The effectivity comparison of TDOA analytical solution methods

Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations

“…In [ 67 ], an example of calculating target coordinates is given, in which the values of K i 1 and K i 2 are both positive. Two variants of target coordinates were obtained.…”

“…If the heights of the sensors differ slightly, the undetectable areas expand significantly ( z C,L,R,U = 8; 10; 12; 14 m, Figure 2 d). With the same BS heights, the target positions are not determined anywhere using the algorithm [ 67 ]. Significant areas, where the target coordinates are not determined, exist for almost all values of the BS coordinates.…”

“…With the addition of the fifth BS, it becomes possible to solve four systems of equations, which will have one common root corresponding to the true position of the target. An analytical solution to the problem of determining the location of an object in 3D for a positioning system of 4 BSs was obtained in [ 67 ], but in [ 67 ], not all values of the coefficients are given, which complicates the direct use of the algorithm. In addition, in [ 67 ], the problem of eliminating ambiguity in determining the coordinates was not solved.…”

“…A good description of analytical methods is presented in [ 66 , 67 , 68 ]. Transformation of the coordinates of a hyperbola during a shift and rotation on a plane can be found in [ 66 ].…”

“…Transformation of the coordinates of a hyperbola during a shift and rotation on a plane can be found in [ 66 ]. According to this transformation in [ 67 ], the effectiveness of two methods of TDOA analytical solution was compared based on the task of finding intersection points of hyperboloids (possible positions of a target). The first method analyzed was based on coordinate transformation from the initial system to a new system to simplify equations solving, and the second one was based on matrix.…”