An optimal design of GNSS interference localisation wireless security network based on time-difference of arrivals for the Arlanda international airport

Eshagh, Mehdi

doi:10.1515/jogs-2022-0142

Cited by 2 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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 ]…”

Section: Optimisation Criteria For Localisation Networkmentioning

confidence: 99%

“…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.…”

Section: Optimisation Criteria For Localisation Networkmentioning

confidence: 99%

“…The first constraint (31) controls the coordinate updates in such a way that the MSs move towards some specified directions. The mathematical derivations of them are available in [ 36 ]. D and d have the following structures:

where Az stands for the specified azimuth in which the MSs should move during the optimisation process.…”

Section: Optimisation Model and Required Constraintsmentioning

confidence: 99%

“…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 ]:

…”

Section: Optimisation Model and Required Constraintsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Eshagh

2023

Sensors

Self Cite

View full text Add to dashboard Cite

A smart city is a city equipped with many sensors communicating with each other for different purposes. Cybersecurity and signal security are important in such cities, especially for airports and harbours. Any signal interference or attack on the navigation of autonomous vehicles and aircraft may lead to catastrophes and risks in people’s lives. Therefore, it is of tremendous importance to develop wireless security networks for the localisation of any radio frequency interferer in smart cities. Time of arrival, angle of arrival, time-difference of arrivals, received signal strength and received signal strength difference (RSSD) are known observables used for the localisation of a signal interferer. Localisation means to estimate the coordinates of an interferer from some established monitoring stations and sensors receiving such measurements from an interferer. The main goal of this study is to optimise the geometric configuration of the monitoring stations using a desired dilution of precision and/or variance-covariance matrix (VCM) for the transmitter’s location based on the RSSD. The required mathematical models are developed and applied to the Arlanda international airport of Sweden. Our numerical tests show that the same configuration is achieved based on dilution of precision and VCM criteria when the resolution of design is lower than 20 m in the presence of the same constraints. The choice of the pathloss exponent in the mathematical models of the RSSDs is not important for such low resolutions. Finally, optimisation based on the VCM is recommended because of its larger redundancy and flexibility in selecting different desired variances and covariances for the coordinates of the transmitter.

show abstract

“…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 ]…”

Section: Optimisation Criteria For Localisation Networkmentioning

confidence: 99%

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

Section: Optimisation Criteria For Localisation Networkmentioning

confidence: 99%

where Az stands for the specified azimuth in which the MSs should move during the optimisation process.…”

Section: Optimisation Model and Required Constraintsmentioning

confidence: 99%

“…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 ]:

…”

Section: Optimisation Model and Required Constraintsmentioning

confidence: 99%