Study On Parabolic Equation Method For Low-Frequency Groundwave Propagation Prediction In Large-Area Complex Environment

Low-frequency(LF)radio navigation system plays an important role in national position,navigation,and timing(PNT)systems.It has been identified as the best backup for the global navigation satellite system(GNSS)to counteract the vulnerabilities of the GNSS such as poor anti-jamming capability,extremely low power of signals,and out-of service in underwater or shielded environments,etc.Currently,accurate prediction of LF groundwave propagation time delay is the key factor to improve the service accuracy of LF radio navigation system.In the existing methods on LF groundwave propagation,the parabolic equation(PE)method has incomparable advantages in terms of computational accuracy and speed over other methods in large-area complex environment modeling,which prompts its use in LF groundwave propagation prediction.Nevertheless,with the deep use of the PE method in LF groundwave propagation modeling,its shortcomings have gradually emerged,including the limitation of the assessment method to select the optimal PE form,the neglect of backward reflected wave generated from the obstacles,the incapability of characterizing pulse evolution due to the lossy surface dispersion,and the intractability of analyzing the effect of near-source complex topography on radio coverage,etc.In view of the above shortcomings of the PE method,this dissertation aims to study the PE method for LF groundwave propagation prediction in complex environments,and meanwhile to develop the high-efficiency and high-accuracy PE methods for LF groundwave propagation modeling.This is of great significance and application value for the knowledge of LF groundwave propagation characteristics in large-area complex environments,and for the improvement of service accuracy of LF radio navigation system.The main contributions and innovations of this dissertation are as follows:1.A dispersion method is proposed for evaluating the accuracy of the PE forms in the transformed coordinates,thereby ascertaining the optimal PE method based on conformal mapping model that can be solved by the split-step Fourier transform(SSFT).The dispersion method provides the theoretical basis for the assessment of the optimal PE method in transformed coordinates for the first time.The dispersion relations of several PE forms are derived by substituting the plane wave solution in terms of the transformed coordinates into the PE forms.It is firstly found that the PadéPE gets higher accuracy than the Taylor PE,and the Barrios and Donohue-Kuttler PEs have comparable accuracy.Also,when the sunny terrain slope is larger than about17~o or the shady terrain slope is larger than about 5~o,the accuracy of the Barrios and Donohue-Kuttler PEs are even worse than the Taylor PE.Hence,it is concluded that the Taylor PE is the optimal PE form in the transformed coordinates that can be solved by the numerical SSFT solution.Furthermore,the limitations of the optimal PE method are analyzed and its applicable conditions in LF groundwave propagation are given further.The validity of the optimal PE method in realistic long-range complex propagation paths is substantiated by calibrating against the measured data.2.An improved two-way PE(2W-PE)method is proposed to model LF groundwave propagation in the presence of steep terrain.The method combines the staircase terrain model and the conformal mapping model together instead of using the single staircase terrain model in the traditional 2W-PE method for irregular terrain modeling.By using the advantages of the conformal mapping model to compensate for the limitations of the staircase terrain model,the improved 2W-PE method obtains higher accuracy both in forward and backward propagation prediction than the traditional 2W-PE method while maintaining its high efficiency.Calibrated against the FDTD method,the utility and limitations of the 2W-PE methods are analyzed both in single-and multiple-mountain cases,and their applicability are also given.3.Two hybrid time-domain PE(TDPE)methods are presented for the modeling of LF pulse groundwave propagation in different near-source environments.One of them is the flat-earth formula(FEF)-TDPE method for situations with smooth near-source surfaces,and the other is the FDTD-TDPE method for problems involving near-source complex topography.By using the advantages of each method,the presented hybrid TDPE methods improve the accuracy of the traditional TDPE method through making up for the poor-accuracy defect of the traditional TDPE method in short range with large propagation angles.In this way,the hybrid TDPE methods achieve both high-accuracy and fast-speed prediction capability for LF pulse groundwave propagation in the large-area complex environment.On the basis of the hybrid TDPE methods,the time-domain characteristics of Loran-C signal propagating over the lossy media surface are analyzed and the Loran-C pulse evolution due to the dispersion effect is clarified.In addition,the theoretical selection guidelines of sites for Loran-C transmitters are given for the first time via studying the effect of near-source topographic complexities on the radio coverage.Moreover,the effectiveness of the two hybrid TDPE methods in realistic complex propagation paths is verified by comparison against measured data.4.The PE method is employed to solve the LF groundwave propagation problems with temporal and spatial variations of the atmospheric refractivity and temporal variations of the ground conductivity,and thus to reveal the influence law and degree of each factor variation on LF groundwave propagation characteristics.This further perfects the theory of LF groundwave propagation characteristics.The effect of each factor variation on LF groundwave propagation characteristics is investigated by analyzing the temporal-and spatial-variation characteristics and law of atmospheric refractivity,as well as the temporal-variation mechanism of the ground conductivity.It is shown that the effect of temporal and spatial variations of atmospheric refractivity and temporal variations of ground conductivity on field strength is almost negligible.But for phase,at a propagation distance of 1000km,the spatial and temporal variations of the atmospheric refractivity would cause about hundreds of and several tens of nanoseconds of phase error,respectively.Meanwhile,the phase error resulted from the temporal variations of ground conductivity could reach about hundreds of nanoseconds.