1. Introduction
Following mandatory requirement since 2020 in large parts of the worldwide airspace, commercial aircraft use the ADSB (Automatic Dependent Surveillance–Broadcast) system (blythe2011ads) to broadcast messages that are received by airtraffic control (ATC) and observation networks^{1}^{1}1such as Flightradar24, FlightAware, and OpenSky Network.. ADSB allows an aircraft to transmit its satellitenavigation derived location, which then enables it to be tracked throughout its flight time. The broadcast messages are received by ADSB sensors which are typically placed arbitrarily onground by volunteers and system designers. The wide benefits of ADSB ranging from surveillance coverage, cost efficiency to environmental sustainability make it widely adopted by most commercial aircraft in Europe and North America, and it is expected to replace the radar system as a part of the Next Generation Air Transportation System (NextGen) (NextGen).
The placement of sensors is critical for the functioning of ADSB. The current deployment of ADSB sensors often places them arbitrarily on the ground (e. g., by volunteers contributing to the OpenSky Network (schafer2014bringing)), which creates some overcrowded areas and others without any coverage. For instance, it was shown in (MAVPro) that only 44% of ADSB messages in central Europe are received by four or more sensors, while the remaining areas are either covered by fewer sensors or not covered at all. Optimal sensor placement has typically been investigated as an availability problem: How to place the receivers such that they provide the best coverage for a geographical area (Maurosensors; NSGA2BasedNodePlacementOptimization; 5873254)? Placing them too close to each other leads to high and possibly unnecessary redundancy, whereas placing them too far apart may result in lost observation areas because the wireless channel is faulty and messages may get lost.
However, the open communication of ADSB where messages are sent without encryption and integrity protection also suffers from the risk of spoofing and jamming attacks. To counter this risk, attack detection and prevention techniques have been deployed or developed for the ADSB context: (1) A common approach to detect tampering with ADSB messages and the reported aircraft locations is the use of Multilateration (MLAT) (MantillaGaviria2015), which allows to validate the reported locations in the messages with computed locations based on measurements from multiple sensors. MLAT requires the message to be received by four (or more) receivers onground in order to derive the aircraft’s location. (2) Other approaches for validity checking rely on a smaller number of received messages. Strohmeier et al. (Strohmeier2015LightweightLV)
have proposed a lightweight approach to validate the received aircraft location claim based on the KNearest Neighbors algorithm (KNN), requiring only two sensors for location verification in two dimensions (2D). This approach leads to less accuracy than MLAT, but can be used in geographic areas covered by only two sensors. (3) To counter jamming attacks, finally, it is beneficial to place sensors in maximum distances to decrease the probability that all sensors in the reception range of a certain geographic area are impacted by a jamming attack.
The aim for an optimized placement of ADSB sensors that does not only target coverage (i. e., availability of the ADSB service), but supports the deployment of defense mechanisms (i. e., considers the security aspect of sensor deployment) creates the following challenge: How can the different security requirements on the numbers and locations of ADSB sensors best be fulfilled? We note that MLAT does not only need messages from at least four sensors, but its accuracy also relies on the level of Dilution of Precision (GDOP) (zhu1992calculation) which again depends on the locations and number of sensors. From a practicality aspect, we further need to consider that realworld deployments cannot easily be modified to reflect optimal sensor placements. This creates a second challenge: Knowing what an optimal sensor placement from the security perspective would be, how can existing placements of ADSB sensors best be enhanced by placing a certain number of additional sensors in a given area?
As a reaction to these questions, we tackle the problem of Optimal Sensor Placement (OSP) for ADSB from the security perspective, incorporating the constraints imposed by attack detection techniques. In particular, we define a multiobjective optimization (MOOP) problem and propose a set of solutions that satisfy these objectives simultaneously. We tackle this problem with respect to three security dimensions: First, we consider MLAT for verifying aircraft locations claims in the received ADSB messages. In this objective, we aim to provide a sensor placement solution where each broadcast message is to be received by at least four sensors and can accordingly be verified by an MLAT check. Second, since the cost of MLAT checks is relatively high, and it requires at least four sensors, which is hard to guarantee, we introduce a second objective: Location verification checks at a lower cost level but with less accuracy compared to MLAT. Finally, in our third objective, we aim to provide a sensor setup that behaves favorably under jamming attacks. We discuss three directions that can potentially reduce the effect of jamming attacks, (1) Maximize the distance between the sensors, (2) Maximize the distance between the jammer and the sensors, (3) Minimize the number of sensors within therange of the jammer. Thus the solution should be optimized concerning to all of these dimensions.
We treat each security dimension as an objective function to be optimized. Our target is to solve the OSP problem by providing solutions for sensor coverage that allow the aircraft to be tracked during their flight time while allowing the deployment of security checks that enable to verify ADSB messages and place sensors in a way that mitigates the effect of a jamming attack. The main key of our approach is that all objective functions are optimized simultaneously, where each solution is nondominated by another one. For this purpose, we adopt the Nondominated Sorting Genetic Algorithm (NSGAII)
(NSGAII) algorithm.In short, our main contributions in this paper are:

We model the problem of ADSB sensor placement under security considerations as a MultiObjective Optimal Sensor Placement Problem (OSP) with respect to three concrete security objectives—two for location verification (MLAT & leightweight verification) and one for jamming prevention.

We specify and formally introduce the three security objectives and investigate their impact on ADSB sensor locations. For the case of jamming attacks, our approach consists of a systematic way of including three security directions that impact the success of jamming attacks.

We provide a set of nondominated solutions for the proposed problem. Each solution provides a sensor placement with respect to the defined objective.
2. Preliminaries
2.1. Problem Statement
In this paper, we address the following two research questions:

Optimal Setting: How can we determine the minimum number of ADSB sensors and their nearoptimal locations that are required to cover a specific geographic area while supporting the deployment of security mechanisms, in particular locationverification checks and jammingprevention techniques?

RealWorld Setting: For a geographic area containing already deployed ADSB sensors (with possibly insufficient coverage), how can we find the minimum number of new sensors and their locations that should be added to the existing sensors to reach a closetooptimal sensor deployment?
2.2. AirtoGround ADSB Signal Propagation
For the transmitted message to be received by a receiver, the LineofSight (LOS) condition must be met. There are several factors with affect on the signal reception such as the transmitter power, the antenna gain of both transmitter and receiver, the distance between transmitter and receiver, Earth curvature, and environmental obstacles such as mountains and high buildings. The maximum message reception range corresponds to the radio horizon (schafer2014bringing) and under the tropospheric refraction, is given by (strohbehn1968line):
where represents the effective earthradius factor and (resp. ) the transmitter (resp. receiver) antenna height in meter. Through linear approximation of the refractivity gradient, it is shown in (blaunstein2007radio) that .
If the receiver is located beyond the radio horizon of the transmitter, it will not receive the transmitted message and we say it is located out of the reach of the transmitter. It follows that from Equation 2.2 in order for the broadcast message from a transmitter to be received by the sensor , the following condition must be met:
(1) 
2.3. TimeofArrival Localization
TimeofArrival (TOA) is one of the most widely adopted techniques to localize objects in radar systems, wireless sensor networks, and Internet of Things environments. The idea of this method is to determine the location of a transmitter using the time of arrival of broadcast messages by multiple, typically four, receivers. In more details, assume that there are four distributed receivers at locations . The TOA of a signal sent from a transmitter at location to the sensor is given by (Ichen2009wireless):
(2) 
where is the signal transmission time, the speed of light, and the measurement error.
The location estimation of the transmitter
can be derived by solving the above formula of three TOA differences. There are some factors that affect the accuracy of the obtained results, like the transmission range error and location of the sensors. MLAT is an example that has been used to localize aircraft using TDOA.2.4. Geometric Dilution of Precision (GDOP)
To improve the accuracy of MLATbased aircraft location estimation, the impact of the geometric dilution of precision (GDOP) should be controlled or decreased. The GDOP is affected by the geometry of locations of the receiving sensors: Placing the receivers close to each other will increase the GDOP value and consequently degrade the accuracy of MLAT, while the accuracy will be improved if the receivers are placed far away from another. The GDOP is defined as (zhu1992calculation):
(3) 
where
(4) 
and are the direction cosines from the aircraft to the sensor and
is the trace of the GDOP matrix. Assuming independent range measurement errors with equal variance
, it holds (manolakis1996efficient):(5) 
where is the covariance matrix of the estimation error on the transponder location. To compute the GDOP value, we must derive the matrix defined in Equation (4) that one would obtain from estimating the location of the transmitter aircraft using the measured ranges of four receivers in the ECEF (EarthCentered, EarthFixed) coordinate system. If and are the geodetic latitude and longitude of
respectively, then the vector
pointing from the aircraft to the sensor in the NorthEastDown (NED) frame is given by:(6) 
where the rotation matrix is :
It follows that:
(7) 
The GDOP at location can subsequently be computed from Equation (3) using the closedform expression derived in (zhu1992calculation).
2.5. Genetic Algorithm
Traditional methods for solving multiobjective function optimization problems scalarize all the objectives into one objective using a weight vector (NSGA_old). In such a scalarization process, the obtained solution depends on the weights that are specified by the user and it can be highly sensitive to this weight vector; the user needs to have prior knowledge of the problem in order to specify suitable weights. Moreover, such methods derive one possible solution only, whereas it may be interesting to get more than one solution. Genetic Algorithms (GA) (GA_Katoch2021ARO) solve MultiObjective Optimization Problems (MOOP) by providing a set of Paretooptimal solutions. Although the GA gives encouraging results, it shows a level of bias towards some regions since the set of solutions that are given by GA they are not disrupted fairly over the specified area where the way that select the population does not do fairly random selection of candidates (GA_thesis).
Nondominated Sorting Genetic Algorithm (NSGA) (NSGA_old) has been proposed by Srinivas & Deb to solve this issue and eliminate the bias by distributing the population over the entire Paretooptimal region. However, as demonstrated in (NSGA_996017), issues with NSGA include computation complexity and lack of elitism. Thus, NSGAII (NSGA_996017) has been proposed to solve these issues and to provide solutions for MOOP. NSGAII is well known to be a elitepreserving, fast sorting multiobjective genetic algorithm. Unlike other optimization algorithms, NSGAII optimizes all objectives simultaneously, where each objective solution is nondominated by other objective solutions.
Crowding Distancing (YANG2014197) of NSGAII reflects how far the solution is from the solution boundary, so if there are two solutions, the solution with a better rank will be selected; however, if these two solutions have the same rank then the solution is selected based on its crowding distance. Thus, the key features of applying the elitist, and the attention of using the nondominated solutions encourage us to adopt NSGAII to solve our OPS problem.
3. Threat Model
We consider two types of attacks with impact on ADSB communication:

ADSB Location Spoofing: The attacker exploits the open nature of ADSB communication to modify the content of transmitted ADSB message that are within the attacker’s range. He/she can insert own messages or modify the broadcast location of the aircraft which leads to receiving a modified location by the onground sensors. The success of the attack depends on whether the attacker is located in a geographical area that is only covered by few sensors, where location verification methods cannot be applied.

ADSB Jamming: The attacker tries to block the communication that is received by the onground sensors by causing interference on the wireless channel to prevent the reception of ADSB messages. The attacker can use any software radios with amplifiers that are typically cheap and affordable.
Consequences of such attacks can lead to incorrect observations of flight paths to disaster accidents when aircraft are no longer (correctly) tracked by the ATC system.
4. Overview: Objective Functions
We aim to solve the Optimal Sensor Placement (OSP) problem under the consideration of multiobjective functions (MOF) that provides defense mechanisms in addition to full coverage. We use the NSGAII algorithm (NSGA_996017) to derive the best solution that satisfies all required objectives as best as possible in order to place the sensors on ground. Since we are dealing with multiobjective functions, the NSGAII may derive more than one solution, where each solution reflects the tradeoff between the corresponding coverage and security level of all objectives.
We tackle the OSP problem from two dimensions: First, we consider a geographical area without ADSB receiver coverage in an idealized scenario, where we aim to derive an optimal distribution of the sensors from scratch as an upper bound of how good the best solution can be. Second, we take realworld considerations into account and consider a geographical area where sensors are deployed already but their number and locations do not provide an optimal placement – we aim to identify how close this scenario can come to the idealized optimal solution when new sensors are added.
Our approach provides several solutions with tradeoffs as will be later shown in Section 8. Here, we next describe the set of security objectives that these derived solutions are based on; for each objective we provide a detailed specifications and security level.
4.1. Objective Function 1: Multilateration (MLAT) surveillance under GDOP
MLAT is a standard technology to localize aircraft or verify the received location from aircraft. Whenever we say the airspace supports MLAT checks we refer to verifiable location claims. Since MLAT requires four or more sensors to receive a message, by this first objective, we will identify the best sensors deployment solution such that each message can be received by at least 4 sensors on the ground.
Let us assume an airspace contains the expected ADSB traffic. Then we take sample locations from the volume space:
where, represents the required GDOP value at . In addition, given a placement of ADSB sensors, we write to denote the achieved GDOP value at the location due to the particular geometry of . For readability, we omit the subscript and write .
In order to find the best deployment of ADSB sensors and their corresponding locations from , to satisfy a perlocation GDOP requirement for a given airspace , we assume to be the tolerance parameter on the GDOP at any location, where can only be accepted if:
which is equivalent to , where represents the supnorm defined by
The Mean Squared Deviation (MSD) between the achieved and the required GDOP in the entire airspace of our first objective is:
(8) 
4.2. Objective Function 2: Lightweight Location Check with Transmission Range Evaluation
As described in Section 2, the Lightweight Location Estimation (Strohmeier2015LightweightLV) is based on TDOA, where the received message is received by at least two sensors. We can thus design our second objective to provide another security check with fewer sensors: only two sensors are required. However, the accuracy of this check must be assumed to be less than for the MLATcheck (objective 1), but still, this lightweight method can provide fine results with small budget, and it can be used in areas where MLAT is not available either due to lack of a number of sensors or an attack that affects the area and disrupts some of the sensors.
To achieve the second objective, we use the transmission range or distance as an evaluation principle to deploy the sensors. In more details, given an airspace with uniformly sample locations from , the following spatial data matrix is defined:
where, represents the best minimal distance from to sensor , the required one. In addition, given a placement of ADSB sensors, we write to denote the achieved distance from the location to due to the particular geometry of . For readability, we omit the subscript and note .
Now, to find the minimal number of ADSB sensors and their corresponding deployment to guarantee a perdefined transmission range requirement for a given airspace , let us assume be the tolerance parameter of at any location. A sensor placement can only be accepted if:
where represents the supnorm defined by:
The Mean Squared Deviation (MSD) between the achieved and the required in the entire airspace under consideration is
(9) 
4.3. OF 3: Low Sensor Density under Jamming
Tackling jamming attacks requires more sophisticated considerations to optimize the locations of sensors on ground. The aim of this objective is to reduce the effect of jamming by placing the sensors in a way that guarantees good coverage, while keeping the number of sensors affected by the jammer to a minimum. We incorporate three directions for the network topology of deployed sensors:

Direction 1: Maximize the distance between any two sensors , where and are any two sensors in . The aim is to select the best candidates of sensors that are placed in locations far away from each other, in other words, the best low sensor density network.
In more details, given the an airspace like in the first two objectives, we need to fully cover it by a set of ADSB sensors. Now, to find the minimal number of ADSB sensors and their corresponding deployment to guarantee full coverage for given airspace and low sensor density, let us assume be the tolerance parameter of between any two sensors. A sensor placement can only be accepted if:
where represents the supnorm defined by:
The Mean Squared Deviation (MSD) of the distance between any two sensors under consideration is:
(10) 
Direction 2: Maximize the distance between the jammer and the sensors . This direction aims to reduce the JammingtoSignal (JSR) ratio (manuals).
(11) where, and are the transmission power and antenna gain of the jammer, the and the transmission power and antenna gain of the transmitter, and the , are the distance from the transmitter to the sensor, and the distance from the jammer to the sensor respectively.
As we can see from the Eq. 11, we can reduce the ratio either by changing the transmitter characteristics which is here the ADSB outdevice on all aircraft, or maximize the distance between the jammer and the receiver. Since it is hard to change the already deployed transmitters, we can work on the distance between the jammer and the receiver.
Given list of jamming attacks at different locations within the airspace , let us assume be the tolerance parameter of between and jammer and any sensor. A sensor placement can only be accepted if:
where represents the supnorm defined by:
The Mean Squared Deviation (MSD) of the distance between any jammer and any sensor under consideration is written:
(12) 
Direction 3: Minimize the number of sensors within the range of the jammer. As jammer tries to interfere with all the sensors that are within its range. We aim by this objective to reduce the number of sensors that are within the range of the jammer, where at anytime the number of affected sensors is minimal as possible.
In more details, given the airspace , list of sensors , and list of jamming attacks , with the assumption that is the tolerance parameter of the required number of sensors within the jammer range. A sensor placement can only be accepted if:
which is equivalent to:
The Mean Squared Deviation (MSD) of the achieved and required number of sensors within the LoS of the jammer under consideration is written:
(13)
5. System Approach and Methodology
5.1. Assumptions
For finding the optimal placement locations of sensors we make the following simplifying assumptions:

Receivers are assumed to be deployed on the geoid surface.

We neglect the obstructing effect of buildings or mountains on the ADSB signal reception probability.

The earth curvature is as the major impediment to the direct visibility between aircraft and groundbased sensors.
5.2. System Nodes Representation
Under the consideration that all system nodes are deployed on the geographical surface, their locations are specified by their geodetic latitude, longitude, and altitude. Accordingly, for our surface area , we represent all the nodes within the latitude () and longitude () boundaries of this area.

Pick uniformly distributed points on the surface area . , where, each point in represents the potential location of aircraft in space. .

Place uniformly sensors on the specified area space . , where, .

Place uniformly distributed jammers across the whole area . , where, .
where and are the longitude and latitude of the points, sensors, jammers nodes respectively. For each set of nodes to be added uniquely, the following constraint is added:
where represent. the and respectively.
The geoid boundaries of the set is specified with this constrain:
where (resp. ) and (resp. ) are the lower and upper bounds on each node longitude (resp. latitude).
5.3. Fitness/Cost Function
The fitness function is designed according to our multiobjective optimization problem based on the MSD that we described in Section 4. The MSD computes the fitness of selected subsets of sensors from that are chosen by the NSGAII algorithm. It evaluates the placement of each subset of sensors by measuring the average of errors between the achieved value and the required one to get the final score. NSGAII searches for the optimal Pareto frontier (Miettinen1998NonlinearMO), and more precisely we consider all solutions with first Pareto front, non dominated solutions.
As antijamming space objective function 4.3 considers three optimization directions; two maximization problems and one minimization problem, we deal with them as one objective by using Weighted Sum Method (Weighted_sum_method). Each direction can be assigned a weight, which reflects the importance of this direction against the other two directions, and then combine them together as one score.
(14) 
where is the weight for objective direction , and .
In addition, we define a cost or penalty function to increase our security. The cost function searches for the Pareto frontier of all defined objectives in Section 4 versus the cardinality of the selected sensor set. Thus, we formulate our problem as a Knapsackequivalent (knapsack_problems), where the 2D surface area is split into rectangles, where each can be assigned a senor and this will be assigned a weight 1 () or () if there is no sensor is assigned to the rectangle. The target is to have a few rectangles that are assigned a sensor (minimize the number of sensors that are needed to be deployed) while optimizing all of our objectives. We formulate the following penalty function on the selected set of sensors.
(15) 
Eventually, the weighted fitness function can subsequently be obtained from MSD of the objective functions in 4 and (15) as:
(16) 
where is the Pareto weight of the cost function .
Finally, since we are working with multiobjective functions and each objective implies different checks and consequently different unit scales, we normalize all the obtained scores by the following equation for each objective:
(17) 
where, is the obtained score from the objective function using NSGAII, and the , are the maximum and minimal required scores of this objective, and the best value is assigned at the end of all generations.
5.4. Procedure to solve OSP Problems
To solve the OSP problems that we define in Section 7, we adopt the MSD to get the scores of all defined objectives as we explained in Section 4. Before that, we compute and derive the following structures to be used through objective computations.

Compute direction cosines matrix for all points in to all sensors in . , where, are the direction cosines from the airspace point to the sensor.

Compute direction cosines matrix for all jammers in to all sensors in . , where are the direction cosines from the jammer to the sensor.

Compute the distance from each point in to all sensors in using the defined expression of Euclidean Distance. , where, are the distance from the airspace point to the sensor.

Compute the distance from each jammer in to all sensors in . , where, are the distance from the jammer to the sensor.

Compute the distance between all sensors in . , where are the distance from the sensor to the sensor.
After Preparing all the matrices, we compute the objective functions. Each procedure is applied at every generation of NSGAII.
5.4.1. Objective 1: Minimal GDOP

Find the set of all ADSB receivers for which Inequality (1) is valid.

If , set . (The GDOP cannot be evaluated if there are less than 4 sensors in LOS condition with the aircraft)

Otherwise, compute the GDOP at for all 4sized subsets of using the closedform expression proved in (zhu1992calculation). Then set to the minimal value found.
5.4.2. Objective 2: Minimal transmission range

Find the set of all ADSB receivers for which Inequality (1) is valid.

If , set . (The lightweight location check can not be evaluated if the umber of sensors are less than two)

Get the distance from each point in to the all selected sensors from from the matrix .

Get the to the minimal two values, which represent the closest two sensors, and assign it to the .
5.4.3. Objective 3: AntiJamming area

For each subset of selected sensors from get the distance between them from the

Get the best subset that has the maximum distance from all sensors (Direction 1).

For each jammer in , find the set of all ADSB receivers that are within the range jammer.

If , set (Direction 2), and (Direction 3) (Best solution).

Otherwise, get the distance from each for all sensors from the , and then get the minimum one to get the score of , and repeat step 3 and step 4 for all subsets of sensors to find the and assign it to .
6. Selecting the Optimum
The optimization technique of NSGAII, as we explained in Section 2.5, optimizes all the objective functions simultaneously where each solution can not be dominated by any other. However, there is no solution that can satisfy all the objectives together. In more detail, if there are three solutions , , and , where and belong to the first Pareto frontier and belongs to the second one. We can say solution can not be dominated by solution since gives better solution for an example objective one, while gives better solution for objective where both of them are dominated by solution because they offer better solution for and than .
Selecting the best solution depends on few factors like the Budget, the security level, level of redundancy and level of noise (Appendix 6 for more details). There is no one solution that satisfies all objectives. The optimal solution is relative here. More details will be explained in Section 8.
Selecting the best solution, the best number of sensors, and their locations as in our problem depends on some factors, which include:

Budget: Sensor placement is restricted to the number of available sensors that would have to place. More available sensors give flexibility and simplify the process of choosing the best numbers.

The required security level: As we explained in Section 4, there are different security checks and each one has some requirements and at the same time provides a level of accuracy, as an example MLAT is more accurate than lightweight location verification. Thus, the best solution depends on the required security level, if the system is critical then the solution which gives better scores for objective number one should be chosen. On other hand, if the system is restricted to number of sensors and at the same time there is should be a level of security, then another solution that satisfies this requirement would be more valuable for this case.

The level of redundancy: Network leakage could be caused by some factors, like the sensor goes turned off because of an empty battery or any reason or by infecting it by an attack. For whatever reason, if the area is covered by only this sensor, then all broadcast messages will not be received. Taking into consideration this factor, a solution that gives a fine level of redundancy has to be chosen.

Level of noise from crowded sensors: Placing many sensors close to each other may potentially produce level of noise, and as a result reflects on MLAT accuracy.
7. OSP problems and Case Studies
7.1. Scenario 1: OSP from Scratch
In this scenario, we consider the situation where the volume space is uncovered by any sensor. Thus, we have to find the best minimal number of ADSB receivers and their locations to cover it. That is, each in is assigned the required GDOP value, and the required (closest) distance from this to the ground, . In addition, the bestrequired distance between the jammers and sensors, and the required distance between sensors are defined.
In an ideal scenario, we wish to cover with a budget of sensors where all objectives in Section 4 are satisfied and the differences between achieved and required values of all objectives are equal to zero. Although this case is hard to achieve in practice, we optimistically look to find a sensor placement solution that is as close as possible to this ideal case.
7.2. Scenario 2: Optimal Network Augmentation
In reality, there are already deployed ADSB receivers on the ground. However, the current deployment does not guarantee full coverage, and as a consequence security checks can not be applied. By this scenario, we wish to augment the current deployment by adding additional receivers to the existing ones to provide a nearoptimal solution. We assume the current sensors network consists of deployed receivers at known locations that are obtained from OpenSky database. We look to find the best number of new sensors that can be added to the deployed ones to provide the best nearoptimal solution.
Suppose new sensors must be deployed. Then . The set of new receivers are chosen from a predefined set of candidate ones , where the locations of these candidates are already known.
8. Experimental Evaluation
8.1. First Findings and Observations (”Random Sensor Placement”)
OF1  OF2  OF3  
Fitness Value  0.02203632  0.02732189  0.05420901 
To evaluate the effectiveness of our system and check the objective function of the proposed solutions by NSGAII, we consider a small geographical area between 47.4 to 51.4 latitudes decimal degrees and 5.71 and 9.71 longitudes decimal degrees. We were able to get the location of 21 ADSB receivers from OpenSky for this specified area. The current deployment of these sensors is placed randomly by the users. Thus, we evaluate the current deployment and we check the fitness values of all objective functions. We test the individual objective function and all the combinations of objectives to check how far is the current deployment to the optimal solution. Table 1 shows the fitness function values of the objective functions. We consider these values as a reference point to show how far is the current deployment from the optimal scenario.
As our first objective targets to have full coverage while minimizing the GDOP value, we test how are the kcoverage and GDOP values of the 21 ADSB receivers from OpenSky. Figure 1 represents the heatmap of the sensor’s coverage (kcoverage) of the specified area across different heights (altitude). As we can see from the figure, aircraft at low height have low coverage which limits the MLAT check during takeoff and landing phases (the most critical and important phases of aircraft path), but once the aircraft goes up it will be visible (within LOS) to more sensors. However, such deployment also produces a significant amount of GDOP values which reduce the accuracy of the MLAT verification test as figure 2 reflects the condense of GDOP values for this random placement.
Moreover, we evaluate the resistance of the current deployment against the jamming attack (our third objective). To test that, we generated 75 jamming attacks across the whole area at different altitudes. We assume the attacks could be at different locations, like on the high building, or even on the aircraft. We check how many sensors out of 21 sensors are affected by such a setup. Figure 3 reflects how successfully the attackers at m and m are able to jam almost all the deployed sensors since they are placed close to each other and they are within the range of the attackers. For test purposes, we assign almost the same weight for all three directions of our third objective ( ), however, these values can be adjusted by system designers to serve their desires.
8.2. Results
Now, we are considering the same area of study and with new sensors that we are wishing to place considering the objective functions that we have. First of all, we use the basic GA to get the fitness value of each objective alone and then the fitness value of all together across different number of sensors. Figure 4 depicts the fitness function values of the three objectives and the number of generations that are needed to reach the nearoptimal solution with . The third objective takes more generations to get the nearoptimal solution, hence it combines three directions; two maximization problems and one minimization problem. Also, we test how the GA algorithm is able to get a solution of all objects together. Based on the experiments, we observed that at the genetic algorithm stops improving the fitness value, so it will be best minimum number of sensors that are required to cover the whole area of study in respect to the three objectives that we defined. Thus, we fix the number of sensors to for the rest of experiments.
The obtained solution by GA considers all objectives together, where the system designers are not able to select the best solution for each objective. Thus, We run the NSGAII and we got a set of solutions where each solution is nondominated by another. Figure 5 shows set of solutions to place new sensors with their fitness function. We have to illustrate that each solution represents the locations of the sensors that we are wishing to place. The solution with minimal fitness value considers better than the one with high values. As an example, from the figure 5, we can say the solutions that are located close to the bottom left corner are nearoptimal solutions for the first and second objectives, while the solutions are considered near optimal based on the third objective where they are close to the ground surface of the cube.
Figure 6 shows the location of the already deployed sensors, candidates sensors, and the selected sensors out of . As we can see the deployed ones are concentrated close to each other, while the obtained solution from NSGAII distributed the sensors over the whole area in away guarantee full coverage and at the same time satisfies the objective functions.
Moreover, we consider the scenario where we have to add new sensors to the already deployed ones to get a nearoptimal solution. We assume we have to add new sensors and we need to check the set of solutions to place them with the sensors from OpenSky. Figure 7 presents the set of sensors with their fitness values. As shown, the set of solutions go slightly to the rightup which means still we can be close to the optimal scenario with sensors and the solutions could be enhanced if we increase the number of sensors, but we restrict ourselves here to to show how the system designers with low budget can get benefit of our method to place their sensors with the already deployed ones.
As we are considering increasing the coverage and reducing the GDOP values, we test the kcoverage and GDOP distribution for one of the obtained solutions from NSGAII. As we can see from figure 10 how the selected sensors can still achieve good coverage where MLAT or Lightweight checks can be used to verify the aircraft locations while the GDOP value is reduced significantly as shown in figure 11.
The percentage of the distribution of GDOP values is presented in Figure 8 and Figure 9 . The figures shows that the GDOP of the current deployment sensors above is mostly around , while it is reduced to only with the selected ones.
Lastly, we test how the locations of the selected solution of sensors are resistant to the jamming attack. As we can see from figure 12 the number of sensors that are affected by the jamming is reduced compared with the one of the deployed ones. Also, we have to mention that, these numbers are across the whole area, while the ones that are shown in 3 are all concentrated within the range of deployed sensors.
9. Related Work
Aircraft tracking becomes vital with the widespread of cyberattacks. Thus, some existing approaches verify the trustworthiness of these received messages. Multilateration (MLAT) (MantillaGaviria2015) is one of the most famous approaches that have been used. However, the percentage of messages that can be veritably by MLAT with GDOP is only around 5.24% from the whole messages (strohmeier2018k) because such verification requires at least four sensors to receive the message. Another KNN based approach (strohmeier2018k) is proposed to verify the messages that are received by two sensors. This approach increases the percentage of the messages that can be verified up to 41.48% but in 2D dimensions. Other solutions (MAVPro) also proposed to verify the messages that are received by one sensor but with less accuracy.
All of these location checks depend on the number and the location of the receiving sensors. In an unstructured placement of ADSB receivers, the location verification checks become inapplicable and the aircraft may not be tracked by the ATC. Recently, the OSP problem in an avionic context has been investigated (monteiro2015detecting). The authors disregard the requirement of aircraft height (altitude) verification and they only verify the latitude and longitude, they did that based on the assumption that MLAT applied with coplanar receivers generally results in a poor vertical dilution of precision. Such a way could minimize the horizontal error that is computed as the ratio between the common intersection area between all k receiving sensors (also known as the kcoverage or kintersection area) and the cumulative area that is covered by those receivers. However, this approach is inaccurate for location verification since the aircraft has to be considered. We believe that, if the receivers are placed and spread carefully, then the coplanarity assumption can be broken due to the Earth curvature.
In (nijsure2016adaptive) the authors addressed the problem of optimal sensors selections through the aircraft tracking phase. This method assumes the deployed sensors are thoughtfully placed, thus, if the sensors are poorly chosen then an acceptable GDOP value can be achieved.
Authors in (Maurosensors) proposed a procedure to place the ADSB to enhance the modeS multilateration stations for airport surveillance. Their approach takes into account the LoS, and the GDOP along with Cramer–Rao Lower Bound (CRLB) (ucinski2004optimal) analysis. Their standard was able to enhance the MLAT by using the GA to get the station locations. However, all of the discussed methods were targeting only one objective and non of them targets the jamming attack reduction. Thus, our work addresses the OSP as MOOP and solves it using the NSGAII that provides nondominated solutions.
10. Conclusion
A MultiObjective Optimization Problem (MOOP) to place the ADSB sensors onground is proposed by this paper. The Optimal Sensor Placement Problem has been tackled with respect to three objective functions. The first and the second objectives aim to provide an optimal solution that guarantees full coverage where each ASDB message has to be received by at least one receiver and at the same time allows location checks of the aircraft to verify the trustworthiness of the received claim location in the ADSB message. While in our third objective, we aim to reduce the effect of jamming attacks by placing sensors in a way where the number of sensors that are affected by the attackers is minimized. We use the Nondominated Sorting Genetic (NSGAII) algorithm to optimize and get our set of solutions. The results show, how the obtained solutions are optimized simultaneously and each solution is nondominated by another which gives the system designer the flexibility to select the best optimal solution based on their budget and needs.
Acknowledgments
This work is supported by the Center for Cyber Security at New York University Abu Dhabi (NYUAD). The authors gratefully acknowledge financial support of and interaction with armasuisse Science & Technology. We would like to thank the OpenSky Network for support, more specifically Martin Strohmeier for his collaboration and feedback at the early stages of this work.