## 1 Introduction  
There is a shortage of new construction workers in the industry due to the trend of laborers wanting to avoid extreme environments [1]. Particularly, due to the retirement of older workers, there is a shortage of skilled workers. Therefore, research is being conducted on autonomous trucks and construction robots that can replace humans at construction sites. Excavators are considered low risk because they do not travel at high speeds, and they perform repetitive tasks. Hence, their automation is highly feasible. For this reason, major construction equipment manufacturers are incorporating various types of automation [2, 3]. Diverse research was carried out in line with this trend. For example, several publications examined the automated determination of excavation spaces and related control techniques [4, 5, 6, 7, 8, 9, 10, 11]. An excavator dips up and transports loads into the cargo box of heavy-duty dump trucks. Excavators feature long joints and are often positioned at the rear of a truck to load materials. After the cargo box has been loaded sufficiently, the process is repeated for additional trucks. To automate this process, it is vital that the excavator acquire accurate information about the cargo box's three-dimensional (3D) position for analysis. [PERSON] introduced a method for recognizing a truck's cargo box after segmenting a truck from dense Lidar data [12]. The truck's cargo box is scanned using a dense LIDAR sensor. After segmenting the cargo box from dense rider data, the 3D position of the dump truck is determined by the upper plane of the cargo box. However, suppose the excavator is positioned higher than the truck, and the truck is parked to the excavator's side. Stereo cameras are efficient sensors that provide dense 3D depth maps. [PERSON] introduced technology for recognizing the location of a truck using depth information obtained from a stereo camera [13]. The 3D pose is estimated using the 3D shape information of the truck. A truck cargo box is formed from several faces. The 3D position of the truck is calculated by matching all cargo box planes and the plane of the initial 3D model. Therefore, 3D shape information of the entire truck is required. This method can be used for very large excavators, but it is difficult to apply to general excavators with a low height. Moreover, there is a way to load a load into a truck by using the structure after installing a special structure [14]. Since the truck is located inside the special structure and the excavator knows the 3D position of the special structure, the truck's location is naturally estimated. This method allows the excavator to locate the truck's 3D location reliably, but it is costly and limited in the location of the structure. Another option is to place the sensor in a third location other than excavators and trucks [15]. After installing the GNSS sensor that indicates the location of the truck and excavator, the initial 3D location of the truck and excavator is expressed in a global coordinate system. Next, the three-dimensional position of the truck is estimated using four lidar sensors and fish-eye cameras installed on the excavator. This method increases the cost of configuring the sensor. Despite the wide variety of dump truck types available, their cargo boxes generally resemble hexahedrons. Furthermore, the box's door is a flat plane shape for simplified fabrication. This paper describes a technique that enables an excavator at the rear of the loading truck to recognize its 3D cargo box and to estimate the 3D position of the loading space and the volume of the load inside using data obtained from a novel sensing device assembled for this purpose. Specifically, this research provides the following three innovations:  
1. A novel dump truck cargo box sensing device;
2. A method of automatically estimating the 3D position of the loading space;
3. A method of automatically estimating the volume of the load. The sensing device combines two two-dimensional (2D) LiDAR sensors and a stereo camera.