Strong tracking CKF adaptive interactive multiple model tracking algorithm based on hypersonic target
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摘要:
高超目标运动状态复杂且具有高机动性，传统的交互多模型(IMM)跟踪精度低、收敛速度慢，基于此，提出了一种基于多重渐消因子的强跟踪容积卡尔曼滤波(CKF)自适应交互多模型(AIMM)跟踪算法。以IMM-CKF算法为基础，通过对CKF算法的结构进行分析，在时间更新和量测更新的协方差矩阵中引入强跟踪算法的渐消因子，在线实时调整滤波增益，减小模型不匹配导致的滤波精度下降；在IMM的模型集中选择Singer模型、“当前”统计模型和Jerk模型，并针对模型扩维导致CKF算法中无法 Cholesky分解的问题引入奇异值分解(SVD)算法；对IMM算法中马尔可夫矩阵提出自适应算法，通过模型似然函数值对转移概率进行自适应修正，增强匹配模型所占比例。仿真结果表明：所提算法跟踪收敛速度提高了约37.5%，跟踪精度提高了16.51%。
Abstract:Hypersonic targets have complex motion states and high maneuverability. The conventional interactive multiple model (IMM) technique converges slowly and tracks poorly. Based on numerous fading variables, an adaptive interactive multiple model (AIMM) algorithm with strong tracking for cubature Kalman filter (CKF) is proposed. The structure of CKF is examined based on IMM-CKF, and the fading factor of the strong tracking algorithm is added to the covariance matrix of time updating and measurement updating. This allows for the online and real-time adjustment of the filter gain, which can lessen the decrease in filter accuracy brought on by model mismatch. Choose the Singer, ‘current’ and Jerk models from the IMM model collection. These models introduce singular value decomposition (SVD) decomposition as a solution to the issue that the model dimension expansion prevents Cholesky decomposition in CKF. An adaptive algorithm for Markov matrix in IMM algorithm is proposed. The transition probability is adaptively modified by the value of the model likelihood function to enhance the proportion of the matching model. Simulation results show that the proposed algorithm improves tracking convergence speed by 37.5% and tracking accuracy by 16.51%.
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图 7 渐消因子算法位置均方根误差
Figure 7. Root mean square error of position of fading factor algorithm
图 12 Jerk模型位置增益矩阵迹值变化
Figure 12. Change of trace value of position gain matrix of Jerk model
表 1 仿真初始参数设置
Table 1. Simulation initial parameter settings
参数 数值 仿真步长/s 1 弱化因子 1 遗忘因子 0.95 采样时长/s 350 初始模型概率 ${\boldsymbol{u}} = \left[ {\begin{array}{*{20}{c}} {1/3}&{1/3}&{1/3} \end{array}} \right]$ 马尔可夫转移矩阵 $ {{\boldsymbol{P}}_{\text{m}}} = \left[{\begin{array}{*{20}{c}} 0.9&0.05&0.05 \\ 0.05&0.9&0.05 \\ 0.05&0.05&0.9 \\ \end{array}}\right] $ 状态误差协方差矩阵 $ {\boldsymbol{Q}} = {\text{diag}}\left( {{{100}^2}}, {{{100}^2}}, {{{100}^2}} \right) $ 观测噪声协方差矩阵 $ {\boldsymbol{R}} = {\text{diag}}\left( {{{0.5}^2}}, {{{0.5}^2}}, {{{500}^2}} \right) $ 初始误差协方差矩阵 $\begin{gathered} {\boldsymbol{P}} = {\text{diag}}\left({5\;000^2},{ {3\;00}}{{ {0}}^2}{ {,10}}{{ {0}}^2}{ {,}}{5\;000^2},\right. \\ \qquad \left. { {3\;00}}{{ {0}}^2}{ {, }} { {10}}{{ {0}}^2}{ {,}}{5\;000^2}{ {, 3\;00}}{{ {0}}^2}{ {,10}}{{ {0}}^2}\right) \\ \end{gathered} $ 
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表 2 3种算法均方根误差均值对比
Table 2. Comparison of mean values of root mean square error of three algorithms
算法 位置均方根误差均值/m 速度均方根误差均值/(m·s−1) x轴 y轴 z轴 整体 x轴 y轴 z轴 整体 IMM-CKF 449.2 213.7 164 537.3 52.7 56.2 51.9 104.1 IMM-STCKF 447.9 207 158.2 530.2 37.9 56.3 49.5 92.7 AIMM-STCKF 381.9 171.3 97.1 448.6 19.4 27.7 41.4 66.9
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