Trajectory Estimation of Autonomous Surface Vehicle Using Extended Kalman Filter

Autonomous Surface Vehicle (ASV) is a ship that can move autonomously in the water surface. In this work, we focus on Touristant ASV with the following specifications: length 4 meters, diameter 1.5 meters and height 1.3 meters. The main objective of this work is estimating the position of ASV based on the linear ASV model under the influence of wind speed and wave height, where the linear model is obtained from the linearization of the original nonlinear ASV model. In this work, we apply the Extended Kalman Filter (EKF) method to the linear ASV model in order to produce a small error in position. There are 2 simulations for the implementation of the EKF method, with 200 and 300 iterations. The error of position resulting from the simulation shows that the estimation accuracy of position is 95% - 98% where the error of position in the x-axis is 0.01 meters, the error of position in the y-axis is 0.012 meters and the error of position in the plane XY is 0.011 meters.


Introduction
An unmanned surface ship or commonly called Autonomous Surface Vehicle (ASV) is a surface vessel capable of automatically moving without any crew on it. One of many ways utilizing a surface vessel is as a tourist attraction. Developing unmanned surface vessels or ASVs can help the government revitalize the mode of marine tourism across the NKRI teritory [1].
ASV can also increase the income of a country, especially from the marine tourism sector. Some marine tourisms in the water area of East Java, Indonesia, namely Gresik Delegan Beach in the north coast of Java and Papuma Beach -Jember in the south coast of Java. Delegan Gresik Beach is one of the touristic places located in Gresik by, offering numerous natural attractions of marine environment and coastal views in the north coast of Java. To make visitors enjoy the beauty of the beach, Delegan Beach is provided with a simple boat controlled by humans, but it could be risky. Such a boat can get an accident due to its operator's negligence, lack of professionalism, or other misconduct [2].
In the last few years, there is a rapid development of technology in Autonomous Surface Vehicle (ASV). Unmanned Surface Vehicle (USV) or ASV (Autonomus Surface Vehicle) is a boat robot that can move from one location to another in an automatic fashion. Such automatic movement requires the estimation of position of the ASV. Many studies have been conducted related to position estimation including its application to ASV by leveraging the Ensemble Kalman Filter and Square Root Ensemble Kalman Filter methods [1,3], estimation for the pathways of Autonomous Underwater Vehicle (AUV) using EnKF and EnKF-SR [4,5], and Fuzzy Kaman Filter [6], estimation for missiles using EnKF-SR [7]. In this paper, the estimation of position was applied to the 3-DOF (surge, sway and yaw) linear model resulting from the linearization of the 3-DOF nonlinear model. The position estimation was made by using the Extended Kalman Filter method, which is an extension of the classical Kalman Filter method, observed quite reliable in the linear model. The estimation of ASV position is used to observe the ASV position to check whether it had passed the predetermined trajectory. The objective of this work was the estimation of ASV position by using the linearized motion models.

Autonomous Surface Vehicle
The Touristant ASV considered in this work contains Global Positioning Systems (GPS), gas, sensors, bluetooth, pH sensors, and telemetry. The complete profile and specification of Touristant ASV are written in Figure 1 and Table 1.  The study uses the equation of water vehicle motion with 3 degrees of freedom from 6 degrees of freedom, that is, surge, sway and, yaw. [7].
By using a simplified nonlinear model [8]: Next, the examples are written as follows: From the above examples of and , then substituted into the equation ( ) , so that

Extended Kalman Filter (EKF)
The Extended Kalman Filter (EKF) algorithm can be seen in [8]: 1. System and measurement models.

Time Update
Estimation : Error covariance:

Measurement Update
Kalman gain :

Linearization of Nonlinear Model of ASV
The linear model that we want to get is as follows: To determine ( ) the Jacobi matrix can be formed given as follows: [ ] From equation (15) to differentiate controls in sway and yaw motion then will be redefined for sway and for yaw. For more details, it will be written as follows: To determine ( ) can be taken as identity matrix and .

Computational Result
In this section, we discuss the simulation of the application of the Extended Kalman Filter (EKF) algorithms to the linearized model of AUV. The simulation results were assessed, and the real system was compared to the estimation results obtained using EKF method. Two types of simulation were carried out, that is, the first simulation by 100 iterations, and the second one by 200 iterations.   Figures 2 and 3, we can observe that the ASV can move along the predefined path at the xaxis, where the EKF method has high accuracy of around 96%. The error in the case of 300 iterations is 0.00865 m for position in the X direction and 0.00876 m for position in the Y direction. Figure 4 displays that the Touristant AUV can also follow the predefined path in the XY plane by first moving forward and then dragging to the left direction, forward motion until 80 meters at the simulation time of 300 seconds. From the graph, we can see that the EKF method has a high accuracy of approximately 96% -97,6%. Table 1 also shows the ration of position error generated from the simulation using the 200 and 300 iterations. Accurate position errors are generated by assuming that ASV operates in waters where wind speed and wave height do not occur or cause significant changes. However, with the presence of environmental factors it can also affect ASV performance, although the environmental factors that affect it are not too strong, but still have an effect on performance, if compared to those without environmental factors.
In Table 2, it appears below that by 300 iterations it gives a higher accuracy 200 iterations. According to the numerical results, the EKF method has a sufficiently high accuracy in the case of 200 or 300 iterations. However, from the computation time, the EKF with 200 iterations is faster since there is no looping for a number of iterations. Thus, we can conclude that the EKF method can be implementated on an ASV platform.

Conclusion
According to the simulation results and the analysis in the previous section, the Extended Kalman Filter (EKF) could be used as a method to estimate the trajectory of a Touristant ASV with sufficiently high accuracy.
If the number of iterations is higher, we obtain a higher accuracy, however the computational time is also longer.
We can see from the numerical results that the accuracy of estimation for EKF that generates 300 iterations is higher than 200 iterations.
. Open problem. How to implement H-infinity for the estimation of ASV position