基于INT-VSMM算法的目标航迹跟踪和外推

任宣铭; 汤新民; 刘雨生; 鲁其兴

doi:10.13700/j.bh.1001-5965.2023.0724

基于INT-VSMM算法的目标航迹跟踪和外推

doi: 10.13700/j.bh.1001-5965.2023.0724

1.
南京航空航天大学民航学院，南京 211106
2.
中国民航大学交通科学与工程学院，天津 300300

基金项目:

国家重点研发计划(2021YFB1600500)；国家自然科学基金(61773202,52072174)；中国民航管理干部学院民航通用航空运行重点实验室开放基金(CAMICKFJJ-2019-04)；高端外国专家引进计划(G2023202003L)；天津市科技计划项目(24JCZDJC00090)

详细信息

通讯作者:
E-mail：tangxinmin@nuaa.edu.cn

中图分类号: V249
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出版历程
- 收稿日期: 2023-11-05
- 录用日期: 2023-12-11
- 网络出版日期: 2023-12-27
- 整期出版日期: 2026-01-31

Target trajectory tracking and extrapolation based on INT-VSMM algorithm

1.
College of Civil Aviation，Nanjing University of Aeronautics and Astronautics，Nanjing 211106，China
2.
School of Transportation Science and Engineering，Civil Aviation University of China，Tianjin 300300，China

Funds:

National Key Research and Development Program of China (2021YFB1600500); National Natural Science Foundation of China (61773202,52072174); Open Fund of the Key Laboratory of General Aviation Operations, Civil Aviation Management Institute of China (CAMICKFJJ-2019-04); High-End Foreign Experts Recruitment Program (G2023202003L); Tianjin Science and Technology Support Program (24JCZDJC00090)

More Information

Corresponding author: E-mail：tangxinmin@nuaa.edu.cn

摘要

摘要:
针对常规变结构多模型(VSMM)算法计算时间长，难以满足实时性的问题，通过广播式自动相关监视(ADS-B)捕获的目标状态和飞行意图信息作为模型先验信息，利用该先验信息以变结构多模型为理论框架，提出一种基于飞行意图的变结构多模型(INT-VSMM)算法。将航空器在航路飞行阶段的运动模式分解，建立完备的运动模型集;根据有向图切换原理，设计以“硬”切换为主，以“软”切换为辅的模型集切换算法；采用INT-VSMM算法对目标航空器的航迹进行跟踪，并根据目标状态估计进行了短期航迹外推。仿真结果表明:基于INT-VSMM算法的目标跟踪性能和计算时间均优于对比算法，外推轨迹在短期内误差较小，可以满足冲突探测需要。
- 变结构多模型 /
- 飞行意图 /
- 有向图切换 /
- 机动目标跟踪 /
- 航迹外推
Abstract:
In order to address the issue of the traditional variable structure multiple model (VSMM) algorithm's lengthy computation time and difficulty meeting real-time constraints, we developed the intent variable structure multiple model (INT-VSMM) algorithm. This algorithm uses the target state and flight intent data collected by automatic dependent surveillance-broadcast (ADS-B) as the model’s priori data, combining it with the VSMM theoretical framework. The motion pattern of the target in the flight phase of the flight path is decomposed, and a complete set of motion models is established. According to the principle of directed graph switching, a model set switching method is designed, which is mainly based on "hard" switching and supplemented by "soft" switching. The INT-VSMM algorithm is used to track the trajectory of the target aircraft, and short-term trajectory extrapolation is performed based on the target state estimation. According to the simulation results, the INT-VSMM algorithm outperforms the compared current approaches in terms of target tracking performance and computing time. Additionally, the extrapolated trajectory has a lower short-term inaccuracy, which can satisfy conflict detection requirements.
- variable structure multiple model /
- flight intention /
- digraph switching /
- maneuvering target tracking /
- trajectory extrapolation

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图 1 报文解析结果

Figure 1. Message analysis result

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图 2 有向图示意图

Figure 2. Schematic diagram of directed graph

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图 3 模型集切换原理图

Figure 3. Schematic diagram of directed graph

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图 4 本文算法流程

Figure 4. Flow of the proposed algorithm

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图 5 目标跟踪轨迹曲线

Figure 5. Curves of target tracking trajectory

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图 6 位置跟踪误差对比

Figure 6. Comparison of position tracking error

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图 7 速度跟踪误差对比

Figure 7. Comparison of velocity tracking error

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图 8 模型集随时间切换

Figure 8. Model set switching over time

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图 9 真实轨迹与外推轨迹曲线

Figure 9. Real trajectory and extrapolated trajectory curves

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图 10 外推轨迹误差

Figure 10. Error of extrapolated trajectory

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表 1 目标运动状态与模型子集的关系

Table 1. Relationship between target motion states and model sub-set

模型集U	运动模式	模型子集C_i
U₁	恒定高度直线飞行	C_ALNG、C_VLNG、C_SLNG、 C_ALAT、C_VLAT、C_SLAT
U₂	恒定高度转弯飞行	C_ALNG、C_TLNG、C_SLNG、 C_ALAT、C_TLAT、C_SLAT
U₃	恒定航向升降	C_ALNG、C_ALAT、C_AQNE、 C_SLNG、C_SLAT、C_SQNE
U₄	升降过程中转弯	C_TLNG、C_TLAT、C_VQNE、 C_SLNG、C_SLAT、C_SQNE

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表 2 模型初始参数

Table 2. Model initial parameters

模型集	模型子集	目标初始状态	初始模型概率	初始模型转移概率
U₁	经度方向$ {\boldsymbol{\alpha}} $	$ {\boldsymbol{\alpha}} _0 = {\left[ {{x_0},{{\dot x}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.3}&{0.4}&{0.3} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.1}&{0.1} \\ {0.1}&{0.8}&{0.1} \\ {0.1}&{0.1}&{0.8} \end{array}} \right] $
	纬度方向$ {\boldsymbol{\beta}} $	$ {\boldsymbol{\beta}} _0 = {\left[ {{y_0},{{\dot y}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.3}&{0.4}&{0.3} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.1}&{0.1} \\ {0.1}&{0.8}&{0.1} \\ {0.1}&{0.1}&{0.8} \end{array}} \right] $
	高度方向$ {\text{γ}} $
U₂	经度方向$ {\boldsymbol{\alpha}} $	$ {\boldsymbol{\alpha}} _0 = {\left[ {{x_0},{{\dot x}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.2}&{0.6}&{0.2} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.1}&{0.1} \\ {0.1}&{0.8}&{0.1} \\ {0.1}&{0.1}&{0.8} \end{array}} \right] $
	纬度方向$ {\boldsymbol{\beta}} $	$ {\boldsymbol{\beta}} _0 = {\left[ {{y_0},{{\dot y}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.2}&{0.6}&{0.2} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.1}&{0.1} \\ {0.1}&{0.8}&{0.1} \\ {0.1}&{0.1}&{0.8} \end{array}} \right] $
	高度方向$ {\text{γ}} $
U₃	经度方向$ {\boldsymbol{\alpha}} $	$ {\boldsymbol{\alpha}} _0 = {\left[ {{x_0},{{\dot x}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $
	纬度方向$ {\boldsymbol{\beta}} $	$ {\boldsymbol{\beta}} _0 = {\left[ {{y_0},{{\dot y}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $
	高度方向$ {\text{γ}} $	$ {\text{γ}} _0 = {\left[ {{h_0},{{\dot h}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\text{γ}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\text{γ}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $
U₄	经度方向$ {\boldsymbol{\alpha}} $	$ {\boldsymbol{\alpha}} _0 = {\left[ {{x_0},{{\dot x}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\alpha}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $
	纬度方向$ {\boldsymbol{\beta}} $	$ {\boldsymbol{\beta}} _0 = {\left[ {{y_0},{{\dot y}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\boldsymbol{\beta}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $
	高度方向$ {\text{γ}} $	$ {\text{γ}} _0 = {\left[ {{h_0},{{\dot h}_0},0,0} \right]^{\text{T}}} $	$ {\boldsymbol u}_i^{\text{γ}} = \left[ {\begin{array}{*{20}{c}} {0.5}&{0.5} \end{array}} \right] $	$ {\boldsymbol p}_{j\left\| i \right.}^{\text{γ}} = \left[ {\begin{array}{*{20}{c}} {0.8}&{0.2} \\ {0.1}&{0.9} \end{array}} \right] $

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表 3 算法位置和速度误差性能对比

Table 3. Performance comparison of algorithm position and velocity error

算法	最大位置跟踪误差/m	最大速度跟踪误差/(m·s⁻¹)	位置误差均值/m	速度误差均值/(m·s⁻¹)
IMM^[11]	502.212	75.984	44.692	13.077
VSMM^[21]	334.424	65.026	34.157	11.985
INT-VSMM	289.142	59.258	31.822	9.768

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表 4 轨迹跟踪仿真计算时间

Table 4. Simulation time of trajectory tracking

算法	计算时间/s
IMM^[11]	3.522
VSMM^[21]	4.900
INT-VSMM	4.308

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