## 1 Introduction
Compared with filtering algorithms, such as EKF, UKF, and PF, CKF has better nonlinear performance, higher numerical accuracy, and better filter stability, and it is relatively simple to implement. However, when CKF is applied to a nonlinear system, it needs to know the mathematical model of the object to be studied and the prior knowledge of noise statistical properties. In practice, it is difficult to obtain the prior knowledge of the noises statistics. The inaccurate mathematical model and inaccurate noise statistics may lead to large state estimation error, or even divergence. To solve these problems, scholars further study the CKF technique combined with an adaptive filter. The typical research results are mainly divided into two types. The first types of typical results proposed are improved CKF algorithms based on the strong tracking filter (STF), which can be used to solve the filter divergence problem caused by inaccurate system models. Aiming at the problem of CKF precision degradation caused by model uncertainty, the literature [19] established a strong tracking CKF algorithm (STCKF). The literature [20] proposed a strong tracking adaptive CKF algorithm viewing STF as the basic theory framework and making D replace EKF, and the algorithm improved the filtering performance of the existing system model uncertainty. To overcome the outliers caused by the model uncertainties, the literature [21] designed a robust strong tracking CKF and developed a noise statistic estimator based on the principle of maximum a posterior. The CKF used in the above method are all three-degree algorithms. Further, to improve the estimation accuracy, [PERSON] and [PERSON] [22] proposed an improved high-degree CKF combined with the STF algorithm, named as the adaptive high-degree CKF (AH-CKF). In the AH-CKF, by introducing the STF into the high-degree CKF and modifying the predicted states' error covariance with a fading factor, the residual sequence is forced to be orthogonal so that the robustness of the filter and the capability to deal with uncertainty factors are improved. However, these results are only for research on low- and medium-dynamic applications. The second types of typical research results are improved CKF methods based on the robust M-estimation technique. [PERSON] (2018) proposed a class of robust CKF algorithms with statistical regression to solve the problem that the conventional CKF declines in accuracy and further diverges when the noise is not Gaussian noise. [PERSON] (2018) proposed a robust CKF based on generalized M-estimation to reduce the influence of measurement outliers on a target tracking system. Similarly, in order to address the degradation of the standard CKF due to outliers in measurement, [PERSON] _et al._ (2018) presented a robust version of CKF using [PERSON]'s M-estimation methodology and square-root filtering framework. Essentially, the above research results are all effective improvements to the standard CKF or square-root CKF using he robust M-estimation technique. The solved problem is the degradation or divergence of the standard CKF caused by the inaccuracy of measurement noise. However, these robust M-estimation methods cannot adjust the noise covariance adaptively when it does not match with the truth. The problem will become more severe in the case of significant outliers [PERSON] _et al._ (2018). To overcome this deficiency, [PERSON] and [PERSON] and [PERSON] (2018) came up with a new way and proposed an adaptive Huber's M-estimation-based CKF (AHCKF) which can automatically adjust the measurement noise and gain adaptivity. The AHCKF has enhanced outlier robustness, reliability, and high estimate accuracy. This method, however, does not consider the problem of when the model uncertainties exist. The above two types of improved CKF methods are developed respectively for the uncertainty of the model and the inaccuracy of measurement noise.