EKF 和 UKF 算法在双观测站纯方位目标跟踪中的应用

成春彦; 李亚安

doi:10.11993/j.issn.2096-3920.202203014

EKF 和 UKF 算法在双观测站纯方位目标跟踪中的应用

doi: 10.11993/j.issn.2096-3920.202203014

西北工业大学航海学院, 陕西西安, 710072

基金项目: 国家自然科学基金项目资助(11874302).

详细信息

作者简介:
成春彦(1996-), 男, 在读硕士, 主要研究方向为水下目标跟踪

中图分类号: TJ630.1; U764.7
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- 被引次数: 0
出版历程
- 收稿日期: 2022-03-28
- 修回日期: 2022-05-24
- 网络出版日期: 2022-07-25

Applications of EKF and UKF Algorithms in Bearings-only Target Tracking with a Double Observation Stations

School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

摘要

摘要: 为了对水下运动目标进行实时跟踪, 以静止双观测站纯方位跟踪系统为研究对象, 分别结合扩展卡尔曼滤波(EKF)算法和无迹卡尔曼滤波(UKF)算法的原理, 对基于EKF和UKF算法的双观测站纯方位跟踪系统进行了仿真分析及比较。结果表明, 基于2种算法的双观测站纯方位系统都能适用于水下运动目标实时跟踪, 但后者具有更快的收敛速度和更好的鲁棒性。同时, 分别分析了双站距离和方位角量测误差对实时跟踪效果的影响, 仿真结果表明, 2个观测站距离过近或过远都会降低目标跟踪的效果, 基于EKF和UKF算法的双观测站系统在两站距离800 m时都能得到较满意的跟踪效果; 随着方位角量测误差的增大, 基于2种算法的双观测站系统的跟踪性能都会下降, 但UKF算法在EKF算法跟踪失效时仍然具有较好的跟踪性能。
- 水下运动目标 /
- 双观测站 /
- 纯方位目标跟踪 /
- 扩展卡尔曼滤波 /
- 无迹卡尔曼滤波
Abstract: For tracking underwater moving targets in real time, a bearings-only tracking system with a stationary double observation station was investigated. By combining the extended Kalman filter(EKF) algorithm and the unscented Kalman filter(UKF) algorithm, the bearings-only tracking system based on the EKF and UKF algorithms was simulated and compared. The results demonstrated that the double observation station system based on the two algorithms can be applied to real-time tracking of underwater moving targets, but the latter shows faster convergence and better robustness. The influence of the distance between the two stations and bearings measurement error on the real-time tracking effect was also analyzed. Simulation results showed that the effect of target tracking is reduced if the distance between the two observation stations is too small or too large. The double observation stations system based on EKF and UKF algorithms can achieve satisfactory tracking results when the distance between the two stations is 800 m; with the increase in the bearing measurement error, the tracking performance of the double observation stations system based on the two algorithms decreases, but the UKF algorithm still exhibits better tracking performance when the EKF algorithm fails to track.
- underwater moving target /
- double observation stations /
- bearings-only target tracking /
- extended Kalman filter /
- unscented Kalman filter

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图 1 目标与观测站几何态势

Figure 1. Geometrical situation between target and observation stations

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图 2 R = 1°时EKF和UKF目标跟踪航迹图

Figure 2. Target tracking trajectory of EKF and UKF with R = 1°

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图 3 R = 1°时EKF和UKF目标位置RMSE

Figure 3. RMSE of position of EKF and UKF with R = 1°

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图 4 R = 1°时EKF和UKF目标速度RMSE

Figure 4. RMSE of velocity of EKF and UKF with R = 1°

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图 5 EKF位置RMSE平均值折线图

Figure 5. Curves of average of position RMSE with EKF

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图 6 EKF速度RMSE平均值折线图

Figure 6. Curves of average of velocity RMSE with EKF

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图 7 UKF位置RMSE平均值折线图

Figure 7. Curves of average of position RMSE with UKF

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图 8 UKF速度RMSE平均值折线图

Figure 8. Curves of average of velocity RMSE with UKF

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图 9 R = 4°时EKF和UKF目标跟踪航迹

Figure 9. Target tracking trajectory of EKF and UKF with R = 4°

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图 10 R = 4°时EKF和UKF位置和速度RMSE

Figure 10. Position and velocity RMSE of EKF and UKF with R = 4°

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图 11 不同方位角量测误差时EKF和UKF位置平均RMSE

Figure 11. Position average RMSE in EKF and UKF with different bearing measurement errors

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图 12 R = 8°时EKF和UKF目标跟踪航迹

Figure 12. Target tracking trajectory of EKF and UKF with R = 8°

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图 13 R = 8°时EKF和UKF位置和速度RMSE

Figure 13. Position and velocity of RMSE in EKF and UKF with R = 8°

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表 1 EKF位置RMSE平均值

Table 1. Average of position RMSE with EKF

两站距离 /m	x方向位置平均RMSE/m	y方向位置平均RMSE/m	位置平均 RMSE/m
100	41.35	14.34	43.78
200	35.96	17.42	40.00
300	31.91	17.43	36.40
400	28.22	16.05	32.51
500	26.41	16.76	31.29
600	25.79	16.11	30.41
700	20.58	17.24	26.85
800	19.68	15.50	25.05
900	18.54	17.75	25.71
1 000	20.58	19.44	28.32
1 100	19.42	17.70	26.29
1 200	22.57	18.79	29.37
1 300	30.29	21.73	37.28
1 400	33.90	22.45	40.66
1 500	33.51	20.64	39.36

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表 2 EKF速度RMSE平均值

Table 2. Average of velocity RMSE with EKF

两站距离/m	x方向速度平均RMSE/(m/s)	y方向速度平均RMSE/(m/s)	速度平均 RMSE/(m/s)
100	0.119 3	0.247 6	0.274 9
200	0.142 2	0.259 4	0.295 8
300	0.150 8	0.256 2	0.297 3
400	0.151 5	0.247 7	0.290 4
500	0.161 5	0.238 4	0.288 0
600	0.161 9	0.225 0	0.277 3
700	0.179 5	0.229 4	0.291 3
800	0.180 3	0.207 4	0.274 8
900	0.200 8	0.213 5	0.293 1
1 000	0.215 5	0.212 9	0.303 0
1 100	0.215 8	0.189 2	0.287 1
1 200	0.230 6	0.182 2	0.291 3
1 300	0.252 1	0.198 8	0.321 0
1 400	0.261 8	0.195 4	0.326 7
1 500	0.261 6	0.172 5	0.313 5

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表 3 UKF位置RMSE平均值

Table 3. Average of the position RMSE with UKF

两站距离/m	x方向位置平均RMSE/m	y方向位置平均RMSE/m	位置平均RMSE/m
100	32.43	10.41	34.06
200	31.05	10.49	32.81
300	28.88	11.78	31.29
400	26.30	11.96	28.89
500	26.22	12.08	28.90
600	19.85	12.32	23.37
700	20.62	13.02	24.40
800	18.27	12.47	22.11
900	18.32	12.98	22.45
1000	20.78	14.04	25.10
1100	21.47	14.32	25.81
1200	23.78	15.75	28.52
1300	31.27	16.78	35.50
1400	32.42	18.56	37.36
1500	33.73	19.19	38.81

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表 4 UKF速度RMSE平均值

Table 4. Average of velocity RMSE with UKF

两站距离/m	x方向速度平均RMSE/(m/s)	y方向速度平均RMSE/(m/s)	速度平均 RMSE/(m/s)
100	0.160 6	0.205 6	0.260 9
200	0.167 9	0.208 0	0.275 6
300	0.169 0	0.204 1	0.276 3
400	0.151 1	0.228 9	0.274 3
500	0.165 8	0.223 5	0.278 3
600	0.175 3	0.222 7	0.283 5
700	0.186 9	0.222 4	0.281 3
800	0.173 0	0.207 1	0.269 9
900	0.193 0	0.200 9	0.278 5
1000	0.212 7	0.203 2	0.294 3
1100	0.229 5	0.197 1	0.302 7
1200	0.230 3	0.184 2	0.295 2
1300	0.251 1	0.178 2	0.308 1
1400	0.260 7	0.192 7	0.324 2
1500	0.260 4	0.151 9	0.301 5

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表 5 不同方位角量测误差时EKF位置平均RMSE

Table 5. Average of position RMSE with different bearing measurement errors in EKF

R/(°)	x方向位置平均RMSE/m	y方向位置平均RMSE/m	位置平均 RMSE/m
1	20.05	16.93	26.26
2	38.05	29.05	47.95
3	60.64	40.20	72.84
4	71.30	47.15	85.48
5	78.07	56.53	96.39
6	92.78	66.90	114.50
7	116.67	78.82	140.97
8	131.07	86.97	157.40
9	137.30	99.63	170.10
10	139.63	108.20	176.64

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表 6 不同方位角量测误差时EKF速度平均RMSE

Table 6. Average of velocity RMSE with different bearing measurement errors in EKF

R/(°)	x方向速度平均RMSE/(m/s)	y方向速度平均RMSE/(m/s)	速度平均 RMSE/(m/s)
1	0.187 0	0.219 6	0.287 5
2	0.200 7	0.309 0	0.368 2
3	0.211 1	0.348 5	0.408 0
4	0.212 4	0.3685	0.425 3
5	0.242 6	0.402 5	0.470 0
6	0.262 5	0.413 6	0.490 2
7	0.290 8	0.414 5	0.506 7
8	0.297 7	0.421 7	0.516 2
9	0.335 0	0.490 0	0.594 2
10	0.336 8	0.512 3	0.613 1

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表 7 不同方位角量测误差时UKF位置平均RMSE

Table 7. Average of position RMSE with different bearing measurement errors in UKF

R/(°)	x方向位置平均RMSE/m	y方向位置平均RMSE/m	位置平均RMSE/m
1	18.48	12.67	22.41
2	35.35	19.97	40.62
3	42.80	29.55	51.78
4	55.65	35.24	65.87
5	61.44	41.87	74.35
6	65.60	46.47	80.39
7	68.42	56.48	88.72
8	73.69	59.42	94.67
9	87.07	64.40	108.30
10	93.47	71.74	117.83

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表 8 不同方位角量测误差时UKF速度平均RMSE

Table 8. Average of velocity RMSE with different bearing measurement error in UKF

R/(°)	x方向速度平均RMSE/(m/s)	y方向速度平均RMSE/(m/s)	速度平均 RMSE/(m/s)
1	0.172 5	0.203 3	0.266 6
2	0.180 5	0.226 6	0.289 7
3	0.216 8	0.236 7	0.321 0
4	0.200 8	0.226 5	0.302 7
5	0.204 7	0.240 2	0.315 6
6	0.196 7	0.261 2	0.327 2
7	0.205 5	0.269 9	0.339 6
8	0.231 9	0.268 5	0.354 6
9	0.258 3	0.304 2	0.402 2
10	0.263 1	0.329 1	0.421 7

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