| Citation: | SU B Z，WANG L，ZHANG H W，et al. Relative navigation method based on modified likelihood filtering for unmanned aerial vehicle formation[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（3）：569-579 （in Chinese） doi: 10.13700/j.bh.1001-5965.2021.0313
|
A modified likelihood cubature Kalman filtering (ML-CKF) is proposed to solve the problem that the measurements of vision-based relative navigation sensor for unmanned aerial vehicle formation are randomly delayed by multiple steps. The measurement model is modified by the Bernoulli random variables to describe the random delay. The likelihood function of the filtering is calculated by marginalizing out the delay variable to extract accurate information from the delayed measurements. The third-degree spherical-radial rule is utilized to compute the Gaussian-weighted integrals for the nonlinear system. The proposed modified likelihood filtering has the property of adaptive filtering because the weighting factors of the filtering are tuned based on the characteristics of the received measurements. By utilizing the Rodrigues parameters to denote the attitude errors, the relative navigation filter of unmanned aerial vehicle formation is designed based on the ML-CKF. Simulation results indicate that the proposed filtering algorithm could accurately estimate the relative position, velocity and attitude between the leader and follower. Moreover, the estimation accuracy of ML-CKF is superior to cubature Kalman filtering and conventional randomly delayed filtering.
| [1] |
ZHU Y F, SUN Y R, ZHAO W, et al. A novel relative navigation algorithm for formation flight[J]. Journal of Aerospace Engineering, 2020, 234(2): 308-318.
|
| [2] |
ELLINGSON G, BRINK K, MCLAIN T. Relative navigation of fixed-wing aircraft in GPS-denied environments[J]. Navigation, 2020, 67: 255-273. doi: 10.1002/navi.364
|
| [3] |
万九卿, 布少聪, 钟丽萍. 基于混合动态信念传播的多无人机协同定位算法[J]. 北京航空航天大学学报, 2016, 42(5): 934-944. doi: 10.13700/j.bh.1001-5965.2015.0321
WAN J Q, BU S C, ZHONG L P. Cooperative localization algorithm of multi-UAVs based on dynamics hybrid belief propagation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(5): 934-944(in Chinese). doi: 10.13700/j.bh.1001-5965.2015.0321
|
| [4] |
FOSBURY A M, CRASSIDIS J L. Relative navigation of air vehicles[J]. Journal of Guidance, Control and Dynamics, 2008, 31(4): 824-834. doi: 10.2514/1.33698
|
| [5] |
JEONG J, KIM S, SUK J. Parametric study of sensor placement for vision-based relative navigation system of multiple spacecraft[J]. Acta Astronautica, 2017, 141: 36-49. doi: 10.1016/j.actaastro.2017.09.020
|
| [6] |
XU Z, QI N, CHEN Y. Parameter estimation of a three-axis spacecraft simulator using recursive least-squares approach with tracking differentiator and extended Kalman filter[J]. Acta Astronautica, 2015, 117: 254-262. doi: 10.1016/j.actaastro.2015.08.010
|
| [7] |
JULIER S J, UHLMANN J K, DURRANT-WHYTE H F. A new method for the nonlinear transformation of means and covariances in filters and estimators[J]. IEEE Transaction Automatica Control, 2000, 45(3): 77-482.
|
| [8] |
卢道华, 付怀达, 王佳, 等. 基于IMU与UKF的船舶升沉运动信息测量方法[J]. 北京航空航天大学学报, 2021, 47(7): 1323-1331. doi: 10.13700/j.bh.1001-5965.2020.0223
LU D H, FU H D, WANG J, et al. Measurement of ship’s heave motion information based on IMU and UKF algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(7): 1323-1331(in Chinese). doi: 10.13700/j.bh.1001-5965.2020.0223
|
| [9] |
ARASARATNAM I, HAYKIN S. Cubature Kalman filters[J]. IEEE Transaction Automatica Control, 2009, 54(6): 1254-1269. doi: 10.1109/TAC.2009.2019800
|
| [10] |
李兆铭, 杨文革, 丁丹, 等. 多星对合作目标的分布式协同导航滤波算法[J]. 北京航空航天大学学报, 2018, 44(3): 462-469. doi: 10.13700/j.bh.1001-5965.2017.0150
LI Z M, YANG W G, DING D, et al. Distributed coordinated navigation filtering algorithm for cooperative target by multi-satellite[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(3): 462-469(in Chinese). doi: 10.13700/j.bh.1001-5965.2017.0150
|
| [11] |
崔乃刚, 王小刚, 郭继峰. 基于Sigma-point卡尔曼滤波的INS/Vision相对导航方法研究[J]. 宇航学报, 2009, 30(6): 2220-2225. doi: 10.3873/j.issn.1000-1328.2009.06.028
CUI N G, WANG X G, GUO J F. Reserch on relative navigation method based on INS/Vision using Sigma-point Kalman filter[J]. Journal of Astronautics, 2009, 30(6): 2220-2225(in Chinese). doi: 10.3873/j.issn.1000-1328.2009.06.028
|
| [12] |
PLETT G L, ZARZHITSKY D, PACK D J. Out-of-order sigma-point Kalman filtering for target localization using cooperating unmanned aerial vehicles[M]. Berlin: Advances in Cooperative Control and Optimization, 2007: 21-43.
|
| [13] |
KIM Y, HONG K, BANG H. Utilizing out-of-sequence measurement for ambiguous update in particle filtering[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(1): 493-501. doi: 10.1109/TAES.2017.2741878
|
| [14] |
HERMOSO-CARAZO A, LINARES-PEREZ J. Extended and unscented filtering algorithms using one-step randomly delayed observations[J]. Applied Mathematics and Computation, 2007, 190(2): 1375-1393. doi: 10.1016/j.amc.2007.02.016
|
| [15] |
HERMOSO-CARAZO A, LINARES-PEREZ J. Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems[J]. Applied Mathematical Modelling, 2009, 33: 3705-3717. doi: 10.1016/j.apm.2008.12.008
|
| [16] |
WANG X X, LIANG Y, PAN Q, et al. Gaussian filter for nonlinear systems with one-step randomly delayed measurement[J]. Automatica, 2013, 49: 976-986. doi: 10.1016/j.automatica.2013.01.012
|
| [17] |
张勇刚, 黄玉龙, 赵琳. 一种带多步随机延迟量测高斯滤波器的一般框架解[J]. 自动化学报, 2015, 41(1): 122-135. doi: 10.16383/j.aas.2015.c140293
ZHANG Y G, HUANG Y L, ZHAO L. A general framework solution to Gaussian filter with multiple-step randomly-delayed measurements[J]. Acta Automatica Sinica, 2015, 41(1): 122-135(in Chinese). doi: 10.16383/j.aas.2015.c140293
|
| [18] |
ESMZAD R, ESFANJANI M E. Modified likelihood Kalman filter for systems with incomplete, delayed and lost measurements[J]. System and Control Letters, 2018, 120: 23-28. doi: 10.1016/j.sysconle.2018.08.001
|
| [19] |
ESMZAD R, ESFANJANI M E. Bayesian filter for nonlinear systems with randomly delayed and lost measurements[J]. Automatica, 2019, 107: 36-42. doi: 10.1016/j.automatica.2019.05.025
|
| [20] |
张旭. 基于鲁棒自适应滤波的无人机编队相对导航方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2017: 56-58.
ZHANG X. Research on relative navigation method of UAV formation based on robust adaptive filtering [D]. Harbin: Harbin Institute of Technology, 2017: 56-58(in Chinese).
|
Figures(9) / Tables(3)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
