Estimation of Surface Duct Using Ground-Based GPS Phase Delay and Propagation Loss

Liao, Qixiang; Sheng, Zheng; Shi, Hanqing; Xiang, Jie; Yu, Hong

doi:10.3390/rs10050724

Cited by 13 publications

(13 citation statements)

References 47 publications

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“…Furthermore, the optimal solution obtained does not necessarily converge to the real value. In fact, similar conclusions can be reached from the results shown in Reference [51]. Therefore, we can conclude that increasing the known information may not effectively improve the retrieved effect in the actual operation process when the number of inversion parameters is certain.…”

Section: Results and Discussion Of The Joint Inversion Of Atmosphericsupporting

confidence: 84%

“…After we collected the data, we used the new algorithm to solve the practical problem of jointly retrieving atmospheric ducts. The specific framework of the joint retrieval of atmospheric ducts has been elaborated in our previous work [32,51]. This paper takes the problem as a series of practical test problems to verify whether the improved algorithm can be applied in practical conditions.…”

Section: Results and Discussion Of The Joint Inversion Of Atmosphericmentioning

confidence: 99%

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Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

Mai

Shi

Liao

et al. 2020

Sensors

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The traditional method of retrieving atmospheric ducts is to use the special sensor of weather balloons or rocket soundings to obtain information intelligently, and it is very expensive. Today, with the development of technology, it is very convenient to retrieve the atmospheric ducts from Global Navigation Satellite System (GNSS) phase delay and propagation loss observation data, and then the GNSS receiver on the ground forms an automatic receiving sensor. This paper proposes a hybrid decomposition-based multi-objective evolutionary algorithm with adaptive neighborhood sizes (EN-MOEA/ACD-NS), which dynamically imposes some constraints on the objectives. The decomposition-based multi-objective evolutionary algorithm (MOEA/D) updates the solutions through neighboring objectives, the number of which affects the quality of the optimal solution. Properly constraining the optimization objectives can effectively balance the diversity and convergence of the population. The experimental results from the Congress on Evolutionary Computation (CEC) 2009 on test instances with hypervolume (HV), inverted generational distance (IGD), and average Hausdorff distance ∆ 2 metrics show that the new method performs similarly to the evolutionary algorithm MOEA/ACD-NS, which considers only the dynamic change of the neighborhood sizes. The improved algorithm is applied to the practical problem of jointly retrieving atmospheric ducts with GNSS signals, and its performance further demonstrates its feasibility and practicability. the multi-objective optimization can make full use of multi-source observation information and can improve the reliability of the solution. The traditional method can only obtain a Pareto optimal solution that is not necessarily satisfactory to the decision-maker; the rationality of prior knowledge also affects the selection of the optimal solution. This paper proposes a multi-objective evolutionary algorithm (MOEA) for MOP problems in order to obtain a set of Pareto optimal solutions [5,6]. According to the optimization framework, MOEAs can be roughly divided into three categories, namely: (a) Pareto-based approaches [7], (b) indicator-based approaches [8], and (c) decomposition-based approaches [9].Pareto-based methods sort the individuals according to the dominant relationship among them, and then the optimal solution is selected. The Pareto-based approach is the most popular method in the evolutionary multi-objective optimization community. NSGA-II and SPEA2 are the most representative algorithms, and they are very effective when dealing with two or three objective functions [7,10]. However, when the number of objective functions increases to more than three, most of the solutions in the NSGA-II and SPEA2 search spaces become non-dominated solutions, resulting in a rapid decline in search capabilities.Indicator-based MOEAs use the value of performance indicators to guide the search direction, which drives whole generated solutions to the Pareto solution sets. As the calculation of the Pareto dominance relatio...

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Section: Results and Discussion Of The Joint Inversion Of Atmosphericsupporting

confidence: 84%

Section: Results and Discussion Of The Joint Inversion Of Atmosphericmentioning

confidence: 99%

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

Mai

Shi

Liao

et al. 2020

Sensors

Self Cite

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show abstract

“…This can be substituted by a sine or cosine transform because the bottom boundary approximates to a perfectly conducting surface. The SSFT solution of the propagated wave equation is expressed as [16]:u(x+Δx,z)=expfalse(ik(M2−1)Δx/2false)⋅F−1{expfalse(−iπ2p2Δx/(2k)false)F[u(x,z)]}…”

Section: Multi-objective Optimization Using Evolutionary Algorithmsmentioning

confidence: 99%

“…The modified refractivity M, which considers the Earth’s curvature, is related to the radio refractivity N as follows [16]:M=N+0.157×r…”

Section: Multi-objective Optimization Using Evolutionary Algorithmsmentioning

confidence: 99%

“…Anderson [14] tried to infer atmospheric duct with phase delay, but there was a certain gap between the inversion results and the real refractivity profile. Liao et al presented the inversion method of low-elevation ground-based GPS, combining phase delay and propagation loss information to retrieve surface duct parameters, and recently proposed the non-dominated sorting genetic algorithm II combined with simulated annealing algorithm (NSSAGA) with matching fields to improve inversion results [15,16]. However, they neglected to consider the influence of source frequency.…”

Section: Introductionmentioning

confidence: 99%

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A Comparative Study on Evolutionary Multi-objective Optimization Algorithms Estimating Surface Duct

Liao

Sheng

Shi

et al. 2018

Sensors

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The problem of atmospheric duct inversion is usually solved as a single objective optimization problem. Based on ground-based Global Positioning System (GPS) phase delay and propagation loss, this paper develops a multi-objective method including the effect of source frequency and receiving antenna height. The diversity and convergence of solution sets are evaluated for seven multi-objective evolutionary algorithms with three performance metrics: Hypervolume (HV), Inverted Generational Distance (IGD), and the averaged Hausdorff distance (Δ2). The inversion results are compared with the simulation results, and the experimental comparison is conducted on three groups of test situations. The results demonstrate that the ranking of algorithm performance varies because of the different methods used to calculate performance metrics. Moreover, when the algorithms show overwhelming performance using performance metrics, the inversion result is not more close to the real value. In the comparison of computational experiments, it was found that, as the retrieved parameter dimension increases, the inversion result becomes more unstable. When the observed data are sufficient, the inversion result seems to be improved.

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Grey Wolf-Particle Swarm Optimization with Back-Propagation Neural Network for Surface Duct Profile Estimation

Zhang

Yang

Yu-lu

2022

Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery

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Estimation of Surface Duct Using Ground-Based GPS Phase Delay and Propagation Loss

Cited by 13 publications

References 47 publications

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

A Comparative Study on Evolutionary Multi-objective Optimization Algorithms Estimating Surface Duct

Grey Wolf-Particle Swarm Optimization with Back-Propagation Neural Network for Surface Duct Profile Estimation

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