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摘要:
针对纯方位目标跟踪中测量噪声协方差未知和非高斯测量噪声突变问题，提出了一种平方根连续-离散变分贝叶斯最大相关熵容积卡尔曼滤波（SRCD-VBMCCKF）算法。将目标跟踪模型建立为连续状态空间-离散测量空间模型，提高了目标跟踪的解算精度；由变分贝叶斯准则对未知的时变测量噪声进行估计，提升了算法的自适应性；考虑到测量中出现的非高斯突变噪声，由最大相关熵准则构建抗差因子，进一步增强了算法对异常测量值的鲁棒能力。仿真结果表明：所提算法能够对测量中的未知时变噪声和非高斯重尾突变噪声有效抑制，且相比于传统滤波算法，所提算法兼具自适应性和鲁棒性。
Abstract:To address the problems of unknown covariance of measurement noise and non-Gaussian mutation measurement noise in bearings-only target tracking, a square-root continuous-discrete variational Bayesian maximum correntropy cubature Kalman filter (SRCD-VBMCCKF) algorithm is proposed. Firstly, the target tracking model is established as a continuous state space-discrete measurement space model, which improves the accuracy of target tracking; secondly, the unknown time-varying measurement noise is estimated by the variational Bayes criterion, which improves the adaptability of the algorithm; finally, considering the non-Gaussian mutation noise in the measurement, the robustness factor is constructed by the maximum correntropy criterion, which further enhances the algorithm’s robustness to abnormal measurements. The simulation results show that the proposed algorithm can effectively suppress the unknown time-varying noise and non-Gaussian heavy-tail mutation noise in the measurement. Compared with the traditional filtering algorithm, the proposed algorithm is both adaptive and robust.
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图 2 未知时变噪声下各算法的${e_{{\text{RMSEpos}}}}$
Figure 2. ${e_{{\text{RMSEpos}}}}$ of each algorithm under unknown time-varying noise
图 3 未知时变噪声下各算法的${e_{{\text{RMSEvel}}}}$
Figure 3. ${e_{{\text{RMSEvel}}}}$ of each algorithm under unknown time-varying noise
图 4 非高斯突变噪声下各算法的${e_{{\text{RMSEpos}}}}$
Figure 4. ${e_{{\text{RMSEpos}}}}$ of each algorithm under non-Gaussian outlier noise
图 5 非高斯突变噪声下各算法的${e_{{\text{RMSEvel}}}}$
Figure 5. ${e_{{\text{RMSEvel}}}}$ of each algorithm under non-Gaussian outlier noise
图 6 叠加噪声下各算法的${e_{{\text{RMSEpos}}}}$
Figure 6. ${e_{{\text{RMSEpos}}}}$ of each algorithm under superimposed noise
图 7 叠加噪声下各算法的${e_{{\text{RMSEvel}}}}$
Figure 7. ${e_{{\text{RMSEvel}}}}$ of each algorithm under superimposed noise
表 1 异常突变值设置点
Table 1. Set points of outliers
时间/s 测量噪声 150 10$ \boldsymbol{R}_k $ 200 5$ \boldsymbol{R}_k $ 230 15$ \boldsymbol{R}_k $ 250 20$ \boldsymbol{R}_k $ 300 30$ \boldsymbol{R}_k $ 
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