Analysis of the Principle of GPS Area Measuring Instrument from the Angle of Calculus

There are many methods for the area algorithm of plane graphics in mathematics, such as the cut-and-fill method, the integration method, etc. However, there are still many inconvenient factors in applying these methods to the measurement of land area. Therefore, the measurement of land area in industrial and agricultural production often encounters some problems. For this reason, with the development of science and technology, there are some instruments that can quickly and conveniently measure the area. For example, the GPS area measuring instrument is one of them. GPS area measuring instrument is a combination of global positioning technology, electronic technology and mathematical technology. The mathematics of this type of instrument is discussed mathematically.

An important formula in calculus is the Green's formula. This formula converts the double integral in area D into the curve integral over the boundary of area D. Substituting a specific function into the formula yields an area formula (*) for the planar region D: A=12QOLxdy-ydx. The formula requires that the boundary L be positive and at least piecewise smooth. If you do not limit L to be positive, the area is |A| and the area of ​​the polygon is examined by the formula (*). For an n-gon of a plane, if the coordinates of each vertex are known, the area of ​​the area enclosed by the n-side can be obtained. In practical work, the flat area of ​​the land area sought can always be seen as a polygon. When the surveyor walks around the zone boundary with the GPS for a week, the vertices of each vertex can be obtained. The acquired vertex coordinate data is input to the computer, and then the computer can calculate the area of ​​the desired area according to the formula (*). However, the coordinates measured by GPS will have a 2m error in the normal situation. If the rectangular coordinate system is established manually or mechanically, acquiring the vertices of the vertices is quite troublesome, and the formula (*) becomes meaningless.

Formula (**) is designed as a program. Once data a1, a2, +, an and H1, H2,,, Hn are obtained, the area of ​​the requested land can be quickly calculated using the program. It is worth noting that the formula (**) also applies to the situation shown in Fig. 3. It is only necessary to regard the clockwise rotation angle as a positive angle and the counterclockwise rotation angle as a negative angle.

We have analyzed some theories from the calculus and procedural point of view. Then we can understand how the above procedure can be used to calculate the area from small rooms to large fields and pastures. If it is possible to automatically obtain the long side distances and deflection angles of the polygons, a new type of GPS area measuring instrument can be designed. The measuring staff can obtain the area of ​​the area by carrying the GPS area measuring instrument around the area for one week.

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