## 4 Autonomous Trajectory Planning and Optimization
### Coverage Sample Observations  
The system frame of coverage sample observation is shown in Figure 3. The sample data obtained from the marine vehicles are assimilated in the ocean model, and then the sample data variance distribution is evaluated to obtain prediction information of the observation objective. The data evaluation criterion decides the vehicles' path planning and sample objective. Through mission assignment, we choose the suitable vehicle, and integrate variance distribution and prediction of sample data to plan the marine vehicles' paths. Figure 3: Coverage sample observation. It is difficult to get comprehensive information with a single vehicle, so multiple vehicles are required to sample in a formation or maintain some relative position with respect to each other to obtain multiple data sets from different locations at the same time. KF and EKF are utilized for the sample instrument noise and the ocean spatially correlated noise. The ocean features are nonlinear, and cannot be expressed in explicit functions. However, with the understanding and the knowledge of the ocean features, EKF provides an approximate method to describe and estimate their variance. The sampling processes are affected by the ocean currents, marine vehicles' velocity and endurance, so the cooperative observation control module optimizes vehicles' formation and plans vehicles' desired velocity to adjust for any disturbance of the environment. Lastly, marine vehicle platforms execute the desired velocity control and data sampling. Detailed descriptions of observation data evaluation, observation path planning and cooperative observation control are as follows:  
1. Observation data evaluation: Criteria of observation data evaluation determine the effectiveness of data sampling. From numerical simulation and data assimilation, ocean environment prediction results can be achieved. In this study, the criterion is defined as the output uncertainty variance of the environmental prediction. The environmental prediction can be obtained from ocean numerical simulation in a constant-interval sequence form. It is known that, the longer of interval, the less the accuracy of the prediction results. Distribution of uncertainty variance reflects the accuracy of the prediction results: uncertainty variance of adjacent sequence reflects the spatial correlation of the ocean dynamic process, and uncertainty variance of the same network cell at different times reflects the temporal correlation of ocean dynamic process. 2. Observing path planning: Combining objectives, the ability of marine vehicles and environmental constraints, we transform the observation path and constraints as objective functions and constraint functions. The objective functions can be the shortest time, minimum energy, or validity of the observation data. In this study, the distribution of uncertainty prediction variance is selected as the objective function to improve the accuracy of environmental predictions. Repeated observations are carried out at the position of maximum uncertainty variance to access the interesting data. The constraints include velocity and endurance of marine vehicles, initial sampling position constraints, and observation operation (trajectory) mode, environmental constraints and so on. Mixed Integer Linear Programming (MILP) is proposed to solve the path optimal problems and design suitable marine vehicles' trajectories to obtain comprehensive and uniformly distributed sample data. For continuous cross section observation, vehicles' trajectory is restricted to a straight line in a longitudinal plane. In virtual observation mooring array observation, marine vehicles are constrained in a small radius circle, and then the trajectory of the array circle center is planned. For hierarchical observations, the vehicles' trajectory is pre-planned on the closed-loop curve, such as a circle, ellipse, or square.