# A Satellite Selection Strategy of SURF IA in Airport Intelligent Monitoring

Authors: Weiwei Zhao; Lizhi Duan; Xuhong Jian
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The implementation of Enhanced Traffic Situational Awareness on the Airport Surface with Indications and Alerts (SURF IA) monitoring in airports improves the safety and efficiency of airport surface operation. Navigation accuracy category for position (NACP), navigation accuracy category for velocity (NACV), and other data are obtained from Automatic Dependent Surveillance-Broadcast (ADS-B) IN, and these data will be the only data source of SURF IA. In this paper, we use the Beidou System (DBS) and Global Positioning Symbol (GPS) dual system as the positioning data source of the ADS-B. In cases where all visible satellites meet the performance requirements of the SURF IA, particle swarm optimization (PSO) and a new particle swarm optimization (APSO) are used to screen the integrated navigation satellites to meet the requirements of SURF IA by using fewer satellites, and the satellite selection ability of the two is compared. The simulation results show that under the same conditions, by using fewer navigation satellites can meet the minimum monitoring performance requirements for the implementation of SURF IA operation. And the star selection ability of APSO is better. This improves the performance of airport surface intelligent monitoring.


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## Body

## 1. Introduction

In airport operations, it is essential to use new technology to guide and monitor aircraft taxiing, especially when the pilot has low visibility or a complex taxiing route is followed. The ADS-B [1] uses data links to perform traffic surveillance and flight information transmission.The functional framework of SURF IA consists of two systems: airborne surveillance system and ground system, as shown in Figure1. Because SURF IA monitoring technology can be used in the final approach segment, the initial takeoff segment, and the surface operation segment at the same time, the ground system is not necessary. The airborne surveillance system of SURF IA is composed of two subsystems: the transmitting subsystem and the receiving subsystem. The transmitting subsystem broadcasts the received ADS-B signal, which is generated by data sources such as navigation sensor, air pressure altitude, and flight management. The receiving subsystem receives ADS-B data from the air and the ground at the same time, and the generated data report is transmitted to the SURF IA equipment. The processed data are displayed to the crew by Cockpit Display Traffic Information (CDTI). Just like vehicle path planning, using the received data, the aircraft on the airport surface can organize and plan the path according to the demand, time, and priority [2].Figure 1
The functional framework of SURF IA.BDS is an independent satellite navigation system, which integrates navigation and communication capabilities. It provides real-time, accurate, safe, stable, and reliable navigation information [3].In 2020, Zhang et al. analyzed the feasibility of SURF IA operation on the surface [4]. The research showed that using multiconstellation combinations satisfies the performance requirements of the SURF IA operation monitoring. In such cases, the system does not need to rely on the wide-area or local difference and only requires a single point absolute positioning. Based on the definition of the geometric factor of accuracy (GDOP), Ding and Wei also proposed a new algorithm for solving the GDOP of combined satellite systems [5]. A satellite selection algorithm was also proposed based on irregular triangulation projection and the imperial competitive optimization algorithm (ICA) to reduce the number of screening satellites and the GDOP value [6, 7]. Mosavi and Divband used the swarm intelligence algorithm to carry out satellite screening research, and successively proved the effectiveness of the algorithm and improved the positioning accuracy [8, 9]. Some scholars have improved the traditional star selection algorithm by defining the weight of each satellite to the total GDOP [10]. In 2014, Teng and Wang strictly deduced the GDOP formula and studied the influence of adding satellites of different constellations on GDOP [11].In this paper, we consider the combination of Beidou and GPS as the ADS-B horizontal position information sources. We then use the particle swarm optimization algorithm to screen all visible satellites to improve the timeliness of navigation satellite positioning and improve the SURF IA surface monitoring performance.


## 2. Transmission Network and Communication Link

ADS-B equipment has two functions: OUT and IN, both of which are based on data link communication technology [12]. ADS-B OUT is to send its own position, altitude, speed, and other information to other aircraft and air traffic control ground monitoring system to provide real-time position data for air traffic controllers. The ADS-B IN function means that the aircraft receives the broadcast information sent by other surrounding aircraft and displays it on the CDTI. In addition to the SURF IA function on the ground, the self-organizing network of mutual monitoring between aircraft in the air can also be realized to present the status of the surrounding aircraft to the pilot in real time, as shown in Figure 2. Wireless networks are composed of a group of sensor nodes, which sense the monitored environment and transmit this information to the ground station or receiver through a wireless link [13].Figure 2
ADS-B monitoring network.


## 3. The Introduction of SURF IA

### 3.1. The Application of SURF IA

Airport Surface Situational Awareness (ASSA) and Final Approach and Runway Occupancy Awareness (FAROA) are the two applications of the SURF IA system [14]. ASSA uses the airport map database to display the necessary airport elements on the CDTI, such as taxiway, runway, and buildings, but it does not need to display all the airport information. FAROA is used in the final approach segment, the initial takeoff segment, and runway crossing to improve the crew’s perception of the surrounding scene.The SURF IA system also includes two different components, namely, SURF IA indication and SURF IA alarm. The SURF IA indication is used for normal operations with the risk of conflict. The SURF IA alarm is used for abnormal operations with a risk of conflict or imminent conflict. When the aircraft is in the SURF IA indication stage, it is usually safe, but there is a risk of collision after a period of time. When the situation is urgent, the SURF IA alarm will appear. The prompt voice or information given by the monitoring system can prevent collisions between aircraft. At this time, the crew must make effective countermeasures.


### 3.2. Analysis of the Minimum Operation Performance Standard for SURF IA Monitoring

SURF IA interoperability is the minimum requirement for airport monitoring quality indicators. Evaluating the monitoring quality indicators determines whether the position and speed data obtained from the SURF IA satisfies the required accuracy level.The monitoring quality index includes position and speed navigation accuracy indexes, the navigation accuracy category for position (NACP) and the navigation accuracy category for velocity (NACV). The monitoring requirement of SURF IA is NACP ≥ 9 (95%), in which the indication and alarm functions are only used if NACP is 10 or 11, and when NACP ≥ 10 (95%), the position accuracy requirement of implementing all functions of SURF IA is satisfied [14]. In cases where SURF IA is active, the speed-accuracy requirement is NACV ≥ 1 (95%) [15, 16]. This means that the probability that the monitoring quality index reaches the standard level is more than 95%.With the increasing accuracy of navigation satellite positioning, the obtained NACP is greater than or equal to 7 in the actual calculation process, and the value of NACP is determined based on the estimate of position uncertainty (EPU). The EPU refers to a circular area with the ADS-B reported position as the center and the EPU as its radius. There is a 95% probability that the actual horizontal position of the aircraft is within this circular area. With different NACP values, the corresponding requirements of the EPU are also different. For example, the EPU is less than 185.2 m when the NACP is 7, the EPU is less than 30m when the NACP is 9, and the EPU is less than 10m when the NACP is 10 [15, 17]. If the navigation information is provided by GPS, the EPU is also called HFOM (Horizontal Figure of Merit).The horizontal velocity value (HFOMV) and the vertical velocity value (VFOMV) are important parameters of NACv, and both of them should reach the 95% accuracy range. Similar to the NACP, different NACv values have different requirements for HFOMV and VFOMV. The greater the NACv value, the more stringent the requirements [17].


## 3.1. The Application of SURF IA

Airport Surface Situational Awareness (ASSA) and Final Approach and Runway Occupancy Awareness (FAROA) are the two applications of the SURF IA system [14]. ASSA uses the airport map database to display the necessary airport elements on the CDTI, such as taxiway, runway, and buildings, but it does not need to display all the airport information. FAROA is used in the final approach segment, the initial takeoff segment, and runway crossing to improve the crew’s perception of the surrounding scene.The SURF IA system also includes two different components, namely, SURF IA indication and SURF IA alarm. The SURF IA indication is used for normal operations with the risk of conflict. The SURF IA alarm is used for abnormal operations with a risk of conflict or imminent conflict. When the aircraft is in the SURF IA indication stage, it is usually safe, but there is a risk of collision after a period of time. When the situation is urgent, the SURF IA alarm will appear. The prompt voice or information given by the monitoring system can prevent collisions between aircraft. At this time, the crew must make effective countermeasures.


## 3.2. Analysis of the Minimum Operation Performance Standard for SURF IA Monitoring

SURF IA interoperability is the minimum requirement for airport monitoring quality indicators. Evaluating the monitoring quality indicators determines whether the position and speed data obtained from the SURF IA satisfies the required accuracy level.The monitoring quality index includes position and speed navigation accuracy indexes, the navigation accuracy category for position (NACP) and the navigation accuracy category for velocity (NACV). The monitoring requirement of SURF IA is NACP ≥ 9 (95%), in which the indication and alarm functions are only used if NACP is 10 or 11, and when NACP ≥ 10 (95%), the position accuracy requirement of implementing all functions of SURF IA is satisfied [14]. In cases where SURF IA is active, the speed-accuracy requirement is NACV ≥ 1 (95%) [15, 16]. This means that the probability that the monitoring quality index reaches the standard level is more than 95%.With the increasing accuracy of navigation satellite positioning, the obtained NACP is greater than or equal to 7 in the actual calculation process, and the value of NACP is determined based on the estimate of position uncertainty (EPU). The EPU refers to a circular area with the ADS-B reported position as the center and the EPU as its radius. There is a 95% probability that the actual horizontal position of the aircraft is within this circular area. With different NACP values, the corresponding requirements of the EPU are also different. For example, the EPU is less than 185.2 m when the NACP is 7, the EPU is less than 30m when the NACP is 9, and the EPU is less than 10m when the NACP is 10 [15, 17]. If the navigation information is provided by GPS, the EPU is also called HFOM (Horizontal Figure of Merit).The horizontal velocity value (HFOMV) and the vertical velocity value (VFOMV) are important parameters of NACv, and both of them should reach the 95% accuracy range. Similar to the NACP, different NACv values have different requirements for HFOMV and VFOMV. The greater the NACv value, the more stringent the requirements [17].


## 4. Calculation Model of BDS/GPS Monitoring Performance Parameters

### 4.1. Principle of Satellite Positioning

In single constellation satellite positioning, the clock difference parameters between the ground receiver of the second navigation satellite and the standard time are obtained [17, 18]. The positioning principle of Beidou and GPS integrated navigation satellite positioning is expressed by(1)ρi=ri+c⋅δG+c⋅δBi=1,2,…5,…,where ρi is the measured pseudorange of the ith satellite in the combined satellite, ri is the geometric distance of the ith satellite in the combined satellite constellation, c is the propagation speed of the radio signal, δG is the clock difference between the GPS ground receiver and the standard time, and δB is the clock difference between the BDS ground receiver and the standard time.The nonlinear equation (1) is expanded at the approximate solution using Taylor Theorem. Eliminating the terms after the first partial derivative results in the following linear equation:(2)HΔX+ε=Δρ,where ΔX=Δx,Δy,Δz,δG,δBT and the first three terms are the offset components of the ground user receiver position and the approximate position. In equation (2), ε is the total error vector of pseudorange measurement, Δρ is the vector obtained by subtracting the pseudorange value from the predicted approximate value, and the H is(3)H=wx1wy1wz110⋮⋮⋮10wxiwyiwzi10bx1by1bz101⋮⋮⋮01bxjbyjbzj01.Note thatwi=wxi,wyi,wzi is the cosine of the user’s position pointing to the ith satellite in the GPS satellite system, bj=bxj,byj,bzj is the cosine of the user’s position pointing to the jth satellite in the BDS satellite system. The matrix H has (I + J) rows and 5 columns. To solve the equation, it is required that i+j≥5. By setting b=Δρ−ε , equation (2) is then solved using the least square method, hence:(4)ΔX=HTH−1HTb.It is assumed that the errors of satellite components are independent and identically distributed andε∼N0,σURE2, where σURE is the user ranging error of the space signal and dx denotes the error of position and time estimation, which is obtained as(5)dx=HTH−1HTdρ,=Kdρ.According to the definition of covariance, we can write(6)covdx=Edx⋅dxT,=HTH−1⋅σURE2,where equation (6) is obtained by substituting covdρ=In×n⋅σURE2 in equation (5) and In×n is the identity matrix. The vector dx comprises five components representing the error in the obtained value xT=xu,yu,zu,ctG,ctB. According to the definition of covariance, we can write(7)covdx=σxu2⋯σyu2⋮σzu2⋮σctG2⋯σctB2.By comparing equations (6) and (7), it is seen that each component of the matrix HTH−1 represents a component of dx covariance. The weight coefficient matrix is therefore represented by(8)W=HTH−1.To obtain the accuracy factor in the horizontal direction, each error component needs to be transformed into the station center coordinate system. The geometric observation matrix in the station center coordinate system isH˜, and the weight coefficient matrix is shown in the following equation:(9)W∼=HT∼H∼−1,=w∼11w∼12w∼13w∼14w∼15w∼21w∼22w∼23w∼24w∼25w∼31w∼32w∼33w∼34w∼35w∼41w∼42w∼43w∼44w∼45w∼51w∼52w∼53w∼54w∼55.


### 4.2. Navigation Positioning Accuracy

Navigation and positioning accuracy is mainly affected by the satellite layout or measurement error. The diffusion of precision (DOP) is an important index reflecting the geometric layout of the satellites. The DOP illustrates the amplification effect of the geometric structure of the visible satellites and the receivers on the ranging error [18, 19]. The accuracy factor is inversely proportional to the positioning accuracy, and the smaller the DOP, the higher the positioning accuracy [19]. The GDOP is also expressed as(10)GDOP=w∼11+w∼22+w∼33+w∼44+w∼55.Position differentiation of precision (PDOP) is expressed by(11)PDOP=w∼11+w∼22+w∼33And the horizontal dilution of precision (HDOP) is(12)HDOP=w∼11+w∼22.Similarly, vertical dilution of precision (VDOP) is defined as(13)VDOP=w∼33.Hence, HFOM can be written as the following equation:(14)HFOM=EPU,=2×HDOP×σURE.The EPU value is obtained by using equation (14). Then the corresponding NACP value is found. From equation (14), the VFOM can also be obtained as(15)VFOM=2×VDOP×σURE.According to the relationship between position accuracy and speed accuracy, we can also write(16)HFOMV=HFOM×f+12⋅aH⋅I,VFOMV=VFOM×f+12⋅aV⋅I,where f=0.02s−1, aH=1m/s2, aV=1m/s2, and I=1s. The corresponding NACV values are then obtained according to HFOMV and VFOMV [15].As it is seen above, the FOM and DOP are closely related and proportional. Therefore, by increasing the number of satellites, DOP and FOM are decreased. This means that the accuracy indexes NACV and NACP are increased; hence, monitoring performance is improved.


## 4.1. Principle of Satellite Positioning

In single constellation satellite positioning, the clock difference parameters between the ground receiver of the second navigation satellite and the standard time are obtained [17, 18]. The positioning principle of Beidou and GPS integrated navigation satellite positioning is expressed by(1)ρi=ri+c⋅δG+c⋅δBi=1,2,…5,…,where ρi is the measured pseudorange of the ith satellite in the combined satellite, ri is the geometric distance of the ith satellite in the combined satellite constellation, c is the propagation speed of the radio signal, δG is the clock difference between the GPS ground receiver and the standard time, and δB is the clock difference between the BDS ground receiver and the standard time.The nonlinear equation (1) is expanded at the approximate solution using Taylor Theorem. Eliminating the terms after the first partial derivative results in the following linear equation:(2)HΔX+ε=Δρ,where ΔX=Δx,Δy,Δz,δG,δBT and the first three terms are the offset components of the ground user receiver position and the approximate position. In equation (2), ε is the total error vector of pseudorange measurement, Δρ is the vector obtained by subtracting the pseudorange value from the predicted approximate value, and the H is(3)H=wx1wy1wz110⋮⋮⋮10wxiwyiwzi10bx1by1bz101⋮⋮⋮01bxjbyjbzj01.Note thatwi=wxi,wyi,wzi is the cosine of the user’s position pointing to the ith satellite in the GPS satellite system, bj=bxj,byj,bzj is the cosine of the user’s position pointing to the jth satellite in the BDS satellite system. The matrix H has (I + J) rows and 5 columns. To solve the equation, it is required that i+j≥5. By setting b=Δρ−ε , equation (2) is then solved using the least square method, hence:(4)ΔX=HTH−1HTb.It is assumed that the errors of satellite components are independent and identically distributed andε∼N0,σURE2, where σURE is the user ranging error of the space signal and dx denotes the error of position and time estimation, which is obtained as(5)dx=HTH−1HTdρ,=Kdρ.According to the definition of covariance, we can write(6)covdx=Edx⋅dxT,=HTH−1⋅σURE2,where equation (6) is obtained by substituting covdρ=In×n⋅σURE2 in equation (5) and In×n is the identity matrix. The vector dx comprises five components representing the error in the obtained value xT=xu,yu,zu,ctG,ctB. According to the definition of covariance, we can write(7)covdx=σxu2⋯σyu2⋮σzu2⋮σctG2⋯σctB2.By comparing equations (6) and (7), it is seen that each component of the matrix HTH−1 represents a component of dx covariance. The weight coefficient matrix is therefore represented by(8)W=HTH−1.To obtain the accuracy factor in the horizontal direction, each error component needs to be transformed into the station center coordinate system. The geometric observation matrix in the station center coordinate system isH˜, and the weight coefficient matrix is shown in the following equation:(9)W∼=HT∼H∼−1,=w∼11w∼12w∼13w∼14w∼15w∼21w∼22w∼23w∼24w∼25w∼31w∼32w∼33w∼34w∼35w∼41w∼42w∼43w∼44w∼45w∼51w∼52w∼53w∼54w∼55.


## 4.2. Navigation Positioning Accuracy

Navigation and positioning accuracy is mainly affected by the satellite layout or measurement error. The diffusion of precision (DOP) is an important index reflecting the geometric layout of the satellites. The DOP illustrates the amplification effect of the geometric structure of the visible satellites and the receivers on the ranging error [18, 19]. The accuracy factor is inversely proportional to the positioning accuracy, and the smaller the DOP, the higher the positioning accuracy [19]. The GDOP is also expressed as(10)GDOP=w∼11+w∼22+w∼33+w∼44+w∼55.Position differentiation of precision (PDOP) is expressed by(11)PDOP=w∼11+w∼22+w∼33And the horizontal dilution of precision (HDOP) is(12)HDOP=w∼11+w∼22.Similarly, vertical dilution of precision (VDOP) is defined as(13)VDOP=w∼33.Hence, HFOM can be written as the following equation:(14)HFOM=EPU,=2×HDOP×σURE.The EPU value is obtained by using equation (14). Then the corresponding NACP value is found. From equation (14), the VFOM can also be obtained as(15)VFOM=2×VDOP×σURE.According to the relationship between position accuracy and speed accuracy, we can also write(16)HFOMV=HFOM×f+12⋅aH⋅I,VFOMV=VFOM×f+12⋅aV⋅I,where f=0.02s−1, aH=1m/s2, aV=1m/s2, and I=1s. The corresponding NACV values are then obtained according to HFOMV and VFOMV [15].As it is seen above, the FOM and DOP are closely related and proportional. Therefore, by increasing the number of satellites, DOP and FOM are decreased. This means that the accuracy indexes NACV and NACP are increased; hence, monitoring performance is improved.


## 5. Principle of Satellite Selection

### 5.1. PSO and APSO

#### 5.1.1. What Is a PSO?

The basic idea of PSO is the predatory behavior of the birds [19–21]. The algorithm considers the ant behavior described by important features, and considers the absolute time error and integral time square error in optimization [22]. In PSO, the problem to be solved corresponds to the optimal solution, and the optimal solution is reached through continuous iteration by setting random “particles,” that is, random solutions. In the process of iteration, the randomly generated “particle” constantly updates itself with two “extremes.” The first one is the extreme value of theta, denoted by pbesti=pi1,pi2,…,piD. This extremum is denoted as gbesti=g1,g2,…,gD. As the two solutions iterate to their optimum, the particle updates its new velocity and position(17)Vidk=wVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,Xidk=Xidk−1+Vidk−1,where Xidk is the d-dimensional component of the position vector of the kth iteration of particle i and Vidk is the d-dimensional component of the velocity vector of the kth iteration of particle i. In the above equation, c1, c2∈[0, +∞) are the acceleration constants, which are called the learning factors. These factors adjust the maximum step size of the learning. Note that r1, r2∈(0, 1) are random numbers that are used to increase the search randomness. To prevent blind particle search and improve the efficiency of calculation, the range of d∈[0, D] dimensional position change is limited to [min(Xid), max(Xid)] and the speed range is also limited to [−max(Vid), max(Vid)].


#### 5.1.2. What Is an APSO?

To improve the screening ability of PSO and screen a larger number of satellites, the method of shrinkage coefficient can be used to optimize particle swarm, which is called a new particle swarm optimization (APSO). This algorithm ensures the convergence of the PSO algorithm by selecting appropriate parameters while canceling the boundary restriction of the speed. Each particle is mutated in the operation and if it gets better, the new solution is accepted. Otherwise, the original solution is kept unchanged to forming a new particle swarm optimization (APSO). The velocity formula and contraction factor are as follows:(18)Vidk=φVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,s.t.φ=22−C−C2−4C,C=c1+c2,C>4.In this paper, the parameters setting of PSO are the same as APSO, includingc1, c2∈[0, +∞), the number of iteration maximum step is 100, the size of particle swarm is 30, the range of d∈[0, D] dimensional position change is limited to [0, 5] and the speed range is also limited to [−10, 10].


### 5.2. BDS/GPS Integrated Satellite Screening

In this paper, we use a particle swarm optimization algorithm with the objective function and constraints defined as [12](19)Z=max∏i=15λi,where λi is the eigenvalue of matrix HTH5×5 and H is the observation matrix of the station center position. Using eigenvalues is to address the real-time and numerical stability issues.(20)s.t.w˜11+w˜22+w˜33<36,w˜11+w˜22<1,w˜33<25,m≥5,m∈Z.In equation (20), if the availability of satellites is satisfied i.e., PDOP<6, then NACP10 and NACV 3 in SURF IA monitoring performance are used as the screening criteria. The constraint condition is based on the operation situation. In other words, at least five navigation and positioning satellites are required to obtain the unknown quantity. To see the filtering process visually, the screening process is shown in Figure 3.Figure 3
The process of screening satellites.


### 5.3. The Number of Visible Satellites

This paper selects BDS801 week, GPS109 week, Beidou, and GPS almanac data for simulation of data sources. In this paper, the airport reference point (ARP) selected in Guangzhou Baiyun Airport is used to predict ARP for 12 hours with an interval of 1 hour. The start time is set to 08:00:00 on May 13, 2021 (Beijing time).The simulation results are shown in Figure4, where the BDS + GPS visible satellites are from 17 to 28, and the number of the visible satellites in single BDS and single GPS is from 8 to 14. As it is seen, the average number of visible satellites in the combination of Beidou and GPS is 23, the average number of visible Beidou satellites is 12, and the average number of visible GPS satellites is 11. These are consistent with the official number of visible satellites at N233922E113097.Figure 4
The number of visible satellites.


## 5.1. PSO and APSO

### 5.1.1. What Is a PSO?

The basic idea of PSO is the predatory behavior of the birds [19–21]. The algorithm considers the ant behavior described by important features, and considers the absolute time error and integral time square error in optimization [22]. In PSO, the problem to be solved corresponds to the optimal solution, and the optimal solution is reached through continuous iteration by setting random “particles,” that is, random solutions. In the process of iteration, the randomly generated “particle” constantly updates itself with two “extremes.” The first one is the extreme value of theta, denoted by pbesti=pi1,pi2,…,piD. This extremum is denoted as gbesti=g1,g2,…,gD. As the two solutions iterate to their optimum, the particle updates its new velocity and position(17)Vidk=wVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,Xidk=Xidk−1+Vidk−1,where Xidk is the d-dimensional component of the position vector of the kth iteration of particle i and Vidk is the d-dimensional component of the velocity vector of the kth iteration of particle i. In the above equation, c1, c2∈[0, +∞) are the acceleration constants, which are called the learning factors. These factors adjust the maximum step size of the learning. Note that r1, r2∈(0, 1) are random numbers that are used to increase the search randomness. To prevent blind particle search and improve the efficiency of calculation, the range of d∈[0, D] dimensional position change is limited to [min(Xid), max(Xid)] and the speed range is also limited to [−max(Vid), max(Vid)].


### 5.1.2. What Is an APSO?

To improve the screening ability of PSO and screen a larger number of satellites, the method of shrinkage coefficient can be used to optimize particle swarm, which is called a new particle swarm optimization (APSO). This algorithm ensures the convergence of the PSO algorithm by selecting appropriate parameters while canceling the boundary restriction of the speed. Each particle is mutated in the operation and if it gets better, the new solution is accepted. Otherwise, the original solution is kept unchanged to forming a new particle swarm optimization (APSO). The velocity formula and contraction factor are as follows:(18)Vidk=φVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,s.t.φ=22−C−C2−4C,C=c1+c2,C>4.In this paper, the parameters setting of PSO are the same as APSO, includingc1, c2∈[0, +∞), the number of iteration maximum step is 100, the size of particle swarm is 30, the range of d∈[0, D] dimensional position change is limited to [0, 5] and the speed range is also limited to [−10, 10].


## 5.1.1. What Is a PSO?

The basic idea of PSO is the predatory behavior of the birds [19–21]. The algorithm considers the ant behavior described by important features, and considers the absolute time error and integral time square error in optimization [22]. In PSO, the problem to be solved corresponds to the optimal solution, and the optimal solution is reached through continuous iteration by setting random “particles,” that is, random solutions. In the process of iteration, the randomly generated “particle” constantly updates itself with two “extremes.” The first one is the extreme value of theta, denoted by pbesti=pi1,pi2,…,piD. This extremum is denoted as gbesti=g1,g2,…,gD. As the two solutions iterate to their optimum, the particle updates its new velocity and position(17)Vidk=wVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,Xidk=Xidk−1+Vidk−1,where Xidk is the d-dimensional component of the position vector of the kth iteration of particle i and Vidk is the d-dimensional component of the velocity vector of the kth iteration of particle i. In the above equation, c1, c2∈[0, +∞) are the acceleration constants, which are called the learning factors. These factors adjust the maximum step size of the learning. Note that r1, r2∈(0, 1) are random numbers that are used to increase the search randomness. To prevent blind particle search and improve the efficiency of calculation, the range of d∈[0, D] dimensional position change is limited to [min(Xid), max(Xid)] and the speed range is also limited to [−max(Vid), max(Vid)].


## 5.1.2. What Is an APSO?

To improve the screening ability of PSO and screen a larger number of satellites, the method of shrinkage coefficient can be used to optimize particle swarm, which is called a new particle swarm optimization (APSO). This algorithm ensures the convergence of the PSO algorithm by selecting appropriate parameters while canceling the boundary restriction of the speed. Each particle is mutated in the operation and if it gets better, the new solution is accepted. Otherwise, the original solution is kept unchanged to forming a new particle swarm optimization (APSO). The velocity formula and contraction factor are as follows:(18)Vidk=φVidk−1+c1⋅r1⋅pbid−Xidk−1+c2⋅r2⋅gbd−Xidk−1,s.t.φ=22−C−C2−4C,C=c1+c2,C>4.In this paper, the parameters setting of PSO are the same as APSO, includingc1, c2∈[0, +∞), the number of iteration maximum step is 100, the size of particle swarm is 30, the range of d∈[0, D] dimensional position change is limited to [0, 5] and the speed range is also limited to [−10, 10].


## 5.2. BDS/GPS Integrated Satellite Screening

In this paper, we use a particle swarm optimization algorithm with the objective function and constraints defined as [12](19)Z=max∏i=15λi,where λi is the eigenvalue of matrix HTH5×5 and H is the observation matrix of the station center position. Using eigenvalues is to address the real-time and numerical stability issues.(20)s.t.w˜11+w˜22+w˜33<36,w˜11+w˜22<1,w˜33<25,m≥5,m∈Z.In equation (20), if the availability of satellites is satisfied i.e., PDOP<6, then NACP10 and NACV 3 in SURF IA monitoring performance are used as the screening criteria. The constraint condition is based on the operation situation. In other words, at least five navigation and positioning satellites are required to obtain the unknown quantity. To see the filtering process visually, the screening process is shown in Figure 3.Figure 3
The process of screening satellites.


## 5.3. The Number of Visible Satellites

This paper selects BDS801 week, GPS109 week, Beidou, and GPS almanac data for simulation of data sources. In this paper, the airport reference point (ARP) selected in Guangzhou Baiyun Airport is used to predict ARP for 12 hours with an interval of 1 hour. The start time is set to 08:00:00 on May 13, 2021 (Beijing time).The simulation results are shown in Figure4, where the BDS + GPS visible satellites are from 17 to 28, and the number of the visible satellites in single BDS and single GPS is from 8 to 14. As it is seen, the average number of visible satellites in the combination of Beidou and GPS is 23, the average number of visible Beidou satellites is 12, and the average number of visible GPS satellites is 11. These are consistent with the official number of visible satellites at N233922E113097.Figure 4
The number of visible satellites.


## 6. Simulation and Analysis

According to the calculation method of navigation accuracy presented in Section4.2, the ARP of Guangzhou Baiyun Airport is obtained. The total forecast duration is 12 hours, 1 hour as the time interval, and the starting time is 08:00:00 on May 13, 2021. The GDOP and the PDOP of all available satellites can be obtained (see Figure 5).Figure 5
GDOP/PDOP of all BDS/GPS visible satellites.In all visible satellites, the constellation availability standard isPDOP<6. As it is seen, the combined satellite system meets the availability requirements. To improve the utilization rate of the navigation satellites, PSO and APSO are used to screen all visible satellites. Using these techniques, a smaller number of satellites are used to reach the SURF IA performance standard.


### 6.1. Results of PSO and APSO Screening

In this paper, Guangzhou Baiyun Airport is used as the reference point, and all visible satellites from 8:00 to 20:00 are screened. The GDOP reflects the spatial geometric distribution of the users and visible satellites. The GDOP values of screened satellites are presented in Table1. The number of iterations and fitness values for PSO and APSO at 18:00 are presented in Figure 6.Table 1
GDOP of the combined satellite system.
TimeGDOP of allvisible satellitesGDOP underPSOGDOP underAPSO08:001.4691.6091.55009:001.6251.6761.66510:001.0771.2371.19611:001.3761.4961.41612:001.3451.4581.41913:001.5691.7151.62514:001.5561.6871.63615:001.1801.3801.30016:001.2901.4641.38417:001.3961.5501.50318:001.9142.0011.98319:001.8061.9541.87220:001.2751.4471.375Figure 6
Number of visible satellites to the combined satellite after screening.It can be seen from Figure6, Figure 7, and Table 1 that screening using PSO and APSO significantly reduces the number of satellites. It is also seen that the obtained GDOP value by the screened satellites is similar to the calculated value by using all visible satellites. APSO also has one or two fewer satellites compared with PSO. For the similar number of selected satellites, the obtained GDOP value for PSO and APSO is different, as well as the observation matrix H, and the performance of the satellite matrix selected by APSO is higher. The observation matrix H represents the different satellites. At the same time, it can be seen that the number of iterations and fitness of APSO are lower than that of PSO, which proves that APSO is faster and more stable in selecting satellites.Figure 7
Number of iterations and the fitness values of PSO and APSO.


### 6.2. SURF IA Performance Verification after Screening Satellites

By using the horizontal and vertical precision factors, we can obtain the SURF IA surface operation monitoring performance parameters. The statistical results of the HFOM at the observation points in 12-hour prediction time are presented in Table2. The statistical results of the NACV performance of observation points in 12-hour prediction time are also shown in Table 3. The simulation results are shown in Figure 8.Table 2
NACP performance level of GPS + BDS.
Performance levelPerformance requirementCompliance9HFOM < 30 m100%10HFOM < 10 m100%11HFOM < 3 m0Table 3
NACV performance level of GPS + BDS.
PerformancelevelPerformancerequirementCompliance2HFOMv < 3 m/s and VFOMv < 4.6 m/s100%3HFOMv < 1 m/s and VFOMv < 1.5 m/s100%4HFOMv < 0.3 m/s and VFOMv < 0.46 m/s0Figure 8
Figure of merit for velocity in a 95% accuracy range.The above results suggest that the number of selected satellites is reduced without reducing the positioning accuracy so that it can meet the operation requirements of SURF IA.


## 6.1. Results of PSO and APSO Screening

In this paper, Guangzhou Baiyun Airport is used as the reference point, and all visible satellites from 8:00 to 20:00 are screened. The GDOP reflects the spatial geometric distribution of the users and visible satellites. The GDOP values of screened satellites are presented in Table1. The number of iterations and fitness values for PSO and APSO at 18:00 are presented in Figure 6.Table 1
GDOP of the combined satellite system.
TimeGDOP of allvisible satellitesGDOP underPSOGDOP underAPSO08:001.4691.6091.55009:001.6251.6761.66510:001.0771.2371.19611:001.3761.4961.41612:001.3451.4581.41913:001.5691.7151.62514:001.5561.6871.63615:001.1801.3801.30016:001.2901.4641.38417:001.3961.5501.50318:001.9142.0011.98319:001.8061.9541.87220:001.2751.4471.375Figure 6
Number of visible satellites to the combined satellite after screening.It can be seen from Figure6, Figure 7, and Table 1 that screening using PSO and APSO significantly reduces the number of satellites. It is also seen that the obtained GDOP value by the screened satellites is similar to the calculated value by using all visible satellites. APSO also has one or two fewer satellites compared with PSO. For the similar number of selected satellites, the obtained GDOP value for PSO and APSO is different, as well as the observation matrix H, and the performance of the satellite matrix selected by APSO is higher. The observation matrix H represents the different satellites. At the same time, it can be seen that the number of iterations and fitness of APSO are lower than that of PSO, which proves that APSO is faster and more stable in selecting satellites.Figure 7
Number of iterations and the fitness values of PSO and APSO.


## 6.2. SURF IA Performance Verification after Screening Satellites

By using the horizontal and vertical precision factors, we can obtain the SURF IA surface operation monitoring performance parameters. The statistical results of the HFOM at the observation points in 12-hour prediction time are presented in Table2. The statistical results of the NACV performance of observation points in 12-hour prediction time are also shown in Table 3. The simulation results are shown in Figure 8.Table 2
NACP performance level of GPS + BDS.
Performance levelPerformance requirementCompliance9HFOM < 30 m100%10HFOM < 10 m100%11HFOM < 3 m0Table 3
NACV performance level of GPS + BDS.
PerformancelevelPerformancerequirementCompliance2HFOMv < 3 m/s and VFOMv < 4.6 m/s100%3HFOMv < 1 m/s and VFOMv < 1.5 m/s100%4HFOMv < 0.3 m/s and VFOMv < 0.46 m/s0Figure 8
Figure of merit for velocity in a 95% accuracy range.The above results suggest that the number of selected satellites is reduced without reducing the positioning accuracy so that it can meet the operation requirements of SURF IA.


## 7. Conclusion

SURF IA monitoring and operation technology based on ADS-B IN provide a great application prospect in complex surface and low visibility surface taxiing. This system supports the advanced surface taxiing process and provides guidance and warning functions for pilots.PSO algorithm does not depend on the problem information and uses real number to solve the problem. There are few parameters need to be adjusted, the principle is simple, and the universality is strong. The algorithm uses both the individual local information and the group global information to guide the search. It has a fast convergence speed and does not require high computer memory, so it is easier to fly over the local optimal information. The objective function can only provide very little information to search for the optimal value. In the case that other algorithms can not identify the search direction, the particles of the APSO algorithm have the characteristics of flying over, which makes it possible to fly to the global optimal target value by crossing the obstacle of serious lack of information on the search plane. In this paper, we showed that by using PSO and APSO in the multiconstellation combinations, the required number of satellites is greatly reduced without compromising the accuracy of the system. The number of satellites screened by the APSO is one or two less than that screened by the PSO. Furthermore, the GDOP value of the selected satellite can still meet the performance requirements of SURF IA. Although the APSO only slightly improves the performance beyond the PSO, comparing the observation matrix H obtained from these two methods shows that there is a big difference in the satellite combination arrangement; APSO provides a better GDOP value. In this paper, we showed that through satellite screening, SURF IA operation and monitoring performance criteria can meet with a smaller number of satellites. This provides a method to improve the efficiency of satellite positioning solutions and offers engineering application value.



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*Source: 8966814-2022-06-01.xml*