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

摘要/Abstract

摘要：

针对空基外辐射源定位(airborne external transmitter location, AETL)系统的可观测性问题,建立了AETL系统的二维运动学模型与量测方程,基于离散化的非线性可观测理论求解系统的可观测矩阵,并分析证明了系统不可观测的条件。基于矩阵分析理论的条件数定义了系统的可观测度,并仿真分析了观测站运动参数以及目标和外辐射源的机动参数对系统可观测度的影响。结果表明,当观测站与目标和外辐射源共线或目标和外辐射源保持径向运动时系统不可观测;当系统可观测时,观测站与目标和外辐射源之间的相对速度越小,系统可观测度越大。研究结果可为观测站制定机动策略提高系统定位性能提供有效的参考依据。

关键词: 外辐射源定位, 可观测性分析, 非线性系统, 条件数

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

中图分类号:

TN95

卢雨, 周正. 空基外辐射源定位系统的可观测性分析[J]. 系统工程与电子技术, 2020, 42(6): 1241-1247.

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

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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