Robust Gaussian Approximate Filter and Smoother with Colored Heavy Tailed Measurement Noise
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摘要: 为了解决带有色厚尾量测噪声的非线性状态估计问题，本文提出了新的鲁棒高斯近似（Gaussian approximate，GA）滤波器和平滑器.首先，基于状态扩展方法将量测差分后带一步延迟状态和白色厚尾量测噪声的非线性状态估计问题，转化成带厚尾量测噪声的标准非线性状态估计问题.其次，针对量测差分后模型中的噪声尺度矩阵和自由度（Degrees of freedom，DOF）参数未知问题，设计了新的高斯近似滤波器和平滑器，通过建立未知参数和待估计状态的共轭先验分布，并利用变分贝叶斯方法同时估计未知的状态、尺度矩阵、自由度参数.最后，利用目标跟踪仿真验证了本文提出的带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器的有效性以及与现有方法相比的优越性.
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关键词:
- 非线性状态估计 /
- 有色厚尾量测噪声 /
- 变分贝叶斯 /
- Student's t 分布 /
- 状态扩展方法
Abstract: In this paper, new robust Gaussian approximate (GA) filter and smoother are proposed to solve the problem of nonlinear state estimation with colored heavy tailed measurement noise. Firstly, the nonlinear state estimation problem with one-step delayed state and white heavy tailed measurement noise after measurement differencing is transformed into a standard nonlinear state estimation problem with heavy tailed measurement noise based on the state augmentation approach. Secondly, new GA filter and smoother are designed for the problem of unknown scale matrix and degrees of freedom (DOF) parameter of noise of the model after measurement differencing. The state, scale matrix and DOF parameter are estimated simultaneously by building the conjugate prior distributions for unknown parameters and estimated state and using variational Bayesian approach. Finally, the efficiency and superiority of the proposed robust GA filter and smoother with colored heavy tailed measurement noise, as compared with existing method, are shown in the simulation of target tracking. -
图 1 高斯分布、Student's t 分布、野值干扰导致的厚尾非高斯分布示意图
Fig. 1 Diagrams of Gaussian distribution,Student's t distribution and heavy tailed non-Gaussian distribution induced by outlier interference
图 3 尺度矩阵 R 和自由度参数 $\nu$ 的滤波估计
Fig. 3 The filtering estimations of scale matrix R and degree of freedom parameter $\nu$
图 7 当$\phi=0.1,0.2,\cdots,0.9$时,不同方法的位置ARMSE
Fig. 7 ARMSEs of the position of different methods when $\phi=0.1,0.2,\cdots,0.9$
图 8 当$\phi=0.1,0.2,\cdots,0.9$时,不同方法的速度ARMSE
Fig. 8 ARMSEs of the velocity of different methods when $\phi=0.1,0.2,\cdots,0.9$
图 9 当$\phi=0.1,0.2,\cdots,0.9$时,不同方法的转弯速率ARMSE
Fig. 9 ARMSEs of the turn rate of different methods when $\phi=0.1,0.2,\cdots,0.9$
图 10 当p = 0.05, 0.1,…, 0.3 时, 不同方法的位置ARMSE
Fig. 10 ARMSEs of the position of different methods when p = 0.05, 0.1,…, 0.3
图 11 当$p = 0.05, 0.1,…, 0.3 时,不同方法的速度ARMSE
Fig. 11 ARMSEs of the velocity of different methods when p = 0.05, 0.1,…, 0.3
图 12 当p = 0.05, 0.1,…, 0.3 时,不同方法的\\转弯速率ARMSE
Fig. 12 ARMSEs of the turn rate of different methods when p = 0.05, 0.1,…, 0.3
图 13 当N = 1, 2,…,10时,不同方法的位置ARMSE
Fig. 13 ARMSEs of the position of different methods when N = 1, 2,…,10
图 14 当N = 1, 2,…,10时,不同方法的速度ARMSE
Fig. 14 ARMSEs of the velocity of different methods when N = 1, 2,…,10
图 15 当N = 1, 2,…,10时,不同方法的转弯速率ARMSE
Fig. 15 ARMSEs of the turn rate of different methods when N = 1, 2,…,10
表 1 5种初值选取
Table 1 Five choices of initial values
u0 U0 a0 b0 初值1 4 ∑0 5 1 初值2 4 ∑0 10 1 初值3 4 ∑0 1 1 初值4 4 5∑0 5 1 初值5 4 0:5∑0 5 1 
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表 2 提出的CKF和CKS在不同初值下的位置ARMSE、速度ARMSE、转弯速率ARMSE
Table 2 ARMSEs of position,velocity,and turn rate from the proposed CKF and CKS under different initial values
位置ARMSE(m) 速度ARMSE(m/s) 转弯速率ARMSE(Deg/s) 提出的CKF(初值1) 30.5676 13.4203 1.3568 提出的CKF(初值2) 30.7507 13.4447 1.3639 提出的CKF(初值3) 32.0552 13.7149 1.3736 提出的CKF(初值4) 30.8171 13.4256 1.3649 提出的CKF(初值5) 31.1468 13.5550 1.3702 提出的CKS(初值1) 18.0328 4.8804 0.6006 提出的CKS(初值2) 17.8937 4.8634 0.5996 提出的CKS(初值3) 18.4848 4.9462 0.6041 提出的CKS(初值4) 17.9099 4.8710 0.5999 提出的CKS(初值5) 18.2740 4.9138 0.6024
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