Time-to-go Estimation Method for Anti-ship Missiles with Large Lead Angle in Three-dimensional Space

doi:10.12382/bgxb.2023.0613

Abstract

Abstract:

To solve the problem of large initial lead angle or significant change in lead angle when missile terminal guidance starts, a 3D time-to-go(TGO)estimation method for lead angle is designed for various missile guidance laws. The missile velocity and target velocity projections are decomposed to establish the relationship equations of relative motion between missile and target on Oxy and Oxz surfaces of ground coordinate system. Based on this, a three-dimensional missile-target relative motion model is established. A first-order nonlinear differential equation is established by using the relative motion equation and proportional navigation control equation of missile and target. The relationship between missile-target distance and lead angle is analyzed. The first-order nonlinear differential equation is solved by using McLaughlin formula. An appropriate inner frame angle is selected based on the change in line-of-sight angular velocity to compensate for the lead angle, and the median average filtering method is used to reduce the error caused by the fluctuation of lead angle. The simulation experiments are conducted by using the proposed three-dimensional missile-target relative motion model. The simulated results show that, when the small angle assumption cannot be established, especially when the angle control of guidance law results in significant changes in the lead angle, the convergence time and maximum error value of estimated error of the lead angle TGO estimation method are smaller than those of other TGO estimation methods.

Key words: anti-ship missile, lead angle, guidance law, time-to-go estimation, maneuvering target

CLC Number:

WU Hao, LI Dongguang, WANG Yong’an. Time-to-go Estimation Method for Anti-ship Missiles with Large Lead Angle in Three-dimensional Space[J]. Acta Armamentarii, 2024, 45(5): 1449-1459.

Figures/Tables 14

Fig.1 Relative movement relationship between missile and target

Fig.2 Missile-target motion trajectory of APNG

Fig.3 Lead angle of APNG

Fig.4 TGO estimated error of APNG

Fig.5 TGO estimated error of APNG (without median value average filtering method)

Table 1 APNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现时间/s
TGO1	72.23	-1	47.56	0.02
TGO2	71.64	-1	39.98	0.02
TGO3	32.73	1	32.49	0.01
TGO4			25.88	0.01

Fig.6 Missile-target motion trajectory of BPNG

Fig.7 Lead angle of BPNG

Fig.8 TGO estimated error of BPNG

Table 2 BPNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现的时间/s
TGO1	88.39	-1.00	44.08	14.61
TGO2	84.12	-1.00	38.07	15.43
TGO3	16.93	1.00	38.55	0.01
TGO4	7.60	0.99	31.94	0.01

Fig.9 Missile-target motion trajectory of OGL

Fig.10 Lead angle of OGL

Fig.11 TGO estimated error of OGL

Table 3 BPNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现的时间/s
TGO1	81.73	-1	45.35	0.02
TGO2	78.52	-1	37.77	0.02
TGO3	26.31	1	34.7	0.01
TGO4	14.40	1	28.09	0.01

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