# An Enhanced Fusion Strategy for Reliable Attitude Measurement Utilizing Vision and Inertial Sensors
## 3 The Enhanced Fusion Strategy Based on RBF and CKF
### Fusion Strategy Based on RBF and CKF  
As the sampling frequency of inertial sensor is high and that of visual sensor is low, an inconsistent sampling frequency exists in the inertial and vision integration attitude measurement system. During the intersampling of vision data, only a time update is performed and there is no measurement update. This is because the measurement error is regarded as infinity, and the Kalman gain approaches zero. The attitude measurement cannot be compensated by the slow measurement vector. At the same time, the accuracy and stability of the filtering are difficult to guarantee. To deal with the multi-frequency issue between the inertial and visual data, a fusion strategy based on RBF and CKF algorithm is developed to improve the performance of the integrated attitude measurement system.  
This research uses RBF to establish the network model by training attitude errors while the visual data are available and to compensate attitude by predicted errors without visual data. In the process of training, attitude errors are treated as the input of RBF. The errors are transferred to the weighting sum of output layer by the activation function in the hidden layer. In the process of prediction, the well-trained RBF model outputs the estimated errors. The output attitude angles are obtained by CKF and RBF. CKF is used to estimate the attitude by data fusion, when there are both inertial and visual data. Without the vision data, the well-trained RBF and CKF are employed to predict estimation attitude by the data fusion method. By this method, the attitude estimation accuracy and stability can be improved and strengthened. The specific process of the optimal input-output estimation relationship constructed by RBF can be described as shown in Figure 4.  
Figure 4: Processing of **(a)** RBF training with vision data; and **(b)** RBF prediction without vision data. IMU: inertial measurement unit.  
In our study, the relationship between the past vision data and current attitude angles is investigated to continuously provide estimated error even during intersampling of visual data. It can be concluded from Figure 4a that the training process of RBF goes through when visual sensor works well. The attitude errors are inputs of RBF, and the activation function of hidden layer is used to transfer the error to output layer for weighting sum. The output attitude angles of the system are corrected with the proposed fusion data algorithm. The prediction process of RBF during the intersampling of visual data is shown in Figure 4b. Attitude error is used as an independent input of RBF. The well-trained RBF model can output estimated errors. Inertial data are corrected by the RBF prediction results of output final attitude angles.  
The reliable attitude estimation for integrated attitude measurements is achieved by the data fusion algorithm based on RBF and CKF. The proposed methodology can reduce the side-effect of inconsistent sampling frequency. Furthermore, the problem of divergence resulting from the sampling frequency discrepancy between the inertial and vision data are ameliorated and the accuracy and reliability of the estimated attitude are both improved.