## 2 VDES Data Link Credibility Monitoring Approach
### Radio Interference Detection Based on Message Characteristics
#### 2.1.1 VDES Message Integrity Verification Method Based on the MD5 Algorithm
Assuming the coordinates of monitoring station A are \((x_{A},y_{A})\), those of monitoring station B are \((x_{B},y_{B})\), and the coordinates of the spoofing source S are \((x_{S},y_{S})\); the time difference between the arrival of the VDES message sent by station B to station A and the arrival of the VDES message sent by source S to station A is given by:

Figure 5:9

In the equation, \(t_{AS}\) represents the time at which the VDES message sent by spoofing source S arrives at monitoring station A, and \(t_{AB}\) denotes the time at which the VDES message sent by monitoring station B arrives at monitoring station A.

Consequently, the difference \(\Delta d\) between the distance from monitoring station A to monitoring station B and the distance from monitoring station A to spoofing source S is given by:

Figure 7.0

In the equation, \(t_{AS}\) represents the time at which the VDES message sent by spoofing source S arrives at monitoring station A, while \(t_{AB}\) denotes the time at which the VDES message sent by monitoring station B arrives at monitoring station A, with \(c\) representing the speed of light. The distance \(\Delta d_{BS}\) between monitoring station B and spoofing source S is:

Figure 7.1

In the equation, \(x_{B}\) represents the horizontal coordinate of monitoring station B, \(y_{B}\) represents the vertical coordinate of monitoring station B, \(x_{S}\) represents the horizontal coordinate of spoofing source S, and \(y_{S}\) represents the vertical coordinate of spoofing source S.

In accordance with the definition of a hyperbola, the following is derived:

Figure 7.2

Figure 7.3 The two monitoring stations positioning scenario. Substituting Equations (12) and (13) into Equation (14) yields the equation for the positional range curve of the spoofing source:

Figure 7.4

As per Equation (15), it is evident that the range of the spoofing source's location lies on the circumference with monitoring station B as the center, expressed as follows:

Figure 7.5

When \(N\geq 3\), it indicates that three or more monitoring stations are simultaneously receiving the spoofing source message. By treating the positions of each monitoring station as centers and drawing circles with the signal coverage radius of each station, these circles intersect pairwise. The intersection points of two circles form common chords. From the intersections of three pairs of circles, three common chords can be derived, all intersecting at a single point, which represents the location of the spoofing source. The three monitoring stations positioning scenario is shown in Figure 7.6

We assume the coordinates of monitoring station A are \((x_{A},y_{A})\), monitoring station B are \((x_{B},y_{B})\), and monitoring station C are \((x_{C},y_{C})\), with O \((x_{O},y_{O})\) being the midpoint of stations A and B, where \(x_{O}=\frac{x_{A}+x_{B}}{2}\) and \(y_{O}=\frac{y_{A}+y_{B}}{2}\), and \(r\) represents the signal coverage radius of the VDES monitoring stations. Consequently, the intersections of the signal coverage circles of stations A and B result in two points, E \((x_{E},y_{E})\) and F \((x_{F},y_{F})\). The line connecting intersection point E and intersection point F is termed the common chord EF. The half-length \(r_{ef}\) of the common chord EF is determined as follows:

Figure 7.7

Figure 7.8 The three monitoring stations positioning scenario. The slope \(k_{AB}=\frac{y_{A}-y_{B}}{x_{A}-x_{B}}\) of the line connecting monitoring stations A and B can be used to determine the slope \(k_{EF}\) of the common chord EF. Figure 7.9

According to the theorem of intersecting circles, the line connecting the centers of two intersecting circles bisects the common chord of the two circles.