 36: 1627-1638 CrossRef Google Scholar

[19] Karlgaard C D, Shen H. Robust state estimation using desensitized Divided Difference Filter.. ISA Trans, 2013, 52: 629-637 CrossRef PubMed Google Scholar

[20] Ghoshal T K, Dey A, Sadhu S. Adaptive divided difference filter for parameter and state estimation of non-linear systems. IET Signal Processing, 2015, 9: 369-376 CrossRef Google Scholar

[21] Ma L F, Wang Z D, Han Q L. Consensus control of stochastic multi-agent systems: a survey. Sci China Inf Sci, 2017, 60: 120201 CrossRef Google Scholar

[22] Ma L F, Wang Z D, Lam H K. Distributed Event-Based Set-Membership Filtering for a Class of Nonlinear Systems With Sensor Saturations Over Sensor Networks.. IEEE Trans Cybern, 2017, 47: 3772-3783 CrossRef PubMed Google Scholar

[23] Li J L, Fang J C, Lu Z X. Airborne Position and Orientation System for Aerial Remote Sensing. Int J Aerospace Eng, 2017, 2017: 1-11 CrossRef Google Scholar

[24] He X, He W, Qin H. Boundary vibration control for a flexible Timoshenko robotic manipulator. CrossRef Google Scholar

  • Figure 1

    (Color online) Schematic of transfer alignment for distributed POS.

  • Figure 2

    Lever-arm mechanism between the main POS and the $I$th sub-IMU.

  • Figure 3

    (Color online) Equipment and trajectory of vehicle experiment.

  • Figure 4

    (Color online) Attitude error of the $1$st imaging area.

  • Figure 7

    (Color online) The developed distributed POS.

  • Figure 8

    (Color online) The attitude results of (a) the 1st and (b) the 2nd sub-IMU of distributed POS.

  • Figure 9

    (Color online) The comparison of InSAR image. (a) The InSAR imaging without distributed POS; (b) the InSAR imaging compensated by distributed POS.

  • Table 1   Parameters of the smoother used in experiment
    Horizon position (m) 0.10
    Altitude position (m) 0.15
    $R_{0}$ matrixEast velocity (m/s) 0.01
    (initial measurement precision)North velocity (m/s) 0.01
    Upward velocity (m/s) 0.01
    $X$ gyro ($^{\circ}$/h) 0.01
    $Y$ gyro ($^{\circ}$/h) 0.01
    $Q$ matrix$Z$ gyro ($^{\circ}$/h) 0.01
    (measuring precision)$X$ accelerometer ($\mu$g) 50
    $Y$ accelerometer ($\mu$g) 50
    $Z$ accelerometer ($\mu$g) 50
    Horizon position (m) 0.10
    Altitude position (m) 0.15
    East velocity (m/s) 0.01
    North velocity (m/s) 0.01
    Upward velocity (m/s) 0.01
    Heading ($^{\circ}$) 0.05
    $P_{0}$ matrixPitch ($^{\circ}$) 0.01
    (initial precision)Roll ($^{\circ}$) 0.01
    $X$ gyro bias ($^{\circ}$/h) 0.01
    $Y$ gyro bias ($^{\circ}$/h) 0.01
    $Z$ gyro bias ($^{\circ}$/h) 0.01
    $X$ accelerometer ($\mu$g) 50
    $Y$ accelerometer ($\mu$g) 50
    $Z$ accelerometer ($\mu$g) 50
  • Table 2   Attitude precision of the ground-vehicle distributed POS (RMSE)
    Attitude errors
    Heading ($^{\circ}$)Pitch ($^{\circ}$)Roll ($^{\circ}$)
    1 0.0098 0.0087 0.0044 0.0041 0.0052 0.0040
    2 0.0053 0.0030 0.0035 0.0031 0.0032 0.0029
    3 0.0088 0.0054 0.0058 0.0045 0.0056 0.0042
    Average 0.0079 0.0057 0.0046 0.0039 0.0047 0.0037

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号