Optimization of Basepoint Configuration in Localization of Signal Interference Device

Abstract

Precise navigation, as a method for guiding vehicles from one point to another, is an important subject these days especially in navigation of aircraft. Global navigation satellite systems (GNSSs) are capable tools for such a purpose. Any intentional or unintentional interference in satellite signals may cause risks of deadly accidents. Therefore, it is tremendously important to control airports or harbors and locate any existing radio frequency interference device. This localization can be done based on measuring time of arrival (TOA), angle of arrival (AOA), or time difference of arrival (TDOA) of signals from the device to sensors or receivers at some basepoints. In this article, a method is proposed based on these arrivals for optimizing the configuration created by these basepoints from a large grid of points covering a control area. Furthermore, a simulation test was performed to verify the theory, and after that a control network was designed and optimized for the international Landvetter Airport of Sweden. Our simulation studies show that when the AOA is used, our optimization is more robust with respect to the control grid resolution. In addition, optimization based on the TDOA improves the coverage over the control area with a significant reduction of error of control points, but because of the special geometric shape of the Landvetter Airport, such an optimization was not successful.

Optimal Configuration for Monitoring Stations in a Wireless Localisation Network Based on Received Signal Strength Differences

“…By such definitions, the coordinates of the nodes are derived according to the grid resolution. The transmitter is located amongst these nodes in the localisation process; see [ 35 , 36 ]…”

“…When the VCM is selected for optimisation, its direct mathematical relation with the coordinates of the MSs is needed. To derive it, let us expand the VCM by the Taylor series for a node and four MSs of M, N, O and P (see [ 35 , 36 , 40 , 41 , 42 , 43 ]): where is the estimated VCM of the node of the initial design, and are the coordinate updates to the initial locations of the MSs, and and are, respectively, the partial derivatives of the VCM with respect to the coordinates of the i th MS, with the following expressions (see [ 35 , 36 ]): where the elements of and , are partial derivatives of A or the second-order partial derivatives of the observables. Note that the first-order derivative is taken with respect to the transmitter coordinates and the second-order one with respect to x i and y i -coordinates of the i th MSs.…”

“…The system of Equation (24) should be solved for the coordinate updates in a least-squares sense, but Eshagh [ 35 ] has mentioned that applying some constraints in the quadratic optimisation model is necessary, otherwise, instability and improper configurations are obtained. Therefore, the following optimisation model for solving the system (24) is suggested: …”

“…The second constraint (32) define the search area around each MS, and the coordinate updates are computed in such a way that the MSs remain inside the search area; for details see [ 35 , 36 ]: …”

“…The location of the MSs or in other words, their geometric configuration has a significant role in the quality of localisation. Xu [ 31 ] studied this issue for the hybrid RSS, AOA, and TOA, but Eshagh [ 35 ] applied quadratic optimisation with constraint for obtaining an optimal configuration for the MSs based on the AOA and the TDOA, and concluded the optimal design based on the TDOA is highly dependent on the geometric form of the area, and his efforts for design optimal configuration for the Landvetter airport of Sweden was not successful. However, in another study Eshagh [ 36 ] showed that optimisation can be performed without problem if the area is close to a square and applied to the Arlanda International airport in Sweden.…”