A Real-Time Measurement Method and System for the Harvesting Area of a Grain Combine Harvester

Abstract

A real-time system for measuring harvesting area is crucial for cross-regional operation. In response to the current situation where significant errors often occur in measuring the areas of small and irregular fields, we designed a low-cost and high-precision online real-time measurement system for the harvesting area of grain combines. The real-time measurement hardware system for measuring area was designed using an STM32 microcontroller as the core unit. The system was developed using three modes: intelligent measurement, circular measurement, and fusion measurement. Simulation and field experiments were conducted to verify the performance of the system. The experimental results showed that in the field simulation experiment with four differently shaped operating areas, the average accuracy of the intelligent mode reached 93.76%, and the average accuracy of the circular mode reached 95.48%. In the field experiments, the average accuracy of the intelligent mode reached 95.09%, the average accuracy of the circular mode reached 95.74%, and the average accuracy of the fusion measurement mode reached 98.01%. Therefore, the real-time measurement system for the harvesting area of a grain combine harvester designed in this study has high accuracy when measuring the area of small and irregular farmland, hence meeting the requirements of the design objectives.

1. Introduction

China is a major agricultural country, and vigorously developing agricultural mechanization is essential in modern agriculture [1,2]. At present, the mechanization rates for wheat, corn, and rice harvesting in China are over 94%, 80%, and 82%, respectively [3,4]. In recent years, the annual scale of combine harvesters participating in the “three summer” cross-regional operations has not been less than 250,000 units [5,6]. Due to the lack of reliable, accurate, and online methods for measuring the harvest area, however, disputes over cross-regional operation cost settlement often occur. How to achieve accurate online detection of the harvested area is one of the core objectives for promoting efficient cross-regional operations [7,8].

At present, there are two main methods for measuring grain harvest area: manual measurement and automatic measurement. Manual measurement usually employs tape measures, total stations, and mu meters to measure the area before harvest. This method is inefficient and unsuitable for large-scale farmland measurement. Automatic measurement relies on satellite navigation systems to measure the harvested area. There is a strong demand for this technology in agricultural mechanized harvesting.

The construction of the Beidou satellite navigation system ground-based enhancement station and the development of mobile communication technology have provided high-precision navigation and positioning services [9,10,11,12]. Researchers have developed a series of harvest area detection methods and equipment based on satellite navigation systems. Zhang et al. designed a farmland area measurement instrument based on the Beidou satellite navigation system that could measure irregularly shaped farmland area using a triangulation algorithm. The average relative error of the system was 0.7% [13]. Sun et al. designed a method for measuring the area of agricultural machinery operations based on the improved AlphaShapes algorithm. Their method accurately extracts the contour of the working land and uses the Delaunay triangulation algorithm to calculate the area of agricultural operations. The error rate during measurement was less than 3.5% [14]. Zeng developed a small agricultural machinery operation area measurement system based on multiple sensors, with the STm32 series processor as the core unit. The system can automatically eliminate duplicate areas and achieve accurate measurement of the operation area [15]. Qi et al. developed a machine learning-based method and a system for calculating the area of agricultural machinery operations. Their method used the CNN algorithm to identify the type of operation trajectory, calculated the rate of missed cultivation based on image pixel points, selected appropriate interpolation and area calculation methods using a decision tree algorithm, and finally calculated the operation area [16]. Chen et al. constructed a multi-sensor fusion system for measuring the operation area of agricultural machinery. When the agricultural machinery is in a normal operation status, the status and GPS effective data are transmitted to a cloud data platform according to the transmission cycle, and the operation area is calculated [17]. Lu et al. obtained the walking trajectory of agricultural machinery operations through a combination of GPS and Galileo positioning modules, and then calculated the operating distance to achieve area calculation. However, the system had significant measurement errors for irregular and small areas of land [18]. Xiong et al. designed a high-speed rice transplanter working area measurement system based on STC MCU and GPS positioning technology. Through the analysis and processing of GPS positioning track information, the mechanical dynamic working area was automatically calculated, and the relative error of measurement could reach approximately 1.25% [19]. Yang et al. developed an area measurement device based on GPS satellite positioning that can use the received positioning information to calculate land area, with a relative measurement error of <2.20% [20]. Tang Jun proposed a method to calculate the baseline angle and then calculate the area based on the coordinates measured using two handheld GPS receivers. The accuracy of this method was higher than that of the single-machine operation method, with an accuracy of approximately 0.5% [21]. Dong designed and developed a handheld embedded farmland area measurement terminal that supports multiple GPS positioning methods. The measurement error under the GPS differential mode was less than 5% [22].

However, when faced with small and irregularly shaped farmland, the existing measurement equipment based on satellite systems may form plot boundaries that are difficult to measure compared to large areas of farmland, resulting in an increased error using the above-mentioned methods. Therefore, it is necessary to develop a low-cost and high-precision real-time measurement system for harvesting area based on the actual needs of domestic agricultural operations. This article describes a low-cost and high-precision real-time measurement system for the area harvested by a grain combine. The system uses BDS/GPS dual-mode positioning to obtain real-time operating coordinates of the grain combine. The hardware design of the system was completed using embedded technology with the STM32 microcontroller as the core unit. A human–computer interaction system was developed that has three modes for harvesting area measurement: intelligent measurement, circular measurement, and fusion measurement. The system can achieve the accurate measurement of harvesting area for farmland of any shape. The contributions of this study are as follows:

(1)

The proposed method measures the area of grain harvesting operations for irregularly shaped and sized land parcels with high precision in real time at low cost.

(2)

The system has established a recognition model for the effective identification of operation points from the positioning information, and based on this, the effective travel distance between the operation points within the sampling interval is calculated to obtain harvesting operation area in real time.

(3)

The fusion area measurement algorithm in the system combines intelligent measurement and circular measurement, effectively increasing the accuracy of measurements.

2. Materials and Methods

2.1. Real-Time Measurement System for Harvesting Area

Our research group developed a real-time measurement system for the operating area of grain combine harvesters. As shown in Figure 1, the system consists of three parts: a positioning module, a data-processing terminal, and a display terminal. To better achieve industrialization, this system adopted a low-cost positioning module. This positioning module is a GPS and Beidou module (model: M10U8) produced by Shenzhen Xinghe Microelectronics Technology Co., Ltd., Shenzhen, China. The tracking sensitivity of this module is −164 dBm; the capture sensitivity is −159 dBm, and the cold start sensitivity is −147 dBm. The module has a horizontal positioning accuracy of 2.0 m and a time accuracy of 30 ns in open areas. The data-processing terminal uses the STM32 microcontroller as the core unit, and embedded technology was applied to complete the hardware design of the system. The display terminal adopts an intelligent serial port screen (model: TJC8048x570_011RS_Y) produced by Shenzhen Taojingchi Electronics Co., Ltd., Shenzhen, China. The data-processing terminal collects the output information of the positioning module in real time through the 232 bus and interacts with the display terminal for data.

2.2. Harvest Area Measurement Using the Human–Machine Interaction System

Figure 2 shows the human–machine interaction interface that we developed for the real-time measurement of the operating area of a grain harvester. The human–computer interaction system comprises four parts: the communication serial port settings, job model settings, a real-time data display, and system control. The communication serial port setting implements the setting of the serial port number, baud rate, and the operation of opening and closing the serial port. The operation model setting realizes the input of harvesting operation width and operation mode, for which the system provides three modes: intelligent real-time operation area measurement, plot circle area statistics, and fusion measurement. The data display enables real-time presentation of positioning module data, job trajectory, job itinerary, real-time job area, and cumulative job area. The system control part primarily implements the functions of starting, completing, and exiting the system.

2.3. Real-Time Measurement of the Harvesting Area

The process of real-time measurement of the harvesting area in this system is shown in Figure 3. After powering on the system, there is an initial self-check. After initialization, the system checks whether the serial port is valid; if it is invalid, the system waits for the serial port to open. If the serial port is valid, a query is made about whether to start the job. After detecting the start of the job, the information of the positioning module is read through the serial port interrupt function. Then, the system determines whether the positioning information is valid. If the positioning information is valid, the harvesting area at the current sampling time is measured according to different operation modes. After a single measurement is completed, the system displays real-time information such as job trajectory and job area on the interface and saves the real-time data to a designated file. Finally, the system will check whether the job has ended, and upon completion of the job, the measurement of the local block will be completed; if it is not completed, the system will skip back to the serial port interrupt function and continue the measurement task.

In the intelligent measurement mode, the driver harvests within the plot according to the traditional operation mode, and this system measures the real-time harvesting area based on positioning information. In this mode, the system first determines whether the current position of the harvester is within the non-harvested area. If it is not within the non-harvested area, the stroke is invalid and the operating area is not accumulated. If it is within the non-harvested area, the trip is valid, and the cumulative operating area is calculated as follows:

$$S_{\mathrm{ai}}=S_{\mathrm{ai}}^{\text{'}}+d_{\mathrm{trip}}\times l_{\mathrm{width}}$$

(1)

where S_ai is the area of the harvested plot measured at the current sampling time in the intelligent measurement mode, expressed in m²; $S_{\mathrm{ai}}^{\text{'}}$ is the area of the harvested plot measured at the previous sampling time in the intelligent measurement mode, expressed in m²; d_trip is the effective stroke at the current sampling time, expressed in m; and l_width is the effective cutting width of the combine harvester, expressed in m.

Accurately determining the position of the harvester at the current sampling time is the key to achieving accurate measurement of the harvesting area. As shown in Figure 4b,c, this system describes the actual operating position of the harvester in the field through five coordinate points, where P₀ is the installation position of the system’s GPS module. A rectangular closed interval is formed using the P₀–P₄ position coordinates. If there is any harvester operation position information recorded by the system before the sampling time within this closed interval, the system assumes that the current joint harvester is in the cut area, and the operation point is not a valid point, and thus, the harvest area is not accumulated. Otherwise, the system assumes that the combine harvester is in the uncut area at the current moment, and the operation point is valid, and thus is accumulated in the harvested area.

In the circle measurement mode, the operator needs to drive the combine harvester along the boundary of the land to be harvested. As shown in Figure 4d, the system calculates the area of operation based on the positioning data of the boundary of the harvested land. The location information of the harvested land parcel boundary is a set of discrete data points. To measure the operation area of the harvested land, the system needs to consider both concave and convex points when identifying the compact envelope of these discrete points. To reduce the excessively close relationship between the envelope and scattered data, the system was designed using the ScatterHull concave–convex envelope detection algorithm. This algorithm sorts the scattered data according to the direction of travel and determines the concavity and convexity of the points. For concave points, a threshold is added; the included angle is determined; several concave points are removed, and then, this cycle of judgment is continued until all concave points meet the requirements. After extracting the envelope of the boundary of the harvested plot, the system uses the Monte Carlo algorithm [23,24] to calculate the area of the irregularly harvested plot. The calculation formula is as follows:

$$S_{\mathrm{circle}}=\frac{n_{\mathrm{in}}\left(x_{\max }-x_{\min }\right)\left(y_{\max }-y_{\min }\right)}{n_{\mathrm{all}}}$$

(2)

where S_circle is the area of the harvested plot measured by the circle algorithm, expressed in m²; x_max and x_min are, respectively, the maximum and minimum values of scattered points along the x-axis direction, expressed in m; y_max and y_min are, respectively, the maximum and minimum values of scattered points along the y-axis direction, expressed in m; n_in is the number of probability pins put into the envelope of the harvest boundary; and n_all is the total number of probability needles placed in the rectangle [x_max, x_min, y_max, y_min].

In the fusion mode, after obtaining effective positioning information, the system realizes real-time measurement of the harvested area based on an intelligent measurement algorithm. When the harvesting operation is completed, the circle measurement algorithm is called to recheck the calculation of the harvested area. Finally, the weighted average of the measurement results of these two modes is used as the final harvest area measurement value, calculated as follows:

$$S_{\mathrm{mix}}=\frac{S_{\mathrm{ai}}+S_{\mathrm{circle}}}{2}$$

(3)

2.4. Test Design

To verify the performance of the real-time measurement system for the operating area of grain harvesters proposed in this article, we conducted both simulation and field experiments.

2.4.1. Simulation Test

The simulation test was conducted on a cement field at the Baima Base of the Nanjing Agricultural Mechanization Research Center of the Ministry of Agriculture and Rural Affairs. The site is rectangular, with a length of 50 m and a width of 35 m. We designated different shapes of work areas (rectangular, triangular, fan-shaped, and irregular polygons) and used the real-time measurement system described in this paper to measure the area using a tracked harvester (Model: Wold 4SZ-3.72). The tests followed the traditional harvesting operation mode, and walkthroughs in the experimental area were made to verify the accuracy of the algorithm. The test was repeated three times for each type of work area. To verify the performance of the looping algorithm, we introduced the Convhull convex envelope [25,26] and AlphaShape algorithm [27,28] to compare and verify the accuracy of the work area measurement based on the ScatterHull concave–convex envelope designed in this study. Moreover, the actual area of the experimental shape was manually measured using a Kubota T16 high-precision GPS land-measuring instrument, and the performance of the real-time measurement system for harvesting area designed in this paper was compared and verified.

2.4.2. Field Tests

Field tests were conducted in an agricultural experimental field in Wujiang District, Suzhou City, Jiangsu Province, China. Six experimental fields in the experimental area were selected, and a grain combine harvester (Model: World 4SZ-3.72) installed with the real-time measurement system described in this paper was used for harvesting. The system measured the harvesting area in real time using the fusion model. In this case, the system was able to record measurement data for the three operation modes described in this article. Moreover, the actual area of the experimental plot was manually measured using the Kubota T16 high-precision GPS land measuring instrument, and the performance of the real-time measurement system for harvesting area was compared and verified.

3. Results

3.1. Simulation Test: Intelligent Measurement Results

Figure 5 shows the operating trajectory and effective points of the harvester under different operating scenarios in a set of simulation experiments. During the simulation experiments, the rectangular operation area was relatively simple and was used to ensure that the harvester always operated within the prescribed area. Other job scenarios required high-level control requirements for the harvester. During the experiment, there was a phenomenon of the harvester driving out of the designated operating area. This to some extent affected the final measurement results of the system.

Figure 6 shows the results using the intelligent measurement system designed in this study under different job scenarios. In three repeated experiments, the system measured 735.6 m², 817.5 m², and 713.8 m² for rectangular work plots. For the triangular plot, the measured values of the system were 346.6 m², 341.3 m², and 399.9 m². For the fan-shaped plot, the measured values of the system were 503.1 m², 449.4 m², and 425.5 m². For polygonal plots, the measured values of the system were 679.1 m², 663.8 m², and 771.4 m². There was fluctuation in the measurement values of the system for different job plots. This was largely due to the simulation experiment process, where there were no crops in the operating area, and the estimation of the harvester walking in different experimental groups was different. The system determined effective work points based on the actual walking trajectory, and different effective work points can cause different measurement results.

Table 1. Statistics for the intelligent measurement results in different job scenarios.

Type of Work Area		Rectangle	Triangle	Sector	Polygon
Kubota T16 mu measuring instrument	Measurement value (m2)	725.4	387.2	430.6	653.9
System intelligent mode measurement results	Measurement mean (m2)	755.6	362.6	459.3	704.8
	Absolute error (m2)	30.2	24.6	28.7	50.9
	Accuracy rate (%)	95.84	93.65	93.33	92.22

presents the statistics of the intelligent measurement results for harvesting area under different operating scenarios. The areas of rectangular, triangular, fan-shaped, and polygonal shapes measured using the Kubota T16 acre measuring instrument were 725.4 m², 387.2 m², 430.6 m², and 653.9 m², respectively. The average measurement results of the intelligent measurement mode of the system were 755.6 m², 362.6 m², 459.3 m², and 704.8 m², respectively. In the rectangular operation scenario, the measurement accuracy of the system was the best, reaching 95.84%. In the irregular polygon operation scenario, the measurement accuracy of the system was the worst at 92.22%.

3.2. Simulation Test Circle Measurement Results

Figure 7 shows a set of test results obtained from the system’s circular measurement during the simulated test process. The test results showed that the Convhull algorithm determined the harvest boundary according to the convex points of the envelope, and the algorithm could well distinguish the operation boundary in the standard rectangular operation area (as shown in Figure 7a). However, for irregular work areas, the harvest boundary determined by the Convhull algorithm was larger than the actual work area (as shown in Figure 7b,d). The AlphaShape algorithm and the ScatterHull algorithm had similar effects in determining job boundaries, and the two algorithms could effectively determine job boundaries based on the job area.

Table 2. Statistics for the area measurement results under different operating scenarios.

Type of Work Area				Rectangle	Triangle	Sector	Polygon
Kubota T16 mu measuring instrument		Measurement value (m2)		725.4	387.2	430.6	653.9
System circle measurement mode measurement results	Convhull	Measurement value (m2)	Test 1	704.6	467.7	452.3	680.7
			Test 2	689.4	388.3	500.1	700.8
			Test 3	756	399.5	438.9	759.9
		Measurement mean (m2)		716.7	418.5	463.8	713.8
		Absolute error (m2)		8.7	31.3	33.2	59.9
		Accuracy rate (%)		98.8	91.92	92.29	90.84
	ScatterHull	Measurement value (m2)	Test 1	680.9	386.8	431.4	642.4
			Test 2	674.8	343.4	500.6	655.3
			Test 3	724.6	354.3	423.8	704.8
		Measurement mean (m2)		693.4	361.5	451.9	667.5
		Absolute error (m2)		32	25.7	21.3	13.6
		Accuracy rate (%)		95.59	93.36	95.05	97.92
	AlphaShape	Measurement value (m2)	Test 1	651.9	374.8	432.2	640.4
			Test 2	643.3	343.4	493.3	650.2
			Test 3	753.4	352.6	425.3	703.3
		Measurement mean (m2)		682.9	356.9	450.3	664.6
		Absolute error (m2)		42.5	30.3	19.7	10.7
		Accuracy rate (%)		94.14	92.17	95.42	98.36

presents the statistics for the measurement results under different operating scenarios. The Convhull algorithm had an accuracy of 98.8%, 91.92%, 92.29%, and 90.84% for measuring the harvesting area of rectangular, triangular, fan-shaped, and irregular polygons, respectively, with an average measurement accuracy of 93.46%. The AlphaShape algorithm had an accuracy of 94.14%, 92.17%, 95.42%, and 98.36% for measuring the harvesting area of rectangular, triangular, fan-shaped, and irregular polygons, respectively, with an average measurement accuracy of 95.02%. The accuracy of the ScatterHull algorithm for measuring the harvesting area of rectangular, triangular, fan-shaped, and irregular polygon operating areas was 95.59%, 93.36%, 95.05%, and 97.92%, respectively, with an average measurement accuracy of 95.48%. For different types of harvesting areas, the ScatterHull algorithm improved the measurement accuracy by 4.64% and 0.46%, respectively, compared to the Convhull and AlphaShape algorithms.

3.3. Field Test Result Analysis

Figure 8 shows the results of the real-time measurement system for the harvesting area in plot 4 of the experimental area. The results showed that the system could effectively record the operation trajectory of the harvester in the field. The intelligent measurement algorithm identifies whether the sampling points on the operation trajectory are valid in real time and calculates the real-time operation area based on the valid points (as shown in Figure 8a). The circle measurement algorithm measures the actual work area by determining the envelope at the outermost periphery of the work area in real time (as shown in Figure 8b).

Table 3. Statistical data on the measurement results of harvested area in field experiments.

Type of Work Area			NO. 1	NO. 2	NO. 3	NO. 4	NO. 5	NO. 6
Kubota T16 mu measuring instrument		Measurement value (m2)	1133.3	2066.7	1866.7	1200.0	1800.0	2133.3
Real-time measurement system for harvesting area of grain combine harvesters	Intelligent measurement mode	Measurement value (m2)	1008.2	2157.0	1913.0	1229.5	1779.9	2304.3
		Absolute error (m2)	125.1	90.3	46.3	29.5	20.1	171
		Accuracy rate (%)	88.96	95.63	97.52	97.54	98.88	91.98
	Circular mode	Measurement value (m2)	1234.1	1999.8	1760.1	1259.3	1817.8	2171.9
		Absolute error (m2)	100.8	66.9	106.6	59.3	17.8	38.6
		Accuracy rate (%)	91.11	96.76	94.29	95.06	99.01	98.19
	Fusion measurement mode	Measurement value (m2)	1121.2	2078.4	1836.6	1244.4	1798.9	2238.1
		Absolute error (m2)	12.1	11.7	30.1	44.4	1.1	104.8
		Accuracy rate (%)	98.93	99.43	98.39	96.30	99.94	95.09

presents the statistics for the measurement results of the six plots in the experimental area. For the six harvesting areas, the accuracy percentages using the intelligent measurement mode were 88.96%, 95.63%, 97.52%, 97.54%, 98.88%, and 91.98%, with an average measurement accuracy of 95.09%. The respective accuracy values using the circle measurement mode were 91.11%, 96.76%, 94.29%, 95.06%, 99.01%, and 98.19%, with an average measurement accuracy of 95.74%. The respective values using the fusion measurement mode were 98.93%, 99.43%, 98.39%, 96.30%, 99.94%, and 95.09%, with an average measurement accuracy of 98.01%. From the results, the fusion measurement mode was the best, with increases of 2.92% and 2.27% compared to the measurement accuracy of the intelligent and circular modes, respectively.

Table 4. Statistical results of the f- and t-tests for the field measurement results.

Inspection Method		Real-Time Measurement System for the Harvesting Area of Grain Combine Harvesters			Kubota T16 mu Measuring Instrument
		Intelligent Measurement Mode	Circle Measurement Mode	Fusion Mode
Mean value		1731.983333	1707.166667	1719.6	1700
Variance		263,920.0777	148,205.9267	200,290.956	186,231.112
Number of observations		6	6	6	6
df		5	5	5
f-test	F	1.417164269	0.795817224	1.075496752
	p (F ≤ f)	0.355677915	0.404111828	0.469144136
t-test	Poisson correlation coefficient	0.99253384	0.987858485	0.994531772
	t Stat	0.780891194	0.222890935	0.986601068
	p (T ≤ t)	0.235102153	0.416219903	0.184571957

lists the statistical results of the f- and t-tests for the field measurement results of the real-time measurement system for the harvesting area of grain combine harvesters. The f-test results indicate that the p values of the measurement results of the three modes in this system are all greater than 0.05, indicating that there is no significant difference between the variance of the measurement results of the system and the measurement variance of the measuring instrument. Similarly, the t-test results indicate that the p values of the measurement results of the three modes in this system are all greater than 0.05, indicating that there is no significant difference between the variance of the measurement results of the system and the measurement variance of the measuring instrument. Therefore, this system can be applied to the online measurement of harvesting area during the field operation of grain combine harvesters.

4. Discussion

Currently, the accuracy of ordinary satellite positioning modules can reach ±2.5 m, and the accuracy of differential positioning modules can reach ±0.02 m. Therefore, the position information of agricultural machinery field operations can be monitored through satellite positioning modules, and the position information can be used to calculate the actual operating area. The online measurement methods for harvesting area based on satellite positioning information mainly include the cumulative effective stroke method [16,17,18] and the harvesting boundary closed graph area method [13,14,15,19,20].

The intelligent measurement mode in the real-time measurement system for the harvesting area of grain combine harvesters is the cumulative effective stroke method. One of the key techniques is to determine the effective stroke within the sampling interval. Lu et al. [18] directly used the position information of agricultural machinery collected by satellite positioning modules to calculate the operating area, which can be used to calculate the area of replanting or the area where the seeder missed sowing seeds. However, this does not apply to harvest homework scenarios. This system first establishes a model for determining the effective points of the harvester operation position, and the distance between the two effective points is the effective travel distance. Furthermore, this model can effectively eliminate non-harvesting operations, such as turning around, reversing, and unloading the harvester, thereby improving the accuracy of area calculation.

The circle measurement mode in the real-time measurement system for the harvesting area of grain combine harvesters uses the area method of harvesting closed boundary shapes. Additionally, determining effective harvesting boundaries is critical for this system. The AlphaShape and Convhull algorithms are widely used to solve complex contour extraction. However, the AlphaShape algorithm is mainly applicable to point set data with more uniform density, and the single-parameter AlphaShape algorithm cannot process points when it encounters a large difference in point set density. Reference [14] proposed a dual-threshold AlphaShape algorithm with improved detection accuracy. The Convhull algorithm is mainly used to identify convex point sets of contours. However, the constraint condition of the Convhull algorithm is to minimize the number of polygons formed by the convex point dataset, which results in the inability to recognize concave points within the contour, often resulting in the extracted boundary being larger than the actual one. The ScatterHull algorithm used in this study fully considers the concave and convex points on the contour. For the concave points, a threshold is added, and some concave points are removed through angle judgment, effectively improving the boundary detection accuracy. The area of closed intervals is another key parameter. Constructing triangular and rectangular integrals is a commonly used method [13,14,19,20]. However, using such methods can reduce execution efficiency and prolong calculation cycles. To improve the running speed of the algorithm, the system uses the Monte Carlo method to calculate the area of the closed interval.

In addition, the real-time measurement system for the harvesting area of grain combine harvesters currently uses a regular satellite positioning module, and the accuracy of the positioning module will slightly affect the measurement accuracy of the system. However, with the improvement of the intelligence level of grain combine harvesters, assisted driving technology has been widely applied in grain harvesting. The auxiliary driving system adopts differential positioning technology to detect the position information during the harvesting process. This system provides corresponding differential positioning data access interfaces, which can further improve the measurement accuracy of the system through the geographic location information of differential positioning. Therefore, the system designed in this article can provide drivers and farmers with mutually recognized online measurement services for harvesting area. This solution can effectively reduce disputes over harvesting cost settlement and is conducive to promoting mechanized grain harvesting technology.

5. Conclusions

This study, based on the BDS/GPS dual-mode satellite navigation and positioning system, developed a low-cost and high-precision online real-time measurement system for the area covered by grain combine harvesters. A human–machine interaction system for real-time measurement of the harvesting area was designed with three modes: intelligent measurement, circular measurement, and fusion measurement. In the field simulation experiment, the average accuracy of the intelligent mode of this system reached 93.76% for four different shapes of work areas. In the circular mode, the average accuracy of the ScatterHull algorithm reached 95.48%. The measurement accuracy of the ScatterHull algorithm was 4.64% and 0.46% higher than those of the Convhull and AlphaShape algorithms, respectively. In the field experiments, the average accuracy of the intelligent mode of this system reached 95.09%; the average accuracy of the circular mode reached 95.74%; and the average accuracy of the fusion mode reached 98.01%. Moreover, the f-test and t-test results indicated that the p values of the measurement results of the three modes in this system are all greater than 0.05, indicating that there was no significant difference between the variance of the measurement results of the system and the measurement variance of the measuring instrument. Therefore, the real-time measurement system for the harvesting area of a grain combine harvester designed in this article has high accuracy and can provide technical support for cross-regional operations.