## 1 Introduction  
Globally, many countries are facing constraints on food production due to climate change, aging, and decreasing farming population. For example, as reported in [1], the Korean farm population is predicted to decline by 16.7% from 2015 to 2024 and the percentage of farmers over 65 years of age in the farming population is expected to be 43.8% in 2024. For these reasons, in recent years, demand for the mechanization and automation of agriculture is increasing for efficient agricultural production. In addition, advances in sensor technology and information and communication technology (ICT) are leading to the development of autonomous driving agricultural vehicles. For example, major agricultural machinery manufacturers, such as John Deere, Case IH, Yanmar, and New Holland, developed autonomous driving technology or have a concept/plan to carry it out, and more than 20 of the projects are underway across the world [2,3]. [PERSON] presented an autonomous tractor, the 8320 model with an autonomous system called \"Auto Trac Controller\" in 2017 and it was put on the market in Denmark [4]. As a plug and play kit, it could be adapted to non-brand tractors and it can detect the obstacles using a laser scanner. Case IH mentioned the concept of an autonomous tractor using on-board sensors and a video camera in 2016 [5]. It could be operated remotely using a tablet and the tractor can identify the obstacles using on-board sensors and camera. Yammar presented a self-driving robot tractor, \"Yanmar Robot Tractor\" with precise automatic driving control using a global navigation satellite system (GNSS)-real-time kinematic (RTK) module, and Inertial Measurement Unit (IMU) in 2019 [6]. New Holland designed an autonomous tractor, \"NHDrive\", which detects obstacle using a combination of radar, light detection and ranging (LiDAR), and cameras in 2016 [7]. Because there are few people and no obstacles in areas where agricultural machinery is used, the risk of accidents caused by using self-driving agricultural vehicles is low. Therefore, if an autonomous driving agricultural vehicle with a price similar to non-autonomous driving agricultural machinery is developed, it is expected that its utilization in the agricultural field will increase. Since an autonomous driving agricultural vehicle uses navigational information (i.e., position, velocity, and attitude to control vehicle speed, and steering to follow a specific route), navigation sensors should be equipped for the operation of autonomous driving. A typical navigation sensor is GNSS-RTK, which can provide the position, speed, and heading with an accuracy that is appropriate for autonomous driving. Thus, previous studies dealt with GNSS-RTK-based autonomous driving for agricultural vehicles. For example, [PERSON] et al. [8] developed a four-antenna carrier-phase GPS system for guiding a tractor with the line tracking standard deviation below 2.5 cm. [PERSON] and [PERSON] [9] developed an automatic steering system using GNSS-RTK with a standard deviation of lateral error from 2.5 to 6.9 cm. [PERSON] et al. [10] applied GNSS-RTK for guiding a tractor and its performance in autonomous driving was evaluated to be centimeter level in terms of lateral accuracy. [PERSON] et al. [11] used a low-cost single-frequency GNSS-RTK for the autonomous driving system and the root mean square (RMS) of the path-following error of the developed system was found to be a centimeter-level. As above, GNSS-RTK can provide accurate navigational information in most environments at an affordable price, but GNSS-RTK cannot guarantee continuity and reliability of positioning where the _GNSS_ signal environment is poor, such as an orchard [12]. To overcome this problem and to ensure stable autonomous driving, an autonomous driving system was improved by combining GNSS-RTK as well as a dead reckoning sensor such as inertial measurement unit (IMU), tilt sensor, and gyroscope. [PERSON] et al.