## 4 Numerical Simulation  
To evaluate the performance of the proposed methods, the remote distance passive target tracking scenario [27] is considered. The motion model of the target is the coordinated turn, analyzing the performance changes of the four continuous-discrete robust algorithms proposed in this paper for data with Gaussian noise (Section 4.1), non-Gaussian noise (Section 4.2), or corrupted by outliers (Section 4.3). When considering random interference, coordinated turn motion is a typical nonlinear motion. The continuous-time motion model can be expressed by stochastic differential equation. The state vector of the target is \(\mathbf{x}(t)= \begin{bmatrix}\mathbf{x}(t)&\dot{x}(t)&y(t)&\dot{y}(t)&\omega\end{bmatrix} ^ {\mathrm{T}}\); \(x(t)\) and \(y(t)\), \(\dot{x}(t)\) and \(\dot{y}(t)\) are the position and velocity of the target in the Cartesian coordinate system, respectively; and \(\omega\) is a constant turn rate, which is 0.01 rad/s. The motion of single observer in the CA model with the initial state is \([0\mathrm{km},-0.025\mathrm{km/s},\,0\mathrm{km},\,0.02\mathrm{km/s}]^{ \mathrm{T}}\). The state equation of the system is \(\mathbf{F}(\mathbf{x}(t))= \begin{bmatrix}\dot{\mathbf{x}}(t),-\omega\dot{y}(t),\dot{y}(t),\omega\dot{x}(t),0\end{bmatrix} ^{\mathrm{T}}\). The random noise term is \(\mathbf{w}(t)=[w_{1}(t),w_{2}(t),w_{3}(t),w_{4}(t),w_{5}(t)]^{\mathrm{T}}\), where its increment and state are independent of each other. Initial covariance matrix \(\mathbf{Q}=\mathrm{diag}[0\quad\tau_{1}\quad 0\quad\tau_{1}\quad\tau_{2}]\), where \(\tau_{1}=\sqrt{2}\) and \(\tau_{2}=7\times 10^{-6}\). The initial state \(\mathbf{x}(t_{0})=[40\mathrm{km},\,0\mathrm{km/s},\,50\mathrm{km},\,0.2\mathrm{km/ s},\,0.01\mathrm{rad/s}]^{\mathrm{T}}\), and the initial covariance matrix \(\mathbf{P}(t_{0})=\mathrm{diag}[0.01\quad 0.01\quad 0.01\quad 0.01\quad 0]\). The measurement sampling interval is 1 min. The number of Monte Carlo simulations is 200. The experiment is based on the MATLAB simulation software with an Intel(R) Core (TM) i7-10750H CPU @ 2.60 GHz 2.59 GHz. Among them, the critical value of abnormal error discrimination in the HRSRCD-CKF algorithm is c = 1.345, the \(\alpha\) quantile of the chi-square distribution in the MRSRCD-CKF algorithm is \(\alpha_{1}=0.1\), \(\alpha_{2}=0.1\%\), the Gaussian kernel bandwidth \(\sigma\) in the RSRCD-MCCKF algorithm is selected according to the simulation scenarios, the initial parameters in the VBSRCD-CKF algorithm are \(v_{0}=600\), \(V_{0}=0.01\), \(\rho=1-\exp(-4)\), and the number of internal loops of the algorithm is \(\mathrm{M}=10\). The discrete-time nonlinear measurement model is  
\[\mathbf{z}_{k}= \begin{bmatrix}\tan^{-1}(y_{r}(t_{k})/x_{r}(t_{k}))\end{bmatrix} + \mathbf{r}_{k}, \tag{38}\]  
where \(x_{r}(t_{k})\) and \(y_{r}(t_{k})\) are the relative position of the target and the observer at time \(k\), \(\mathbf{r}_{k}\) is the measurement noise, and the specific expression form is defined according to the simulation scenarios. In order to evaluate the performance of filtering, the Root Mean Square Error (RMSE) of the position state and the velocity state are respectively defined as  
\[\mathrm{RMSE_{pos}}(t_{k})= \begin{pmatrix}\dfrac{1}{N}\sum\limits_{i=1}^{N} \
orm{x(t_{k})-\dot{x}^{i}(t_{k})}_{2}^{2}\end{pmatrix} ^{1/2}, \tag{39}\]  
\[\mathrm{RMSE_{vel}}(t_{k})= \begin{pmatrix}\dfrac{1}{N}\sum\limits_{i=1}^{N} \
orm{\dot{x}(t_{k})-\dot{x}^{i}(t_{k})}_{2}^{2}\end{pmatrix} ^{1/2}, \tag{40}\]where \(N\) is the number of Monte Carlo simulations, \(\hat{x}^{i}(t_{k})\) and \(\hat{x}^{i}(t_{k})\) are the results of the \(i\)-th Monte Carlo state estimation, and \(x(t_{k})\), \(\dot{x}(t_{k})\) are the true position state and velocity state of the target, respectively. The trajectory of target and observer is shown in Figure 1.  
As shown in Figure 1, the bearings-only tracking scenario is tracking a two-dimensional target that is moving in a coordinated turn at a constant turn rate. The observer is maneuvered to achieve observability.