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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...
Wang, Ershen;Shi, Xiaozhu;Deng, Xidan;Gao, Jing;Zhang, Wei;Wang, Huan;Xu, Song
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; firstname.lastname@example.org 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 . 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 . 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 . 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 .Geneticalgorithmisusedtoredistributecontinuityrisk reliability. Integrity algorithm is one of the utmost priorities and integrity risk to achieve VPL optimization . 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 . 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 . 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 . Tis work focuses on VPL computation and correction parameters of the user receiver in the three- the global availability of ARAIM . 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 . 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