# Robust Flow Field Signal Estimation Method for Flow Sensing by Underwater Robotics
## 1 Introduction  
The autonomous underwater vehicle (AUV) is an important tool for marine environment exploration that is widely used. Since the underwater environment is complex, the adaptability of AUV needs to be improved [1, 2]. The main aim of the current study on AUV environmental adaptability is to improve its control [3, 4, 5, 6, 7]. In practical applications, it has been found that the poor environmental adaptability of AUV is due to its inability to sense the surrounding environment [8, 9, 10]. At present, AUVs sense the surrounding environment on the basis of a visual and an acoustic system. However, the sensing range of the underwater visual system is limited because visual signals decay rapidly in the water and are easily affected by the water quality. In the context of underwater target detection, the acoustic signal also has many issues, such as high cost and high-power consumption. In complex environments, the acoustic signal is affected and cannot be properly applied [11, 12, 13]. In addition, the visual and acoustic signals detect targets through reflection and are, thus, indirect signals. They are unable to capture information regarding the flow field, such as the eddy and ocean currents. In a study of marine organisms, bionics researchers found that fish have a sensing organ that they called the lateral line system (LLS). The LLS can help fish acquire extraordinary environmental adaptability [14, 15, 16, 17]. The LLS contains two kinds of sensory neuromasts: the superficial neuromast and the canal neuromast. The superficial neuromast can sense the magnitude and direction of flow velocity, and the canal neuromast is usually used to sense the acceleration of the flow field, such as fluctuations [18, 19, 20, 21, 22]. Fish can make adjustments to the surrounding environment based on the information from the LLS. Thismethod can sense the physical field directly, and the sensing signal is a direct signal. This method has the advantage of being more accurate and comprehensive. However, in the natural environment, the flow field is made complex by numerous uncertain factors, which hinder the success of engineering applications [23; 24; 25]. Machine learning methods can be used to overcome the problem of underwater target recognition based on flow field signals. Three kinds of statistical methods are used for targets recognition, which are as follows:  
1. Novelty recognition: one normal, known state signal is set first. Then, the test signal is compared with the normal signal. Their difference can be used to evaluate an environmental change. In this method, a statistical threshold value is set and used to eliminate the interference [26];
2. Classification recognition: All states of the system are obtained first, and then they are divided into several known types. The test signal characteristics are identified and are used to evaluate an environment change [27];
3. Regression algorithms: The confidence limits of the variables are set to monitor some dynamic processes. The mathematical model of the system evolution can be obtained by a linear or nonlinear algorithm [28; 29; 30]. Novelty recognition and classification recognition are suitable for a steady system, and the states are known. Therefore, in the flow field system, the method based on regression algorithms is the main one and is used to build a mathematical model. Various methods can be used with regression algorithms, such as nonlinear principal component analysis [31], extreme value statistics [32], peaks over threshold [33], machine learning algorithms [34], neural networks [35], Bayesian approaches [36], Mahalanobis distance [37], and others. In all these applications, the nonlinear features of flow field changes can be obtained. However, in the natural environment, there are often multiple influencing factors superimposed on each other, causing the system to be highly nonlinear. Then some cracks, delamination, or chaotic phenomena appear [38].