## 1 Introduction  
Bearings-only tracking [1, 2] uses a sequence of angle measurements to estimate the state (position and velocity) of the target and has universal applications in the field of navigation, especially in passive target tracking. For the system model of bearings-only tracking, the target state is generally built as the discrete time model for convenience. In addition, the angle measurement information for the target is discrete time. This is called the discrete-discrete time system model. However, considering the actual situation of target tracking, the target state is continuous in nature, and the measurement is discrete time. Such a system model is called the continuous-discrete time system [1]. Compared with the discrete-discrete system model, the continuous-discrete system model is closer to the real situation, and its solutions have more advantages, such as high accuracy [3]. Based on the continuous-discrete time system, continuous-discrete filtering, whose model is based on the covariance matrix of random errors, can be established. In [4], the cubature criterion was introduced into the continuous-discrete time system, and the continuous-discrete cubature Kalman filter (CD-CKF) algorithm was obtained. It uses stochastic differential equations (SDEs) to describe the continuous-time target state model, and the accuracy of the SDE solution greatly affects the filtering performance. In [5], [PERSON] summarized the Euler-Maruyama method based on 0.5 order and the Ito-Taylor method, which were proven to have acceptable accuracy. In order to further improve the accuracy of state estimation, high-order numerical approximation methods are used to deal with stochastic differential equations. In [6], [PERSON] described the continuous-time model as the form of its expectation and covariance and then solved the time prediction problem of the continuous model. In [7], the nested implicit Runge-Kutta method was used for the continuous-discrete extended Kalman filter (CD-EKF), and the corresponding application in CD-CKF was discussed in [8]. Subsequently, adaptive methods were proposed. In [9], [PERSON] et al. used adaptive step size to further improve the accuracy. The adaptive feedback strategy [10] reduced the impact of unpredictable errors in the prediction step by means of covariance adjustment; thus, the performance and efficiency were both improved. In the actual measurement environment, harsh conditions such as signal interference will cause non-Gaussian noise [11; 12] or outliers to appear. If they are not dealt with, the Gaussian-assumed filters will be inaccurate or even divergent. For this measurement uncertainty problem, various robust methods [13] are proposed for the discrete-discrete time filtering systems. As a method of modification, robust methods aim to improve robustness in the presence of outliers in the data. For instance, the [PERSON]'s \(M\)-estimation method [14; 15] used the robust cost function to reduce the weight of abnormal data. It is widely used and has proven effective in filtering problems [16]. [PERSON] et al. [17; 18] proposed a more practical robust CKF algorithm based on generalized \(M\)-estimation without the experience threshold of the weight function and statistical characteristics information of outliers. In [19], [PERSON] dealt with the time-varying noise with the variational Bayes criterion in the case of unknown noise covariance. In [20; 21; 22], the maximum correntropy criterion (MCC) was introduced into discrete-discrete filtering systems. The correntropy can utilize the higher-order information of the measurements instead of the second-order moment information of the minimum mean square error criterion, which is more suitable for non-Gaussian systems in the presences of non-Gaussian noise. The above robust methods are successfully used in the discrete-discrete time systems, but sufficient evaluation of the continuous-discrete time systems is not available.