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An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM Availability

An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM... Hindawi Journal of Advanced Transportation Volume 2023, Article ID 8684886, 11 pages https://doi.org/10.1155/2023/8684886 Research Article An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM Availability 1,2 1,3 2 4 1,3 Ershen Wang , Xiaozhu Shi , Xidan Deng , Jing Gao , Wei Zhang , 2 2 Huan Wang , and Song Xu State Key Laboratory of Air Trafc Management System and Technology, Nanjing 210007, China School of Electronic and Information Engineering, Shenyang Aerospace University, Shenyang 110136, China Te 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, China School of Electric Power, Shenyang Institute of Engineering, Shenyang 110136, China Correspondence should be addressed to Jing Gao; gaojing1@sie.edu.cn Received 23 August 2022; Revised 22 October 2022; Accepted 13 April 2023; Published 30 May 2023 Academic Editor: Wen Liu Copyright ©2023ErshenWangetal.TisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Civil aviation transportation equipment is more convenient and faster than other transportation tools and is an essential part of intelligent transportation. It is signifcant to study the reliability of positioning information and enhance trafc safety. Advanced receiver autonomous integrity monitoring (ARAIM) can provide vertical guidance during the diferent navigation stages in civil aviation felds. Te traditional multiple hypothesis solution separation (MHSS) algorithm distributes the probability of hazardous misleading information (PHMI) and probability of false alarm (PFA) uniformly over all visible satellites resulting in reduced global availability of ARAIM. Aiming at this problem, we proposed an adaptive simulated annealing particle swarm optimization (ASAPSO) algorithm to redistribute integrity and continuity risks and establish a protection level optimization model. Based on the real BeiDou navigation satellite system/global positioning system (BDS/GPS) data, the experimental results show that the optimizedalgorithmcanreducetheverticalprotectionlevel(VPL),andtheARAIMglobalavailabilityofBDS/GPSisimprovedby 1.73%∼2.73%. Te optimized algorithm can improve the availability of integrity monitoring at diferent stages of the navigation system and provide a basis for ensuring the reliability of the positioning results. a single failure untenable [5–7]. Te ARAIM provides 1. Introduction localizer precision with vertical guidance up to 200 Te BDS-3 satellite navigation system is operating smoothly feet altitude (LPV-200) for global aircraft landing and achieving global coverage. It is playing an irreplaceable navigation [8]. role in the future and is widely used in road, railway, water, Related scholars have conducted a lot of research on air transportation, and other aspects of transportation. In ARAIM availability optimization. Te Gauss Newton method is used to optimize the model, and the polynomial recentyears,trafcsafetyhasbecomearesearchhotspot.Te satellite navigation system is closely related to trafc situ- coefcient optimization algorithm is integrated to improve ational awareness and safety supervision of intelligent ve- the ARAIM availability [9]. Te integrity risk is allocated by hicle navigation [1, 2]. And satellite navigation is also widely the binary search method to reduce the VPL value [10]. used in the aviation feld [3, 4]. Te integrity monitoring Reduce VPL by optimizing the allocation of integrity risks algorithm provides some assurance of location information [11].Geneticalgorithmisusedtoredistributecontinuityrisk reliability. Integrity algorithm is one of the utmost priorities and integrity risk to achieve VPL optimization [12]. PSO for safety critical GNSS (global navigation satellite system). algorithm is used to optimize the integrity risk allocation Te rapid development of multiconstellation integrated process to reduce the protection level [13]. Trough the navigation systems has assumed a single constellation and maximum minimization method, the fminimax function is 2 Journal of Advanced Transportation used to reasonably allocate the risk probability to reduce the where H represents the observation matrix, y represents the VPL [14]. Tese researches improved the availability of pseudo-range observedfromthenavigationmessageandthe ARAIM in diferent ways. Working Group C defned pseudo-range residual vector calculated using the satellite multiple hypothesis solution separation as the baseline al- position and the receiver clock error. x is the position gorithm [15]. Tis work focuses on VPL computation and correction parameters of the user receiver in the three- the global availability of ARAIM [16]. Traditional risk dimensional space and the receiver clock bias. ε can obey equalization strategy leads to the conservatism of VPL. Tis a Gaussian distribution with a mean value of zero and study reallocated PHMI and PFA by using the ASAPSO to a variance of σ . optimize availability. −1 T (0) (0) x 􏽢 � 􏼐H W H􏼑 HW y � S y, Te efectiveness oftheASAPSOalgorithmwas analyzed 0 0 and validated in terms of global VPL and the ARAIM −1 T (0) (0) availability based on dual constellation by optimizing VPL. S � H W H HW , 􏼐 􏼑 Te results show that the optimization method based on binary constellation diagram optimized the VPL and im- 0 0 0 ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ proved the global ARAIM availability in diferent air nav- ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ σ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ all,1 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ igation stages. In Section 2, the MHSS algorithm and the ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ASAPSO ARAIM algorithm are described in detail. In ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ (2) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1 ⎥ ⎢ ⎥ Section 3, simulations are performed using a dual-frequency ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ carrier-smoothed position solution based on the BDS/GPS ⎢ ⎢ σ ⎥ ⎢ ⎥ ⎢ all,2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ W � ⎢ ⎥, ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ constellation. Finally, the study is concluded in Section 4. ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋮ ⋮ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2. ARAIM Algorithm Analysis ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1 ⎥ ARAIM algorithm uses a dual-frequency technology to ⎥ ⎢ ⎥ ⎢ ⎦ 0 0 0 eliminate ionospheric interference and uses multiple con- all,n stellationstoobtainmoreobservationstoenhancetheglobal where W represents the weight matrix and σ represents availability of LPV-200. Te ARAIM algorithm is an ex- all,i tension of the RAIM algorithm, which requires much higher the standard noise error of the i − th satellite. Te solution performance than the RAIM algorithm. It is a multifre- separation test is as follows: 􏼌 􏼌 quency and multiconstellation integrated navigation RAIM 􏼌 􏼌 􏼌 􏼌 ∆x � 􏼌x 􏽢 − x 􏽢 􏼌, i i 0 algorithm.ISMparameterscarryinformationonSISranging −1 T T error (SISRE) and fault statistics, which refect inherent ⎧ ⎪ x 􏽢 � 􏼐H WH􏼑 H W y � S y, ⎨ (3) 0 i i performance parameters of the core constellation, including −1 ⎩ T T nominal measurement biases b ,the standard deviation of x 􏽢 � 􏼐H WH􏼑 H Wy � S y, nom i 0 ephemeris, and clock error σ . P and P denote the URA sat const where x 􏽢 represents the i − th subset and x 􏽢 represents the satellite failure state probability and the constellation failure i 0 subset with no fault. Furthermore,thedetection threshold of priori probability, respectively. ISM parameters are gener- the vertical position corresponding to the fault subset is as ated and verifed on the ground and transmitted to users as follows: required [17, 18]. sat 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 ∆S (3, i) × b . (4) D � K × σ + 􏽘 􏼌 􏼌 2.1. MHSS ARAIM Architecture. Te MHSS algorithm is i fa,i dv,i i cont,i i�1 shown below [19, 20]. Based on the MHSS traditional ARAIM algorithm, it can be expressed as follows: TeARAIMVPLcalculationcanbeexpressedasfollows: y � Hx + ε, (1) sat ⎧ ⎪ 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 VPL � K × σ + 􏽘 􏼌S (3, i)􏼌 × b , ⎪ 0 md,0 v,0 0 nom,i ⎪ i�1 sat (5) 􏼌 􏼌 􏼌 􏼌 ⎪ 􏼌 ⎪VPL � D + K × σ + 􏽘 􏼌S (3, i)􏼌 × b , ⎪ i i md,i v,i i nom,i i�1 VPL � max VPL ,VPL􏼁 , 0 i Journal of Advanced Transportation 3 where VPL represents VPL corresponding to the fault where Q is the right hand side cumulative distribution subset. i � 0 denotes VPL corresponding to the fault-free function of a zero mean unit Gaussian. N is the number of subset. S represents the fault subset’s weighted least squares fault subsets; traditional allocation of PHMI and PFA will projection matrix, S denotes the i − th fault subset, and b lead to conservative protection levels. Terefore, the PHMI i nom represents the maximum standard deviation of the i − th and PFA are allocated by the ASAPSO algorithm, and this satellite used to evaluate the integrity; it can be expressed as allocation strategy will be discussed. follows: 2.2. VPL Calculation of MHSS ARAIM Algorithm Optimized ∆S � S − S , (6) i i 0 Based on ASAPSO. Te PSO algorithm easily falls into local where σ , σ , and σ can be expressed as follows: convergence, which leads to slowing down the overall v,0 v,i dv,i 􏽲��������� � convergence speed [21, 22]. Terefore, the simulated −1 σ � 􏼐HWH 􏼑 , annealing algorithm is combined with the PSO algorithm. v,0 3,3 Te algorithm is divided into two stages: the standard PSO 􏽱������������ � T −1 (7) algorithm is used for optimization in the early stage and the σ � 􏼐H M WH􏼑 , v,i k 3,3 simulated annealing algorithm is used later to optimize and 􏽱������������� � −1 T search the parameters in the PSO algorithm [23, 24]. σ � ∆S W ∆S . 􏼐 􏼑 dv,i i i 3,3 Tis study proposed an optimization strategy based on theASAPSO algorithmtosolve theproblem thattheaverage Te traditional ARAIM algorithm equally allocates the continuity and integrity risk probability to all visible sat- distribution strategy is not optimal. Te VPL is optimized by introducing an adaptive weight function. Te proposed ellites. Te integrityconstraint coefcient K and K are md,i fa,i determined by PHMI and PFA expressed as follows: optimization algorithm can obviously reduce the vertical protection level and improve the ARAIM availability. PFA −1 K � −Q , 􏼒 􏼓 fa,i Step 1. Calculation of the velocity and position of particles. PHMI −1 K � −Q 􏼠 􏼡, md,0 (8) 2(N + 1) PHMI −1 K � −Q 􏼠 􏼡, md,i P (N + 1) sat,i v (it + 1) � wv (it) + c r pbest − x (it)􏼁 + c r gbest − x (it)􏼁, (9) m m 1 1 m m 2 2 m m x (it + 1) � x (it) + ] (it + 1), (10) m m m where it represents the current particles number of itera- where ω and ω represent themaximumandminimum max min tions, w represents the inertia weight, c and c represent the values of the inertia weight w, respectively. f is the ftness 1 2 acceleration constants, which are used to adjust the velocity value of the particles. f and f are the average and avg min of motion in the pbest and gbest directions, respectively. r minimum ftness values of the particles in the population, and r are the random number between 0 and 1. x rep- respectively [27]. 2 m resents the particle’s position. v represents the moving Ifthetargetvalueregionofeachparticleisconsistentand speed of the particle m [25, 26]. the region is locally optimal, the inertia weight will increase. If the target value of each particle is dispersed, the inertia weight will decrease. Step 2. Selection of adaptive inertia weight. Te method of adaptive inertia weight was introduced to Step 3. Metropolis criterion updating strategy combined balance the global and local search ability of the PSO and with the simulated annealing algorithm. improve the algorithm’s performance. Te formula is as We proposed an update strategy based on the Me- follows: tropolis criterion to solve the particle position update ω − ω 􏼁 f − f 􏼁 ⎧ ⎪ max min min ⎫ problem. First, calculate the particle’s next possible po- ⎪ ⎪ ω − , f ≤ f ⎪ ⎪ min avg ⎪ ⎪ ⎨ f − f ⎬ sition according to the updating equation (9). Ten, judge avg min ω � , ⎪ ⎪ whether it can be accepted as the particle’s next position ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ according to the Metropolis criterion. Finally, the steps w , f > f max avg are as follows: (11) 4 Journal of Advanced Transportation probability, but accepts probability with fit (t) ≤fit (t), ⎧ ⎪ i+1 i ⎪ exp(−fit (t) − fit (t)/T) > rand. Te Metropolis criterion’s ⎨ i+1 i (12) update strategy avoids particle degradation in some extent. ⎪ −fit (t) − fit (t) ⎪ i+1 i rand ≤exp􏼠 􏼡, Step 4. Particle ftness function selection. According to the MHSS algorithms, the probability where fit is the ftness value for the next position of the i+1 averageallocationmethodofPHMIandPFAisadopted,and particle. Te Metropolis criterion is introduced so that the the VPL calculation method can be expressed as follows: particle does not accept the diferent solution with full N N sat sat 􏼌 􏼌 􏼌 􏼌 PFA PHMI 􏼌 􏼌 􏼌 􏼌 −1 −1 􏼌 􏼌 􏼌 􏼌 ∆S (3, i) × b . (13) VPL � −Q 􏼒 􏼓 × σ + 􏼠−Q 􏼠 􏼡􏼡 × σ + 􏽘 􏼌S (3, i)􏼌 × b + 􏽘 􏼌 􏼌 i dv,i v,i i nom,i k cont,i N P (N + 1) sat i�1 i�1 According to equation (13), VPL is taken as the opti- mizationobjective.Teschemesassignedtoeachfaultsubset by PHMI and PFA are as follows: set ⎧ ⎪ ⎪ 􏽘 P ≤PHMI, HMI,k k�1 minmax VPL PHMI , Pfa 􏼁􏼁,s · t · k k k set (14) 􏽘 P ≤Pfa, fa,k k�1 VPL � minVPL (i � 0, . . . , N), where the VPL corresponding to each fault subset is expressed as follows: sat sat 􏼌 􏼌 􏼌 􏼌 PFA PHMI 􏼌 􏼌 􏼌 􏼌 −1 −1 􏼌 􏼌 􏼌 􏼌 S (3, i) × b + 􏽘 ∆S (3, i) × b . (15) VPL � −Q 􏼒 􏼓 × σ + 􏼠−Q 􏼠 􏼡􏼡 × σ + 􏽘 􏼌 􏼌 􏼌 􏼌 i dv,i v,i i nom,i k cont,i N P (N + 1) sat i�1 i�1 Terefore, the weighted sum of VPL is taken as the optimization objective, expressed as follows [17]: min G set ⎪ G � 􏽘 y × VPL , ⎪ i i i i�0 ⎪ σ + σ 􏼐 􏼑 ⎪ dv, i v, i ⎪ y � , ⎪ N N ⎪ set set ⎪ 􏽐 σ + 􏽐 σ i�0 dv, i�0 v, (16) ⎨ i i sat 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 VPL � K × σ + K × σ + 􏽘 S (3, i) × b ⎪ 􏼌 􏼌 ⎪ i fa, dv, i md, i v, i i nom,i i�1 sat ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ + 􏽘 􏼌∆S (3, i)􏼌 × b , i cont,i i�1 Journal of Advanced Transportation 5 where G is optimization objective function and N rep- (4) Judgment termination condition: Judge whether i set resents the total number of particles. the particle reaches the maximum iterations. If this condition is met, the optimized PHMI and PFA allocation strategy will be output to the optimized Step 5. ASAPSO algorithm optimization VPL. VPL. Otherwise, go back to step 2 and continue ASAPSO algorithm is introduced into the optimization iterating updates. Finally, the VPL’s optimal allo- process. Te details are as follows: cation strategy is obtained. (1) Firstly, M visible satellites were extracted and di- vided into M groups. Ten, the PHMI was set to 3. Experimental Verification and 0∼PHMI and the PFA is set to 0∼PFA. Finally, they Results Analysis were randomly divided into M groups and coded to form the initial population n. 3.1. Optimization Simulation of Continuous Risk and Integrity Risk Allocation Method. We extracted navigation in- Pfa , Pfa , Pfa , ..., Pfa m0 m1 m2 mN set ⎣ ⎦ ⎡ ⎤ n � . formation and observation fles from the IGS website to PHMI ,PHMI ,PHMI ...,PHMI m0 m1 m2 mN set verifythealgorithm’sperformance.Tesimulationstartedat (17) 00:00:00 on June 6, 2020, lasted for 12hours, and the simulation step length was 10minutes. Tis study uses the where m �1,2, . . ., n, and n is the number of BDS/GPS constellation dual-frequency carrier smoothing populations. method for simulation, and the experimental conditions are shown in Table 1. (2) Initialize the algorithm parameters. Figure 1(a) shows that the number of visible satellites is (a) Initialize the position of particles in the relatively stable between 20 and 25. Meanwhile, Figure 1(b) population shows that the GDOP is between 1.3 and 2. It can be in- (b) Set the initial temperature, where dicated that the BDS/GPS satellites have a good space dis- T � (−f )/(ln0.2) represents the initial 0 g tribution in general. Figure 2(a) shows that the PFA is temperature allocated by the ASAPSO algorithm. In this algorithm, PFA (c) Initialize each parameter is randomly assigned to diferent satellites as a particle, and Te acceleration coefcient c diferentsatellitesareallocatedtodiferentPFA.Tevalueof � c � 0.2, the 1 2 PFA remains between 2.7e −6 and 3.9e −6. Figure 2(b) population particle size is set to M �50, the maximum iteration times are set to 50, the shows that the value remains between 5.7e −8 and 9.8e −8 by the optimized ASAPSO algorithm from the risk maximum particle moving to speed is v � 2, max allocation of PHMI. Te ASAPSO can optimize the risk and the minimum moving speed is v � −2. min allocation strategy of PHMI and PFA. Both PHMI and PFA Ten, the PHIMI and the PFA of each particle are are less than the threshold value. Te improved algorithm calculated. Ten, the ftness function is calcu- allocates diferent values for diferent visible satellites, which lated. Te distribution method of PHMI and PFA can reduce the VPL and improve the ARAIM availability. generated in the initial population are substituted Figure3shows that the VPL value of the ASAPSO is less than into VPL. Te individual optimal PHMI and the that of the traditional algorithm in any epoch, and both the population optimal PFA are assigned to each particle. traditional algorithm and the optimized algorithm are less than 35m under GPS/BDS dual-frequency dual-system (3) Iterative updating: First, the inertia weight W is combination. Terefore, under the premise of ensuring updated based on equation (11). Next, based on the PHMIandPFA,theASAPSOalgorithmcanreducetheVPL. initial iteration value, the function value of each It can also improve ARAIM availability. particle target is set to the individual optimal value, and the optimal value is selected from the indi- vidual optimal value as the global optimal value. 3.2. Global Availability Simulation Analysis of the Traditional Ten, the particle position and velocity are updated and Optimized Method. Tis experiment uses BDS/GPS according to equations (9) and (10). During each almanac data to analyze global availability. BDS data were iteration, the individual optimal position pbest m downloaded from the Test and Evaluation Center of China and the global optimal position gbest will be Satellite Navigation System Management Ofce and GPS updated. Calculate the probability and generate data were downloaded from the https://celestrak.com a random r. If r < min [1, p], the particle will enter website [27]. Te data were collected on January 2, 2021. a new position and iterate again. Te data simulation time is 3hours with the step of Te particle will move to a new position by 5minutes. accepting a diferent probability. Finally, the tem- Te approach phases of an aircraft can be roughly di- peratureiscooledby T � z × T .Trepresentsthe vided into the nonprecision approach (NPA) and vertical k+1 k temperature, the value of z generally ranges from guidance approach phase, which includes the APV-I, APV- 0.5 and 0.9, and k represents the number of II, and precision approach phase CAT-I, CAT-II, and CAT- iterations. III. Operational risks in diferent civil aviation approach 6 Journal of Advanced Transportation Table 1: ISM parameters setting. Parameters Defnition Setting PHMI Total integrity budget 9.8e −7 P Continuity budget allocated to disruptions because of false alert 4e −6 fa VAL Vertical alert limit 35m EMT Efective monitoring threshold 15m Constellation Navigation constellations GPS/BDS P Priori failure probability of satellites 1e −4 sat P Priori failure probability of constellations 1e −5 const 30 2.5 25 2 20 1.5 15 1 0 2468 10 12 0 2 4 6 8 10 12 Time (h) Time (h) (a) (b) Figure 1: (a) Number of visible satellites and (b) GDOP. -6 ×10 -8 ×10 3.5 2.5 1.5 4 02468 10 12 02468 10 12 Time (h) Time (h) (a) (b) Figure 2: (a) PFA is allocated by the ASAPSO. (b) PHMI is allocated by the ASAPSO. PFA Number of visible satellites GDOP PHMI Journal of Advanced Transportation 7 02468 10 12 Time (h) VPLASAPSO MHSS-VPL Figure 3: VPL value optimized by the MHSS algorithm and ASAPSO algorithm. Table 2: ICAO navigation performance requirements for each approach phase. Phase Precision (95%) Alarm limit Continuity Availability –4 220m (H) 550m (H) 1 ×10 /h 0.99 NPA –8 N/A (V) N/A (V) 1 ×10 /h 0.99999 16m (H) 40m (H) 0.99 –6 APV-I 8 ×10 /15s 20m (V) 50m (V) 0.9999 16m (H) 40m (H) 0.99 –6 APV-II 8 ×10 /15s 8m (V) 20m (V) 0.99999 16m (H) 40m (H) 0.99 –6 LPV-200 8 ×10 /15s 4m (V) 35m (V) 0.99999 16m (H) 40m (H) 0.99 –6 CAT-I 8 ×10 /15s 4∼6m (V) 10m (V) 0.99999 80 80 60 60 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 12 < 15 < 20 < 25 < 30 < 35 < 40 < 50 > 50 < 12 < 15 < 20 < 25 < 30 < 35 < 40 < 50 > 50 VPL (m) - 99.5% VPL (m) - 99.5% (a) (b) Figure 4: VPL before and after optimization. (a) VPL average �19.7652. (b) VPL average �20.4044. Latitude (deg) VPL Latitude (deg) 8 Journal of Advanced Transportation 80 80 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 35, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 95.8% VAL = 35, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 97.53% th acc th acc (a) (b) Figure 5: Before and after optimization global availability of ARAIM under the LPV-200. (a) Traditional algorithm Coverage (99.5%) � 95.80%. (b) Optimized algorithm Coverage (99.5%) �97.53%. 60 60 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 50, HAL = 40, EMT = Inf, σ = Inf, Coverage (99.5%) = 99.37% VAL = 50, HAL = 40, EMT = Inf, σ = Inf, Coverage (99.5%) = 99.06% th acc th acc (a) (b) Figure 6: Before and after optimization global availability of ARAIM under the LPV-250. (a) Traditional algorithm Coverage (99.5%) � 99.06%. (b) Optimized algorithm Coverage (99.5%) �99.37%. phases are diferent, so the integrity requirements of each (Figures 4–8). Te latitude and longitude interval is the grid ° ° phase are also diferent [28]. Te ICAO (International Civil spacing set by simulation, and it is selected as 10 ×10 . Aviation Organization) navigation performance re- Figures 4–8 show the comparison of the global VPL and quirements for each approach phase are shown in Table 2. availability of the traditional method (a) and the optimized Te availability of an integrity monitoring algorithm has method (b) under appropriate ISM parameters in diferent an essential relationship with satellite geometric space dis- navigation stages of the BDS/GPS dual constellation. Fig- tribution, which refers to the percentage of time that system ure 4 shows that the color of the improved algorithm ° ° functions can meet the requirements of integrity perfor- gradually turns green in the range of 100 W-120 W lon- ° ° ° ° ° mance in a certain fight stage. Terefore, it is of great gitude, 40 N-60 N latitude, 0 E-50 E longitude, and 40 E- signifcance to study aircraft availability in diferent navi- 60 E longitude, which plays an optimized efect. Figure 5 gation stages. It is essential to analyze the availability of shows a signifcant improvement in the availability of the ° ° ° aircraft integrity monitoring algorithms at diferent navi- improved algorithm in the range of 25 S-20 N and 20 W to gation stages. Te performance of the optimization algo- 10 E. Te efciency of the improved algorithm is obviously rithm is verifed through simulation and compares whether superior to the traditional MHSS algorithm. Te MHSS it can meet the integrity requirements of the vertical algorithm is based on the spatial distribution of visible GPS guidance approach phase and the precision approach phase satellites and uses the averaging method for risk allocation. Latitude (deg) Latitude (deg) Latitude (deg) Latitude (deg) Journal of Advanced Transportation 9 80 80 60 60 40 40 20 20 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 20, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 8.77% VAL = 20, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 12% th acc th acc (a) (b) Figure 7: Before and after optimization global availability of ARAIM under the APV-II. (a) Traditional algorithm Coverage (99.5%) � 8.77%. (b) Optimized algorithm Coverage (99.5%) �12%. 80 80 60 60 40 40 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 10, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 0% th acc VAL = 10, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 0% th acc (a) (b) Figure8:BeforeandafteroptimizationglobalavailabilityofARAIMundertheCAT-I.(a)TraditionalalgorithmCoverage(99.5%) �0%.(b) Optimized algorithm Coverage (99.5%) �0%. Table 3: Global availability ARAIM comparison between before and after optimization. Navigation stages Traditional algorithm (%) Optimized algorithm (%) LPV-200 95.8 97.53 LPV-250 99.06 99.37 APV-II 8.77 12 CAT-I 0 0 Satellites of diferent Beidou constellations have diferent Te space geometry distribution of GPS satellite is uniform, the constellation fault probability is low, and the protection efects on positioning errors. Terefore, the traditional av- level calculation under various fault assumptions is similar. erage distribution method will lead to VPL being too For BDS/GPS integrated navigation system, BDS perfor- conservative, which will reduce the global availability of manceisweak,andBDSconstellationdistributionisuneven. ARAIM. Latitude (deg) Latitude (deg) Latitude (deg) Latitude (deg) 10 Journal of Advanced Transportation Figures 5–8 show a global availability analysis of navi- optimization of the improved algorithm is diferent. Te gational integrity requirements at diferent navigational availability is improved by 1.73%∼2.73%. It can meet more performance stages. Figure 5 shows that the improved al- stringent navigation phase requirements for integrity ° ° gorithm is signifcantly improved in the range of 20 N–20 S performance. ° ° and 40 N–60 N. And it can be found that the lower the In 2020, the BDS-3 system was built successfully. And it availability before the improvement is, the more obvious the provides global services. Tis study used BDS-3 actual data availability after the optimization algorithm is adopted. validated and compared the optimization and conventional Figure 6 shows that the improved algorithm optimizes the algorithms. Te ARAIM availability was obviously im- ° ° ° ° range of 40 N–60 N and 100 W–120 W. Figure 7 shows proved. With the navigation performance requirement of a signifcant improvement in the area near the tropics. aviation users, the integrity of navigation performance be- Figure 8 shows that neither algorithms can satisfy the comes extremely important. Tis study presented an opti- availability of the CAT-I approach navigation stage. Table 3 mized PHMI and PFA risk allocation method. Te shows the global availability ARAIM comparison before and experiment shows that the proposed algorithm can signif- after optimization in diferent navigation performance icantly improve ARAIM availability and provides more stages. reliable services for aviation users. And the ongoing Table 3 shows that the global availability efect of the transportation revolution (especially autonomous transport traditional allocation method and ASAPSO algorithm is systems) has signifcance in this work. It can provide safer excellent under the LPV-250 because the vertical alarm limit and more reliable positioning information for users. (VAL) of ARAIM is 50m under the LPV-250. Te VAL is much higher than the VPL. It can meet the ARAIM Data Availability availability under LPV-250. However, in the LPV-200 navigation stage, the global availability of the optimized Te data used to support the fndings of this study are in- algorithm is higher, and the availability of the ARAIM is cluded within the article. more than 90%. Te ARAIM VAL is 35m under the LPV- 200. Terefore, the availability of ARAIM under the Conflicts of Interest LPV-200 is signifcantly lower than that of the LPV-250 navigation stage in terms of global availability. Te global Te authors declare that they have no conficts of interest. availability of the traditional and optimized algorithm is about 8% and 12% under the APV-II navigation stage. Acknowledgments Because the VAL required is 20m under the APV-II. In the CAT-I stage, the VAL of ARAIM is stricter than APV-II. Tis study was supported by the National Natural Science And the VAL is 10m, which is far lower than the VPL. It Foundation of China (62173237), the Open Fund of State cannot meet the integrity requirements in the CAT-I nav- Key Laboratory of Air Trafc Management System and igation stage. In addition, it can be seen that the availability Technology (SKLATM202101), the Applied Basic Research of ARAIM under LPV-250 >LPV-200 >APV-II >CAT-I is Programs of Liaoning Province (2022020502-JH2/1013 and under the same ISM parameter. Te improved optimization 2022JH2/101300247), the Open Fund of Key Laboratory of algorithm has the most obvious efect on the ARAIM Civil Aviation Flights Wide Area Surveillance and Safety availability under the LPV-200 and APV-II. However, the Control Technology of Civil Aviation University of China impact of LPV-250 and CAT-I is not obvious and needs (202105), the Open Fund of Key Laboratory of Flight improvement. Techniques and Flight Safety, CAAC (FZ2021KF15 and FZ2021ZZ06), and the Special Funds Program of Shenyang Science and Technology (22-322-3-34). 3.3. 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An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM Availability

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10.1155/2023/8684886
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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 8684886, 11 pages https://doi.org/10.1155/2023/8684886 Research Article An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM Availability 1,2 1,3 2 4 1,3 Ershen Wang , Xiaozhu Shi , Xidan Deng , Jing Gao , Wei Zhang , 2 2 Huan Wang , and Song Xu State Key Laboratory of Air Trafc Management System and Technology, Nanjing 210007, China School of Electronic and Information Engineering, Shenyang Aerospace University, Shenyang 110136, China Te 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, China School of Electric Power, Shenyang Institute of Engineering, Shenyang 110136, China Correspondence should be addressed to Jing Gao; gaojing1@sie.edu.cn Received 23 August 2022; Revised 22 October 2022; Accepted 13 April 2023; Published 30 May 2023 Academic Editor: Wen Liu Copyright ©2023ErshenWangetal.TisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Civil aviation transportation equipment is more convenient and faster than other transportation tools and is an essential part of intelligent transportation. It is signifcant to study the reliability of positioning information and enhance trafc safety. Advanced receiver autonomous integrity monitoring (ARAIM) can provide vertical guidance during the diferent navigation stages in civil aviation felds. Te traditional multiple hypothesis solution separation (MHSS) algorithm distributes the probability of hazardous misleading information (PHMI) and probability of false alarm (PFA) uniformly over all visible satellites resulting in reduced global availability of ARAIM. Aiming at this problem, we proposed an adaptive simulated annealing particle swarm optimization (ASAPSO) algorithm to redistribute integrity and continuity risks and establish a protection level optimization model. Based on the real BeiDou navigation satellite system/global positioning system (BDS/GPS) data, the experimental results show that the optimizedalgorithmcanreducetheverticalprotectionlevel(VPL),andtheARAIMglobalavailabilityofBDS/GPSisimprovedby 1.73%∼2.73%. Te optimized algorithm can improve the availability of integrity monitoring at diferent stages of the navigation system and provide a basis for ensuring the reliability of the positioning results. a single failure untenable [5–7]. Te ARAIM provides 1. Introduction localizer precision with vertical guidance up to 200 Te BDS-3 satellite navigation system is operating smoothly feet altitude (LPV-200) for global aircraft landing and achieving global coverage. It is playing an irreplaceable navigation [8]. role in the future and is widely used in road, railway, water, Related scholars have conducted a lot of research on air transportation, and other aspects of transportation. In ARAIM availability optimization. Te Gauss Newton method is used to optimize the model, and the polynomial recentyears,trafcsafetyhasbecomearesearchhotspot.Te satellite navigation system is closely related to trafc situ- coefcient optimization algorithm is integrated to improve ational awareness and safety supervision of intelligent ve- the ARAIM availability [9]. Te integrity risk is allocated by hicle navigation [1, 2]. And satellite navigation is also widely the binary search method to reduce the VPL value [10]. used in the aviation feld [3, 4]. Te integrity monitoring Reduce VPL by optimizing the allocation of integrity risks algorithm provides some assurance of location information [11].Geneticalgorithmisusedtoredistributecontinuityrisk reliability. Integrity algorithm is one of the utmost priorities and integrity risk to achieve VPL optimization [12]. PSO for safety critical GNSS (global navigation satellite system). algorithm is used to optimize the integrity risk allocation Te rapid development of multiconstellation integrated process to reduce the protection level [13]. Trough the navigation systems has assumed a single constellation and maximum minimization method, the fminimax function is 2 Journal of Advanced Transportation used to reasonably allocate the risk probability to reduce the where H represents the observation matrix, y represents the VPL [14]. Tese researches improved the availability of pseudo-range observedfromthenavigationmessageandthe ARAIM in diferent ways. Working Group C defned pseudo-range residual vector calculated using the satellite multiple hypothesis solution separation as the baseline al- position and the receiver clock error. x is the position gorithm [15]. Tis work focuses on VPL computation and correction parameters of the user receiver in the three- the global availability of ARAIM [16]. Traditional risk dimensional space and the receiver clock bias. ε can obey equalization strategy leads to the conservatism of VPL. Tis a Gaussian distribution with a mean value of zero and study reallocated PHMI and PFA by using the ASAPSO to a variance of σ . optimize availability. −1 T (0) (0) x 􏽢 � 􏼐H W H􏼑 HW y � S y, Te efectiveness oftheASAPSOalgorithmwas analyzed 0 0 and validated in terms of global VPL and the ARAIM −1 T (0) (0) availability based on dual constellation by optimizing VPL. S � H W H HW , 􏼐 􏼑 Te results show that the optimization method based on binary constellation diagram optimized the VPL and im- 0 0 0 ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ proved the global ARAIM availability in diferent air nav- ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ σ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ all,1 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ igation stages. In Section 2, the MHSS algorithm and the ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ASAPSO ARAIM algorithm are described in detail. In ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ (2) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1 ⎥ ⎢ ⎥ Section 3, simulations are performed using a dual-frequency ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ carrier-smoothed position solution based on the BDS/GPS ⎢ ⎢ σ ⎥ ⎢ ⎥ ⎢ all,2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ W � ⎢ ⎥, ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ constellation. Finally, the study is concluded in Section 4. ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋮ ⋮ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2. ARAIM Algorithm Analysis ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1 ⎥ ARAIM algorithm uses a dual-frequency technology to ⎥ ⎢ ⎥ ⎢ ⎦ 0 0 0 eliminate ionospheric interference and uses multiple con- all,n stellationstoobtainmoreobservationstoenhancetheglobal where W represents the weight matrix and σ represents availability of LPV-200. Te ARAIM algorithm is an ex- all,i tension of the RAIM algorithm, which requires much higher the standard noise error of the i − th satellite. Te solution performance than the RAIM algorithm. It is a multifre- separation test is as follows: 􏼌 􏼌 quency and multiconstellation integrated navigation RAIM 􏼌 􏼌 􏼌 􏼌 ∆x � 􏼌x 􏽢 − x 􏽢 􏼌, i i 0 algorithm.ISMparameterscarryinformationonSISranging −1 T T error (SISRE) and fault statistics, which refect inherent ⎧ ⎪ x 􏽢 � 􏼐H WH􏼑 H W y � S y, ⎨ (3) 0 i i performance parameters of the core constellation, including −1 ⎩ T T nominal measurement biases b ,the standard deviation of x 􏽢 � 􏼐H WH􏼑 H Wy � S y, nom i 0 ephemeris, and clock error σ . P and P denote the URA sat const where x 􏽢 represents the i − th subset and x 􏽢 represents the satellite failure state probability and the constellation failure i 0 subset with no fault. Furthermore,thedetection threshold of priori probability, respectively. ISM parameters are gener- the vertical position corresponding to the fault subset is as ated and verifed on the ground and transmitted to users as follows: required [17, 18]. sat 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 ∆S (3, i) × b . (4) D � K × σ + 􏽘 􏼌 􏼌 2.1. MHSS ARAIM Architecture. Te MHSS algorithm is i fa,i dv,i i cont,i i�1 shown below [19, 20]. Based on the MHSS traditional ARAIM algorithm, it can be expressed as follows: TeARAIMVPLcalculationcanbeexpressedasfollows: y � Hx + ε, (1) sat ⎧ ⎪ 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 VPL � K × σ + 􏽘 􏼌S (3, i)􏼌 × b , ⎪ 0 md,0 v,0 0 nom,i ⎪ i�1 sat (5) 􏼌 􏼌 􏼌 􏼌 ⎪ 􏼌 ⎪VPL � D + K × σ + 􏽘 􏼌S (3, i)􏼌 × b , ⎪ i i md,i v,i i nom,i i�1 VPL � max VPL ,VPL􏼁 , 0 i Journal of Advanced Transportation 3 where VPL represents VPL corresponding to the fault where Q is the right hand side cumulative distribution subset. i � 0 denotes VPL corresponding to the fault-free function of a zero mean unit Gaussian. N is the number of subset. S represents the fault subset’s weighted least squares fault subsets; traditional allocation of PHMI and PFA will projection matrix, S denotes the i − th fault subset, and b lead to conservative protection levels. Terefore, the PHMI i nom represents the maximum standard deviation of the i − th and PFA are allocated by the ASAPSO algorithm, and this satellite used to evaluate the integrity; it can be expressed as allocation strategy will be discussed. follows: 2.2. VPL Calculation of MHSS ARAIM Algorithm Optimized ∆S � S − S , (6) i i 0 Based on ASAPSO. Te PSO algorithm easily falls into local where σ , σ , and σ can be expressed as follows: convergence, which leads to slowing down the overall v,0 v,i dv,i 􏽲��������� � convergence speed [21, 22]. Terefore, the simulated −1 σ � 􏼐HWH 􏼑 , annealing algorithm is combined with the PSO algorithm. v,0 3,3 Te algorithm is divided into two stages: the standard PSO 􏽱������������ � T −1 (7) algorithm is used for optimization in the early stage and the σ � 􏼐H M WH􏼑 , v,i k 3,3 simulated annealing algorithm is used later to optimize and 􏽱������������� � −1 T search the parameters in the PSO algorithm [23, 24]. σ � ∆S W ∆S . 􏼐 􏼑 dv,i i i 3,3 Tis study proposed an optimization strategy based on theASAPSO algorithmtosolve theproblem thattheaverage Te traditional ARAIM algorithm equally allocates the continuity and integrity risk probability to all visible sat- distribution strategy is not optimal. Te VPL is optimized by introducing an adaptive weight function. Te proposed ellites. Te integrityconstraint coefcient K and K are md,i fa,i determined by PHMI and PFA expressed as follows: optimization algorithm can obviously reduce the vertical protection level and improve the ARAIM availability. PFA −1 K � −Q , 􏼒 􏼓 fa,i Step 1. Calculation of the velocity and position of particles. PHMI −1 K � −Q 􏼠 􏼡, md,0 (8) 2(N + 1) PHMI −1 K � −Q 􏼠 􏼡, md,i P (N + 1) sat,i v (it + 1) � wv (it) + c r pbest − x (it)􏼁 + c r gbest − x (it)􏼁, (9) m m 1 1 m m 2 2 m m x (it + 1) � x (it) + ] (it + 1), (10) m m m where it represents the current particles number of itera- where ω and ω represent themaximumandminimum max min tions, w represents the inertia weight, c and c represent the values of the inertia weight w, respectively. f is the ftness 1 2 acceleration constants, which are used to adjust the velocity value of the particles. f and f are the average and avg min of motion in the pbest and gbest directions, respectively. r minimum ftness values of the particles in the population, and r are the random number between 0 and 1. x rep- respectively [27]. 2 m resents the particle’s position. v represents the moving Ifthetargetvalueregionofeachparticleisconsistentand speed of the particle m [25, 26]. the region is locally optimal, the inertia weight will increase. If the target value of each particle is dispersed, the inertia weight will decrease. Step 2. Selection of adaptive inertia weight. Te method of adaptive inertia weight was introduced to Step 3. Metropolis criterion updating strategy combined balance the global and local search ability of the PSO and with the simulated annealing algorithm. improve the algorithm’s performance. Te formula is as We proposed an update strategy based on the Me- follows: tropolis criterion to solve the particle position update ω − ω 􏼁 f − f 􏼁 ⎧ ⎪ max min min ⎫ problem. First, calculate the particle’s next possible po- ⎪ ⎪ ω − , f ≤ f ⎪ ⎪ min avg ⎪ ⎪ ⎨ f − f ⎬ sition according to the updating equation (9). Ten, judge avg min ω � , ⎪ ⎪ whether it can be accepted as the particle’s next position ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ according to the Metropolis criterion. Finally, the steps w , f > f max avg are as follows: (11) 4 Journal of Advanced Transportation probability, but accepts probability with fit (t) ≤fit (t), ⎧ ⎪ i+1 i ⎪ exp(−fit (t) − fit (t)/T) > rand. Te Metropolis criterion’s ⎨ i+1 i (12) update strategy avoids particle degradation in some extent. ⎪ −fit (t) − fit (t) ⎪ i+1 i rand ≤exp􏼠 􏼡, Step 4. Particle ftness function selection. According to the MHSS algorithms, the probability where fit is the ftness value for the next position of the i+1 averageallocationmethodofPHMIandPFAisadopted,and particle. Te Metropolis criterion is introduced so that the the VPL calculation method can be expressed as follows: particle does not accept the diferent solution with full N N sat sat 􏼌 􏼌 􏼌 􏼌 PFA PHMI 􏼌 􏼌 􏼌 􏼌 −1 −1 􏼌 􏼌 􏼌 􏼌 ∆S (3, i) × b . (13) VPL � −Q 􏼒 􏼓 × σ + 􏼠−Q 􏼠 􏼡􏼡 × σ + 􏽘 􏼌S (3, i)􏼌 × b + 􏽘 􏼌 􏼌 i dv,i v,i i nom,i k cont,i N P (N + 1) sat i�1 i�1 According to equation (13), VPL is taken as the opti- mizationobjective.Teschemesassignedtoeachfaultsubset by PHMI and PFA are as follows: set ⎧ ⎪ ⎪ 􏽘 P ≤PHMI, HMI,k k�1 minmax VPL PHMI , Pfa 􏼁􏼁,s · t · k k k set (14) 􏽘 P ≤Pfa, fa,k k�1 VPL � minVPL (i � 0, . . . , N), where the VPL corresponding to each fault subset is expressed as follows: sat sat 􏼌 􏼌 􏼌 􏼌 PFA PHMI 􏼌 􏼌 􏼌 􏼌 −1 −1 􏼌 􏼌 􏼌 􏼌 S (3, i) × b + 􏽘 ∆S (3, i) × b . (15) VPL � −Q 􏼒 􏼓 × σ + 􏼠−Q 􏼠 􏼡􏼡 × σ + 􏽘 􏼌 􏼌 􏼌 􏼌 i dv,i v,i i nom,i k cont,i N P (N + 1) sat i�1 i�1 Terefore, the weighted sum of VPL is taken as the optimization objective, expressed as follows [17]: min G set ⎪ G � 􏽘 y × VPL , ⎪ i i i i�0 ⎪ σ + σ 􏼐 􏼑 ⎪ dv, i v, i ⎪ y � , ⎪ N N ⎪ set set ⎪ 􏽐 σ + 􏽐 σ i�0 dv, i�0 v, (16) ⎨ i i sat 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 VPL � K × σ + K × σ + 􏽘 S (3, i) × b ⎪ 􏼌 􏼌 ⎪ i fa, dv, i md, i v, i i nom,i i�1 sat ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ 􏼌 􏼌 ⎪ + 􏽘 􏼌∆S (3, i)􏼌 × b , i cont,i i�1 Journal of Advanced Transportation 5 where G is optimization objective function and N rep- (4) Judgment termination condition: Judge whether i set resents the total number of particles. the particle reaches the maximum iterations. If this condition is met, the optimized PHMI and PFA allocation strategy will be output to the optimized Step 5. ASAPSO algorithm optimization VPL. VPL. Otherwise, go back to step 2 and continue ASAPSO algorithm is introduced into the optimization iterating updates. Finally, the VPL’s optimal allo- process. Te details are as follows: cation strategy is obtained. (1) Firstly, M visible satellites were extracted and di- vided into M groups. Ten, the PHMI was set to 3. Experimental Verification and 0∼PHMI and the PFA is set to 0∼PFA. Finally, they Results Analysis were randomly divided into M groups and coded to form the initial population n. 3.1. Optimization Simulation of Continuous Risk and Integrity Risk Allocation Method. We extracted navigation in- Pfa , Pfa , Pfa , ..., Pfa m0 m1 m2 mN set ⎣ ⎦ ⎡ ⎤ n � . formation and observation fles from the IGS website to PHMI ,PHMI ,PHMI ...,PHMI m0 m1 m2 mN set verifythealgorithm’sperformance.Tesimulationstartedat (17) 00:00:00 on June 6, 2020, lasted for 12hours, and the simulation step length was 10minutes. Tis study uses the where m �1,2, . . ., n, and n is the number of BDS/GPS constellation dual-frequency carrier smoothing populations. method for simulation, and the experimental conditions are shown in Table 1. (2) Initialize the algorithm parameters. Figure 1(a) shows that the number of visible satellites is (a) Initialize the position of particles in the relatively stable between 20 and 25. Meanwhile, Figure 1(b) population shows that the GDOP is between 1.3 and 2. It can be in- (b) Set the initial temperature, where dicated that the BDS/GPS satellites have a good space dis- T � (−f )/(ln0.2) represents the initial 0 g tribution in general. Figure 2(a) shows that the PFA is temperature allocated by the ASAPSO algorithm. In this algorithm, PFA (c) Initialize each parameter is randomly assigned to diferent satellites as a particle, and Te acceleration coefcient c diferentsatellitesareallocatedtodiferentPFA.Tevalueof � c � 0.2, the 1 2 PFA remains between 2.7e −6 and 3.9e −6. Figure 2(b) population particle size is set to M �50, the maximum iteration times are set to 50, the shows that the value remains between 5.7e −8 and 9.8e −8 by the optimized ASAPSO algorithm from the risk maximum particle moving to speed is v � 2, max allocation of PHMI. Te ASAPSO can optimize the risk and the minimum moving speed is v � −2. min allocation strategy of PHMI and PFA. Both PHMI and PFA Ten, the PHIMI and the PFA of each particle are are less than the threshold value. Te improved algorithm calculated. Ten, the ftness function is calcu- allocates diferent values for diferent visible satellites, which lated. Te distribution method of PHMI and PFA can reduce the VPL and improve the ARAIM availability. generated in the initial population are substituted Figure3shows that the VPL value of the ASAPSO is less than into VPL. Te individual optimal PHMI and the that of the traditional algorithm in any epoch, and both the population optimal PFA are assigned to each particle. traditional algorithm and the optimized algorithm are less than 35m under GPS/BDS dual-frequency dual-system (3) Iterative updating: First, the inertia weight W is combination. Terefore, under the premise of ensuring updated based on equation (11). Next, based on the PHMIandPFA,theASAPSOalgorithmcanreducetheVPL. initial iteration value, the function value of each It can also improve ARAIM availability. particle target is set to the individual optimal value, and the optimal value is selected from the indi- vidual optimal value as the global optimal value. 3.2. Global Availability Simulation Analysis of the Traditional Ten, the particle position and velocity are updated and Optimized Method. Tis experiment uses BDS/GPS according to equations (9) and (10). During each almanac data to analyze global availability. BDS data were iteration, the individual optimal position pbest m downloaded from the Test and Evaluation Center of China and the global optimal position gbest will be Satellite Navigation System Management Ofce and GPS updated. Calculate the probability and generate data were downloaded from the https://celestrak.com a random r. If r < min [1, p], the particle will enter website [27]. Te data were collected on January 2, 2021. a new position and iterate again. Te data simulation time is 3hours with the step of Te particle will move to a new position by 5minutes. accepting a diferent probability. Finally, the tem- Te approach phases of an aircraft can be roughly di- peratureiscooledby T � z × T .Trepresentsthe vided into the nonprecision approach (NPA) and vertical k+1 k temperature, the value of z generally ranges from guidance approach phase, which includes the APV-I, APV- 0.5 and 0.9, and k represents the number of II, and precision approach phase CAT-I, CAT-II, and CAT- iterations. III. Operational risks in diferent civil aviation approach 6 Journal of Advanced Transportation Table 1: ISM parameters setting. Parameters Defnition Setting PHMI Total integrity budget 9.8e −7 P Continuity budget allocated to disruptions because of false alert 4e −6 fa VAL Vertical alert limit 35m EMT Efective monitoring threshold 15m Constellation Navigation constellations GPS/BDS P Priori failure probability of satellites 1e −4 sat P Priori failure probability of constellations 1e −5 const 30 2.5 25 2 20 1.5 15 1 0 2468 10 12 0 2 4 6 8 10 12 Time (h) Time (h) (a) (b) Figure 1: (a) Number of visible satellites and (b) GDOP. -6 ×10 -8 ×10 3.5 2.5 1.5 4 02468 10 12 02468 10 12 Time (h) Time (h) (a) (b) Figure 2: (a) PFA is allocated by the ASAPSO. (b) PHMI is allocated by the ASAPSO. PFA Number of visible satellites GDOP PHMI Journal of Advanced Transportation 7 02468 10 12 Time (h) VPLASAPSO MHSS-VPL Figure 3: VPL value optimized by the MHSS algorithm and ASAPSO algorithm. Table 2: ICAO navigation performance requirements for each approach phase. Phase Precision (95%) Alarm limit Continuity Availability –4 220m (H) 550m (H) 1 ×10 /h 0.99 NPA –8 N/A (V) N/A (V) 1 ×10 /h 0.99999 16m (H) 40m (H) 0.99 –6 APV-I 8 ×10 /15s 20m (V) 50m (V) 0.9999 16m (H) 40m (H) 0.99 –6 APV-II 8 ×10 /15s 8m (V) 20m (V) 0.99999 16m (H) 40m (H) 0.99 –6 LPV-200 8 ×10 /15s 4m (V) 35m (V) 0.99999 16m (H) 40m (H) 0.99 –6 CAT-I 8 ×10 /15s 4∼6m (V) 10m (V) 0.99999 80 80 60 60 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 12 < 15 < 20 < 25 < 30 < 35 < 40 < 50 > 50 < 12 < 15 < 20 < 25 < 30 < 35 < 40 < 50 > 50 VPL (m) - 99.5% VPL (m) - 99.5% (a) (b) Figure 4: VPL before and after optimization. (a) VPL average �19.7652. (b) VPL average �20.4044. Latitude (deg) VPL Latitude (deg) 8 Journal of Advanced Transportation 80 80 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 35, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 95.8% VAL = 35, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 97.53% th acc th acc (a) (b) Figure 5: Before and after optimization global availability of ARAIM under the LPV-200. (a) Traditional algorithm Coverage (99.5%) � 95.80%. (b) Optimized algorithm Coverage (99.5%) �97.53%. 60 60 40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 50, HAL = 40, EMT = Inf, σ = Inf, Coverage (99.5%) = 99.37% VAL = 50, HAL = 40, EMT = Inf, σ = Inf, Coverage (99.5%) = 99.06% th acc th acc (a) (b) Figure 6: Before and after optimization global availability of ARAIM under the LPV-250. (a) Traditional algorithm Coverage (99.5%) � 99.06%. (b) Optimized algorithm Coverage (99.5%) �99.37%. phases are diferent, so the integrity requirements of each (Figures 4–8). Te latitude and longitude interval is the grid ° ° phase are also diferent [28]. Te ICAO (International Civil spacing set by simulation, and it is selected as 10 ×10 . Aviation Organization) navigation performance re- Figures 4–8 show the comparison of the global VPL and quirements for each approach phase are shown in Table 2. availability of the traditional method (a) and the optimized Te availability of an integrity monitoring algorithm has method (b) under appropriate ISM parameters in diferent an essential relationship with satellite geometric space dis- navigation stages of the BDS/GPS dual constellation. Fig- tribution, which refers to the percentage of time that system ure 4 shows that the color of the improved algorithm ° ° functions can meet the requirements of integrity perfor- gradually turns green in the range of 100 W-120 W lon- ° ° ° ° ° mance in a certain fight stage. Terefore, it is of great gitude, 40 N-60 N latitude, 0 E-50 E longitude, and 40 E- signifcance to study aircraft availability in diferent navi- 60 E longitude, which plays an optimized efect. Figure 5 gation stages. It is essential to analyze the availability of shows a signifcant improvement in the availability of the ° ° ° aircraft integrity monitoring algorithms at diferent navi- improved algorithm in the range of 25 S-20 N and 20 W to gation stages. Te performance of the optimization algo- 10 E. Te efciency of the improved algorithm is obviously rithm is verifed through simulation and compares whether superior to the traditional MHSS algorithm. Te MHSS it can meet the integrity requirements of the vertical algorithm is based on the spatial distribution of visible GPS guidance approach phase and the precision approach phase satellites and uses the averaging method for risk allocation. Latitude (deg) Latitude (deg) Latitude (deg) Latitude (deg) Journal of Advanced Transportation 9 80 80 60 60 40 40 20 20 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 20, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 8.77% VAL = 20, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 12% th acc th acc (a) (b) Figure 7: Before and after optimization global availability of ARAIM under the APV-II. (a) Traditional algorithm Coverage (99.5%) � 8.77%. (b) Optimized algorithm Coverage (99.5%) �12%. 80 80 60 60 40 40 0 0 -20 -20 -40 -40 -60 -60 -80 -80 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Longitude (deg) Longitude (deg) < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% < 50% > 50% > 75% > 85% > 90% > 95% > 99% > 99.5% > 99.9% VAL = 10, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 0% th acc VAL = 10, HAL = 40, EMT = 15, σ = 1.87, Coverage (99.5%) = 0% th acc (a) (b) Figure8:BeforeandafteroptimizationglobalavailabilityofARAIMundertheCAT-I.(a)TraditionalalgorithmCoverage(99.5%) �0%.(b) Optimized algorithm Coverage (99.5%) �0%. Table 3: Global availability ARAIM comparison between before and after optimization. Navigation stages Traditional algorithm (%) Optimized algorithm (%) LPV-200 95.8 97.53 LPV-250 99.06 99.37 APV-II 8.77 12 CAT-I 0 0 Satellites of diferent Beidou constellations have diferent Te space geometry distribution of GPS satellite is uniform, the constellation fault probability is low, and the protection efects on positioning errors. Terefore, the traditional av- level calculation under various fault assumptions is similar. erage distribution method will lead to VPL being too For BDS/GPS integrated navigation system, BDS perfor- conservative, which will reduce the global availability of manceisweak,andBDSconstellationdistributionisuneven. ARAIM. Latitude (deg) Latitude (deg) Latitude (deg) Latitude (deg) 10 Journal of Advanced Transportation Figures 5–8 show a global availability analysis of navi- optimization of the improved algorithm is diferent. Te gational integrity requirements at diferent navigational availability is improved by 1.73%∼2.73%. It can meet more performance stages. Figure 5 shows that the improved al- stringent navigation phase requirements for integrity ° ° gorithm is signifcantly improved in the range of 20 N–20 S performance. ° ° and 40 N–60 N. And it can be found that the lower the In 2020, the BDS-3 system was built successfully. And it availability before the improvement is, the more obvious the provides global services. Tis study used BDS-3 actual data availability after the optimization algorithm is adopted. validated and compared the optimization and conventional Figure 6 shows that the improved algorithm optimizes the algorithms. Te ARAIM availability was obviously im- ° ° ° ° range of 40 N–60 N and 100 W–120 W. Figure 7 shows proved. With the navigation performance requirement of a signifcant improvement in the area near the tropics. aviation users, the integrity of navigation performance be- Figure 8 shows that neither algorithms can satisfy the comes extremely important. Tis study presented an opti- availability of the CAT-I approach navigation stage. Table 3 mized PHMI and PFA risk allocation method. Te shows the global availability ARAIM comparison before and experiment shows that the proposed algorithm can signif- after optimization in diferent navigation performance icantly improve ARAIM availability and provides more stages. reliable services for aviation users. And the ongoing Table 3 shows that the global availability efect of the transportation revolution (especially autonomous transport traditional allocation method and ASAPSO algorithm is systems) has signifcance in this work. It can provide safer excellent under the LPV-250 because the vertical alarm limit and more reliable positioning information for users. (VAL) of ARAIM is 50m under the LPV-250. Te VAL is much higher than the VPL. It can meet the ARAIM Data Availability availability under LPV-250. However, in the LPV-200 navigation stage, the global availability of the optimized Te data used to support the fndings of this study are in- algorithm is higher, and the availability of the ARAIM is cluded within the article. more than 90%. Te ARAIM VAL is 35m under the LPV- 200. Terefore, the availability of ARAIM under the Conflicts of Interest LPV-200 is signifcantly lower than that of the LPV-250 navigation stage in terms of global availability. Te global Te authors declare that they have no conficts of interest. availability of the traditional and optimized algorithm is about 8% and 12% under the APV-II navigation stage. Acknowledgments Because the VAL required is 20m under the APV-II. In the CAT-I stage, the VAL of ARAIM is stricter than APV-II. Tis study was supported by the National Natural Science And the VAL is 10m, which is far lower than the VPL. It Foundation of China (62173237), the Open Fund of State cannot meet the integrity requirements in the CAT-I nav- Key Laboratory of Air Trafc Management System and igation stage. In addition, it can be seen that the availability Technology (SKLATM202101), the Applied Basic Research of ARAIM under LPV-250 >LPV-200 >APV-II >CAT-I is Programs of Liaoning Province (2022020502-JH2/1013 and under the same ISM parameter. Te improved optimization 2022JH2/101300247), the Open Fund of Key Laboratory of algorithm has the most obvious efect on the ARAIM Civil Aviation Flights Wide Area Surveillance and Safety availability under the LPV-200 and APV-II. However, the Control Technology of Civil Aviation University of China impact of LPV-250 and CAT-I is not obvious and needs (202105), the Open Fund of Key Laboratory of Flight improvement. Techniques and Flight Safety, CAAC (FZ2021KF15 and FZ2021ZZ06), and the Special Funds Program of Shenyang Science and Technology (22-322-3-34). 3.3. 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