Parameter identification of unmanned surface vehicle MMG model based on an improved extended Kalman filter

Table 1. Main parameters of unmanned surface vehicle
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Table 1. Main parameters of unmanned surface vehicle
参数数值参数数值
船长/m 11.00 型宽/m 3.20
吃水/m 0.63 质量/t 8.00

Table 2. EKF parameter identification results

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Table 2. EKF parameter identification results

参数	数值	参数	数值
$ {a'_1} $	−4.72×10−5	$ {a'_2} $	0.009 8
$ {a'_3} $	2.02×10−5	$ {a'_4} $	−0.001 5
$ {X'_{uu}} $	−0.457 8	${X'_{vv}}$	0.893 1
$ {X'_{vr}} $	0.199 6	${X'_{rr}}$	−0.082 7
$ {b'_1} $	1.90×10−4	$ {b'_2} $	−0.014 1
$ {b'_3} $	8.95×10−6	$ {b'_4} $	−7.89×10−4
$ {Y'_v} $	−0.376 2	${Y'_r}$	0.226 4
$ {Y'_{\left\| v \right\|v}} $	0.376 0	$ {Y'_{\left\| r \right\|r}} $	−0.099 6
${Y'_{vvr}}$	−1.653 8	${Y'_{vrr}}$	1.130 4
${c'_1}$	1.24×10−4	${c'_2}$	−0.006 7
${c'_3}$	7.96×10−6	${c'_4}$	−6.19×10−4
$ {N'_v} $	−0.014 6	${N'_r}$	−0.004 2
$ {N'_{\left\| v \right\|v}} $	0.008 2	$ {N'_{\left\| r \right\|r}} $	−0.008 7
${N'_{vvr}}$	−0.048 3	${N'_{vrr}}$	0.130 8

Table 3. Improved EKF parameter identification results

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Table 3. Improved EKF parameter identification results

参数	数值	参数	数值
$ {a'_1} $	−3.88×10−5	$ {a'_2} $	0.009 1
$ {a'_3} $	239×10−5	$ {a'_4} $	−0.001 9
$ {X'_{uu}} $	−0.447 0	${X'_{vv}}$	0.611 5
$ {X'_{vr}} $	0.293 2	${X'_{rr}}$	−0.100 6
$ {b'_1} $	1.94×10−4	$ {b'_2} $	−0.013 7
$ {b'_3} $	5.81×10−6	$ {b'_4} $	−5.45×10−4
$ {Y'_v} $	−0.285 0	${Y'_r}$	0.179 0
$ {Y'_{\left\| v \right\|v}} $	−2.205 4	$ {Y'_{\left\| r \right\|r}} $	−0.045 3
${Y'_{vvr}}$	−10.396 1	${Y'_{vrr}}$	−0.310 8
${c'_1}$	1.16×10−4	${c'_2}$	−0.006 1
${c'_3}$	8.82×10−6	${c'_4}$	−6.78×10−4
$ {N'_v} $	−0.015 1	${N'_r}$	−0.004 4
$ {N'_{\left\| v \right\|v}} $	0.024 9	$ {N'_{\left\| r \right\|r}} $	−0.007 4
${N'_{vvr}}$	−0.060 7	${N'_{vrr}}$	0.127 6

Table 4. Comparison of RMSE values of simulation data
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Table 4. Comparison of RMSE values of simulation data
u v r $ \psi $
EKF 0.194 2 0.153 4 1.245 7 12.788 4
改进EKF 0.176 9 0.124 5 0.996 3 10.351 2
相对误差/% −8.91 −18.84 −20.02 −19.06

Table 5. Comparison of SMAPE values of simulation data
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Table 5. Comparison of SMAPE values of simulation data
u v r $ \psi $
EKF 0.865 3 15.365 9 2.864 5 0.942 4
改进EKF 0.694 3 14.856 9 2.195 6 0.689 5
相对误差/% −19.76 −3.31 −23.35 −26.84

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Pengbo SUN, Zaopeng DONG, Wei LIU, Jinliang SHENG, Zhihao LI. Parameter identification of unmanned surface vehicle MMG model based on an improved extended Kalman filter[J]. Chinese Journal of Ship Research, 2025, 20(1): 38

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