## 5 Experimental and Analysis
### Results and Discussion
#### 5.2.3 Sea State Degree: 3  
A sea state of 3 represents the maximum sea state in which an ROV can operate effectively. Beyond this level, the use of an ROV is not recommended. In such challenging environments, the benefits of the improved algorithm become apparent. Moreover, when the sea surface is affected by slight waves and a gentle breeze, the measurement noise follows a non-Gaussian distribution, \(v_{K}\sim 0.1N(0,R_{1})+0.9N(0,150*R_{2})\), \(R_{1}=diag[0.4,0.3,0.3,0.4],R_{2}=diag[0.2,0.2,0.1,0.003]\). In Figures 9 and 10, it is evident that the estimation error of the CKF algorithm increases as the sea state level rises and the external noise becomes more complex. The filter exhibits multiple divergences in these scenarios. Specifically, when estimating the \(Z\)-axis displacement and bow angle, the CKF algorithm's error is even larger than that of the PF algorithm, which suffers from particle degradation and multiple outliers in the estimation due to its inability to consider the latest measurement information. Moreover, the complexity of the noise model makes it difficult to approximate the mixed Gaussian noise using only a single Gaussian distribution. The CPF algorithm's error starts to increase when estimating the \(X\)-axis displacement after T \(>\) 100 s, and when estimating the \(Y\)-axis displacement after T \(>\) 40 s, indicating that CPF cannot guarantee estimation accuracy over a long time. On the other hand, the algorithm proposed in this paper not only has no outliers, but also avoids divergence in long-term estimates, while significantly improving the accuracy compared to other algorithms. Table 3 and Figures 11 and 12 demonstrate that the RMSE values of \(x,y,z,\psi\) attitudes can be found. 1. In sea state degree 0, the particle filtering has a maximum RMSE in all four attitudes due to the appearance of particle degeneracy. The CKF algorithm performs better than the particle filtering algorithm in a Gaussian noise environment. CPF reduces particle degradation after importance density sampling with CKF, and the estimation accuracy is improved by \(55.37\%,49.35\%,82.06\%,40.41\%\) in \(x,y,z,\psi\) compared to particle filtering, respectively. This indicates that CPF was able to solve the particle  
Figure 9: \(XYZ\)- axis and yaw angular error at sea state of 3. (**a**) \(X\)-axis position estimation error; (**b**) \(Y\)-axis position estimation error; (**c**) \(Z\)-axis position estimation error; (**d**) Yaw angular position estimation error. degradation problem. The algorithm EM-MOGCPF proposed in this paper has the best estimation accuracy, compared with the best phenotypic performance of CPF, and the four attitudes were improved by 32.06%, 27.5%, 24.76%, 38.77%, respectively. 2. In sea state degree 1-2, underwater noise is non-Gaussian distributed under the influence of wind and waves. The RMSE of the CKF algorithm is slightly greater than that of particle filtering for the \(x\)-axis and yaw angular \(\psi\) estimates. CKF's estimation accuracy decreases and it is not suitable for state estimation under non-Gaussian noise. Although CPF combines the applicability of particle filtering for non-Gaussian noise, it is applicable to a single noise model; the EM-MOGCPF algorithm incorporates the MOG model, which effectively improves the estimation accuracy under mixed noise. 3. As the sea state degree rises to 3, the RMSE of CKF in three attitudes is greater than that of particle filtering; it shows that as the noise environment becomes more complex, the accuracy of CKF estimation is worsened. Similarly, the performance of CPF at this sea degree is also poor. By comparison, the estimation accuracy of EM-MOGCPF is also the highest among the four algorithms. RMSE does not show large values as the sea degree increases, and it has good noise immunity in complex environments. Compared to CPF, which has the best relative stability, the accuracy is improved by 53.67%, 81.37%, 81.26%, 68.47%. This shows that EM-MOGCPF has good estimation accuracy even at the maximum operating conditions.