空基外辐射源定位系统的可观测性分析

doi:10.3969/j.issn.1001-506X.2020.06.06

Abstract

Abstract:

Aiming at the observability of the airborne external transmitter location (AETL) system, the two-dimensional kinematics model and measurement equation of the AETL system are established. Based on the discretization nonlinear observable theory, the observable matrix of the system is solved and the unobservable conditions are proved and analyzed. The observability measure of the system is defined by the condition number based on the matrix analysis theory, and the influence of the motion parameters of the observer and the maneuvering parameters of the target and the external transmitter on the observability of the system is analyzed. The system is not observable when the observatory is collinear with the target and the external transmitter or when the target and the external transmitter are in radial motion state. When the system can be observed, the smaller the relative velocity between the observer and the target or the external transmitter, the greater the observable measurement of the system. The analysis results provide an effective reference for the observer to develop maneuver strategies to improve the location performance of the system.

Key words: external transmitter location, observability analysis, nonlinear system, condition number

CLC Number:

TN95

Yu LU, Zheng ZHOU. Observability analysis of airborne external transmitter location system[J]. Systems Engineering and Electronics, 2020, 42(6): 1241-1247.

Figures/Tables 7

Fig.1

Table 1

Fig.2

Table 2

Table 3

Table 4

Table 5

References 28

1	INGSS M . Passive coherent location as cognitive radar[J]. IEEE Aerospace and Electronic Systems Magazine, 2010, 25 (5): 12- 17. doi: 10.1109/MAES.2010.5486536
2	ZHANG C S, TANG X M, HE Y, et al. Passive bistatic radar target location method and observability analysis[M]//Electro-nics and Signal Processing. Berlin Heidelberg: Springer, 2011: 443-451.
3	GUO Y F , THARMARASA R , KIRUBARAJAN T , et al. Passive coherent location with unknown transmitter states[J]. IEEE Trans.on Aerospace and Electronic Systems, 2017, 53 (1): 148- 168. doi: 10.1109/TAES.2017.2649739
4	LEE T S, DUNN K P, CHANG C B. On observability and unbiased estimation of nonlinear systems[M]//System Modeling and Optimizatim. Berlin Heidelberg: Springer, 1981: 258-266.
5	周一宇, 孙仲康. 雷达被动探测定位的可观测性[J]. 电子学报, 1994, 22 (3): 51- 57. doi: 10.3321/j.issn:0372-2112.1994.03.009
	ZHOU Y Y , SUN Z K . Observability for radar passive detection and location[J]. Acta Electronica Sinica, 1994, 22 (3): 51- 57. doi: 10.3321/j.issn:0372-2112.1994.03.009
6	彭冬亮, 文成林, 薛安克. 多传感器多源信息融合理论及应用[M]. 西安: 西安电子科技大学出版社, 2010.
	PENG D L , WEN C L , XUE A K . Multi-sensor and multi-source information fusion theory and application[M]. Xi'an: Xidian University Press, 2010.
7	GOSHEN-MESKIN D , BAR-ITZHACK I Y . Observability analysis of piece-wise constant systems-part Ⅰ: theory[J]. IEEE Trans. Aerospace and Electronic Systems, 1992, 28 (4): 1056- 1067. doi: 10.1109/7.165367
8	GOSHEN-MESKIN D , BAR-ITZHACK I Y . Observability analysis of piece-wise constant systems-part Ⅱ: apply to inertial navigation in-flight alignment[J]. IEEE Trans.on Aerospace and Electronic Systems, 1992, 28 (4): 1068- 1075. doi: 10.1109/7.165368
9	JUNGERS R M , KUNDU A , HEEMELS W P M H . Observability and controllability analysis of linear systems subject to data losses[J]. IEEE Trans.on Automatic Control, 2018, 63 (10): 3361- 3376. doi: 10.1109/TAC.2017.2781374
10	LEE E B , MARKUS L . Foundations of optimal control theory[M]. New York: Wiley, 1967.
11	DENG X P , WANG Q , ZHONG D X . Observability of airborne passive location system with phase difference measurements[J]. Chinese Journal of Aeronautics, 2008, 21 (2): 149- 154. doi: 10.1016/S1000-9361(08)60019-9
12	ZHANG Y F, ZHANG M, GUO F C. Moving scanning emitter tracking by a single observer using time of interception: observability analysis and algorithm[J]. Chinese Journal of Aeronautics, 2017, 30(3): S100093611730078X.
13	YANG Y Q , ZHANG C X , LU J Z . Local observability analysis of star sensor installation errors in a SINS/CNS integration system for near-earth flight vehicles[J]. Sensors, 2017, 17 (12): 167- 180. doi: 10.3390/s17010167
14	YANG Y L , HUANG G Q . Observability analysis of aided INS with heterogeneous features of points, lines and planes[J]. IEEE Trans.on Robotics, 2019, 35 (6): 1399- 1418. doi: 10.1109/TRO.2019.2927835
15	齐昭, 王秋滢, 郭航航. 调制型捷联惯导系统可观测性分析及在线标定技术研究[J]. 系统工程与电子技术, 2014, 36 (5): 965- 972.
	QI Z , WANG Q Y , GUO H H . Observability analysis and research on the on-line calibration technology for modulated strapdown inertial navigation system[J]. Systems Engineering and Electronics, 2014, 36 (5): 965- 972.
16	ANTONELLI G, ARRICHIELLO F, CHIAVERINI S, et al. Observability analysis of relative localization for AUVs based on ranging and depth measurements[C]//Proc.of the International Conference on Robotics and Automation, 2010: 4276-4281.
17	崔平远, 常晓华, 崔祜涛. 基于可观测性分析的深空自主导航方法研究[J]. 宇航学报, 2011, 32 (10): 2115- 2124. doi: 10.3873/j.issn.1000-1328.2011.10.004
	CUI P Y , CHANG X H , CUI H T . Research on observability analysis-based autonomous navigation method for deep space[J]. Journal of Astronautics, 2011, 32 (10): 2115- 2124. doi: 10.3873/j.issn.1000-1328.2011.10.004
18	马朋, 张福斌, 徐德民, 等. 基于条件数的多自主水下航行器协同定位系统可观测度分析[J]. 兵工学报, 2015, 36 (1): 138- 143. doi: 10.3969/j.issn.1000-1093.2015.01.020
	MA P , ZHANG F B , XU D M , et al. Observability analysis of cooperative localization system for MAUV based on condition number[J]. Acta Armamentarii, 2015, 36 (1): 138- 143. doi: 10.3969/j.issn.1000-1093.2015.01.020
19	周伟江, 孙龙. 基于可观测性分析的SINS/CNS降维设计[J]. 计算机测量与控制, 2017, 25 (4): 143- 146.
	ZHOU W J , SUN L . Reduced dimension model of SINS/CNS based on observability analysis[J]. Computer Measurement & Control, 2017, 25 (4): 143- 146.
20	FEDOR B , JOHANN D . Observability analysis and concept of usage of air data attitude and heading reference systems[J]. Navigation, 2017, 64 (4): 427- 446. doi: 10.1002/navi.206
21	KING S , KANG W , XU L . Observability for optimal sensor locations in data assimilation[J]. International Journal of Dynamics and Control, 2015, 3 (4): 416- 424. doi: 10.1007/s40435-014-0120-7
22	MARTINELLI A . Nonlinear unknown input observability: extension of the observability rank condition[J]. IEEE Trans.on Automatic Control, 2019, 64 (1): 222- 237. doi: 10.1109/TAC.2018.2798806
23	ODAIR M , JUN S O F , EDUARDO A P , et al. Piezoelectric sensor location by the observability Gramian maximization using topology optimization[J]. Computational & Applied Mathematics, 2018, 37 (1): 237- 252.
24	WANG Y , ZHAO X B , PANG C L , et al. The influence of attitude dilution of precision on the observable degree and observability analysis with different numbers of visible satellites in a multi-antenna GNSS/INS attitude determination system[J]. IEEE Access, 2018, 6, 22156- 22164. doi: 10.1109/ACCESS.2018.2825338
25	MEZA A G , CORTES T H , LOPEZ A V C , et al. Analysis of fuzzy observability property for a class of TS fuzzy models[J]. IEEE Trans.on Latin America, 2017, 15 (4): 595- 602. doi: 10.1109/TLA.2017.7896343
26	KOLAR B, SCHÖBERL M. Symmetry groups and the observability of PDEs[C]//Proc.of the 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2018, 18(1): e201800019.
27	FELIPE S , ELDER H , WALDEMAR L F . On the error state selection for stationary SINS alignment and calibration Kalman filters-part Ⅱ: observability/estimability analysis[J]. Sensors, 2017, 17 (3): 439- 472. doi: 10.3390/s17030439
28	DIANETTI A D , WEISMAN R , CRASSIDIS J L . Observability analysis for improved space object characterization[J]. Journal of Guidance, Control, and Dynamics, 2017, 41 (3): 1- 12.

状态	情景1	情景2	情景3
(x, y)/km	(1 000, 1 000)	(1 000, 1 000)	(1 000, 1 000)
($\dot x, \dot y$)/(km/s)	(0.58, 0.58)	(0.58, 0.58)	(0.58, 0.58)
(x_t, y_t)/km	(500, 500)	(300, 700)	(500, 500)
(${{\dot x}_t}, {{\dot y}_t} $)/(km/s)	(0.27, 0.28)	(0.27, 0.28)	(0.28, 0.28)
(${{\dot x}_o}, {{\dot y}_o}$)/(km/s)	(0.25, 0.26)	(0.25, 0.26)	(0.25, 0.26)

情景	($\dot x, \dot y $)/(km/s)	($ {{\dot x}_t}, {{\dot y}_t} $)/(km/s)
情景1	(0.27, 0.29)	(0.28, 0.28)
情景2	(0.27, 0.29)	(0.42, 0.42)

情景	$ {{\dot x}_o} $/(km/s)	0.14	0.28	0.42	0.56
情景	$ {{\dot y}_o} $/(km/s)	0.14	0.28	0.42	0.56
情景1	C(Q)_max×10^-6	2.090	2.113	2.093	2.033
情景2	C(Q)_max×10^-6	2.028	2.091	2.113	2.094

情景	($\dot x, \dot y$)/(km/s)	(${{\dot x}_t}, {{\dot y}_t}$)/(km/s)	ω/(rad/s)	ω_t/(rad/s)
情景1	(0.28, 0.28)	(0.28, 0.28)	0.12	0.12
情景2	(0.28, 0.28)	(0.28, 0.28)	0.12	-0.12
情景3	(0.28, 0.28)	(0.28, 0.28)	-0.12	0.12
情景4	(0.28, 0.28)	(0.28, 0.28)	-0.12	-0.12
情景5	(0.28, 0.28)	(0.42, 0.42)	0.12	0.12

情景	${{\dot x}_o}$/(km/s)	0.14	0.28	0.42	0.56
情景	${{\dot y}_o}$/(km/s)	0.14	0.28	0.42	0.56
情景1	C(Q)_max×10^-4	1.307	1.330	1.354	1.379
情景2	C(Q)_max×10^-4	1.448	1.440	1.431	1.424
情景3	C(Q)_max×10^-4	1.443	1.454	1.466	1.480
情景4	C(Q)_max×10^-4	1.315	1.295	1.280	1.265
情景5	C(Q)_max×10^-4	1.307	1.329	1.354	1.378

Observability analysis of airborne external transmitter location system

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