## 1 Introduction  
The adhesion of marine organisms to the anchor chain can significantly reduce its weight support capability. Furthermore, the secretions from these organisms can speed up the corrosion of the steel structure. To ensure proper weight support and extend the lifespan of the steel structure, frequent underwater cleaning of the anchor chain is necessary. This cleaning must adhere to safety regulations set forth by the classification society and the operation area. Given the complexity of the underwater environment, the cleaning process requires a specialized ROV. This type of ROV is strongly coupled and strongly nonlinear [1; 2; 3]. Therefore, the ROV's control accuracy is essential in ensuring that it runs normally. To calculate the current state of the ROV using a series of filtering and data fusion algorithms, state estimation is adopted, which plays a critical role in the control of the ROV. It serves as the intermediary layer between sensor measurement and controller calculation. By using a series of filtering and data fusion algorithms, the current state of the ROV can be accurately calculated. This information can then be used to improve the accuracy of the controller, creating a closed loop that enhances the ROV's performance. Many scholars have carried out a lot of work on the state estimation algorithm. The Kalman filter [4] has been widely used in the model-driven state estimation method because of how straightforward and easy it is to use. Standard Kalman filter theory only applies to linear systems; however, in engineering applications, the system is typically nonlinear. [PERSON] and [PERSON] proposed the extended Kalman filter (EKF) [5], [PERSON] et al. [6] proposed an EKF-based adaptive object tracking method for AUV state estimation, [PERSON] et al. [7] designed a tracking controller based on feedback linearization by using EKF to estimate the state of UVMS, and [PERSON] et al. [8] implemented the adaptive control of UVMSs using EKF to estimate system state and forecast external disturbances, but EKF ignores the high-order terms of the nonlinear system, lowering the estimation accuracy [9]. The original filtering method has been enhanced with further research [10]. The other two frequently used filtering techniques are unscented Kalman filtering (UKF) [11] and the cubature Kalman filter (CKF) [12]. UKF uses a series of sigma points to propagate the state and covariance matrix [13]. CKF calculates the integral; unlike UKF, CKF uses a 2n cubature point propagation state and covariance matrix. When using an identical matrix factorization method, such as the Cholesky method, CKF has a lower calculation burden than UKF and has better stability and higher precision [14]. [PERSON] et al. [15] designed an augmented state cubature Kalman filter to improve the stability of the long-range navigation of surface ships. When the system noise cannot be approximated as a Gaussian noise distribution, the estimation accuracy of the Kalman filter decreases. In this case, a numerical approximation method, the particle filter, is needed [16]. By using a Monte Carlo simulation, a huge number of particles are created, and the distribution of these particles is utilized to estimate the probability distribution of states. Particle filters are used in research [17] to complete attitude estimation during the UAV landing procedure; a particle filter based on multi-model interaction [18] was presented to address the issue of estimating the performance of several rotors, and it minimizes the estimate error when compared to EKF. The correlation filter [19], which combines particle filters and correlation filters, performs well in state estimation; [PERSON] and [PERSON] [20] proposed a particle filter based on color distribution for object tracking, which increased the tracking accuracy by addressing the issue of object tracking illumination changes and occlusion.