Stability of High-Order Linear ItôEquations with Delays

A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p-stability are formulated in terms of M-matrices. Stability analysis of applied second-order It? equations with delay is provided as well. The linearization technique, in combination with the tests obtained in this paper, can be used for local stability analysis of a wide class of nonlinear stochastic differential equations.

Stability Analysis for Stochastic Delayed High-order Neural Networks

In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.

Research of Impact of Geografical Latitute and Residual Ionospheric Noises on Informativeness of Measuring of Zenith Wet Delay of GPS Signals

It is noted that necessity of further increase of accuracy of GPS positioning systems requires de-velopment of more perfect methods to compensate information losses occurred due to residual ionospheric delay by using optimization procedures. According to the conditions of formulated optimization task, the signal/noise ratio in measurements of zenith wet delay depends on the second order ionospheric errors, geographic latitude and day of year. At the same time if we assume that the number of measurements at the fixed geographic site is proportional to geographic latitude and if we accept existence of only two antiphase scenarios for variation of residual ionospheric delay on latitude normed by their specific constant, there should be optimum functional dependence of precipitated water on latitude upon which the quantity of measuring information reaches the maximum. The mathematical grounding of solution of formulated optimization task is given.

Monitoring Seasonal Variations of Ionospheric TEC Using GPS Measurements

The regional ionospheric model is adopted to determine satellite-plus-receiver differential delay. The satellite-plus-receiver differential delay is estimated as constant values for each day. Dual-frequency GPS pseudo-ranges observables are used to compute vertical TEC (VTEC). All the monthly mean VTEC profiles are represented by graphs using GPS data of the Beijing IGS site between 2000 and 2004. The monthly averaged values and amplitudes of VTEC are also represented by graphs. The results indicate that the VTEC has seasonal dependency. The monthly averaged values and amplitudes of VTEC in 2000 are about 2 times larger than that in 2004. The maximum VTEC values are observed in March and April, while the minimum VTEC values are observed in December. The seasonal variations trend is found to be similar after polynomial fitting between 2000 and 2004.

Impact of ionospheric irregularity on SBAS integrity:spatial threat modeling and improvement

The ionosphere, as the largest and least predictable error source, its behavior cannot be observed at all places simultaneously. The confidence bound, called the grid ionospheric vertical error(GIVE), can only be determined with the aid of a threat model which is used to restrict the expected ionospheric behavior. However, the spatial threat model at present widespread used, which is based on fit radius and relative centroid metric(RCM), is too conservative or the resulting GIVEs will be too large and will reduce the availability of satellite-based augmentation system(SBAS). In this paper, layered two-dimensional parameters, the vertical direction double RCMs, are introduced based on the spatial variability of the ionosphere. Comparing with the traditional threat model, the experimental results show that the user ionospheric vertical error(UIVE) average reduction rate reaches 16%. And the 95% protection level of conterminous United States(CONUS) is 28%, even under disturbed days, which reaches about 5% reduction rates.The results show that the system service performance has been improved better.

On ionosphere-delay processing methods for single-frequency precise-point positioning

In single-frequency precise-point positioning of a satellite,ionosphere delay is one of the most important factors impacting the accuracy. Because of the instability of the ionosphere and uncertainty of its physical properties, the positioning accuracy is seriously limited when using a precision-limited model for correction. In order to reduce the error, we propose to introduce some ionosphere parameter for real-time ionosphere-delay estimation by applying various mapping functions. Through calculation with data from the IGS（ International GPS Service） tracking station and comparison among results of using several different models and mapping functions, the feasibility and effectiveness of the new method are verified.

Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields

The frequency-comb structure in the extreme ultraviolet（XUV） and vacuum ultraviolet（VUV） regions can be realized by the high-order harmonic generation（HHG） process driven by frequency-comb fields, providing an alternative approach for the measurement of an unknown frequency in XUV or VUV. We consider the case of two driving frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental-and third-harmonics, respectively.The many-mode Floquet theorem（MMFT） is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the frequency-comb laser fields. Multiphoton transition paths involving both fundamentaland third-harmonic photons are opened due to the coupling of the third-harmonic frequency-comb field. The multiphoton transition paths are superpositioned when the carrier-envelope-phase shifts（CEPs） fulfill the matching condition. And the interference of the multiphoton transition paths can be controlled by tuning the relative envelope delay between the fields.We find that the quasienergy structure, as well as the multiphoton resonant high-order harmonic generation（HHG） spectra,driven by the two frequency-comb fields can be coherently controlled via the interference of multiphoton transition paths.It is also found that the spectral intensities of the generated harmonics can be modulated, and the modulation behavior is harmonic-sensitive.

Novel adaptive Hatch filter to mitigate the effects of ionosphere and multipath on LAAS

It has been proven that carrier smoothing and differential global positioning system （DGPS） are effective to improve the accuracy of pseudorange by reducing the noise in it and eliminating almost all the common mode errors between the ground station and user. However, another issue coming with local area augmentation system （LAAS） is how to find an adaptive smoothing window width to minimize the error on account of ionosphere delay and multipath. Based on the errors analysis in carrier smoothing process, a novel algorithm is formulated to design adaptive Hatch filter whose smoothing window width flexibly varies with the characteristic of ionosphere delay and multipath in the differential carrier smoothing process. By conducting the simulation in LAAS and after compared with traditional Hatch filers, it reveals that not only the accuracy of differential correction, but also the accuracy and the robustness of positioning results are significantly improved by using the designed adaptive Hatch filter.

Global modeling 2^(nd)-order ionospheric delay and its effects on GNSS precise positioning

Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution.

Predictive Control of High-Order Fully Actuated Nonlinear Systems with Time-Varying Delays

This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and universal,a novel nonlinear predictive control method is proposed.The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays.At the same time,the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived.Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.

New Stability Criteria for High-Order Neural Networks with Proportional Delays

This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation yi(t) = ui( et)(i = 1, 2,..., n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and timevarying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.

Quasi-4-dimension ionospheric modeling and its application in PPP

Ionospheric delay modeling is not only important for Global Navigation Satellite System(GNSS)based space weather study and monitoring,but also an efficient tool to speed up the convergence time of Precise Point Positioning(PPP).In this study,a novel model,denoted as Quasi-4-Dimension Ionospheric Modeling(Q4DIM)is proposed for wide-area high precision ionospheric delay correction.In Q4DIM,the Line Of Sight(LOS)ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude,but also satellite elevation and azimuth.Both Global Ionosphere Map(GIM)and Slant Ionospheric Delay(SID)models that are traditionally used for wide-area and regional ionospheric delay modeling,respectively,can be regarded as the special cases of Q4DIM by defining proper grids in latitude,longitude,elevation,and azimuth.Thus,Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision.Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network(EPN)stations.The results indicate that Q4DIM is compatible with the GIM products.Moreover,it is proved that by inducting the elevation and azimuth angle dependent residuals,the precision of the 2-dimensional GIM-like model,i.e.,Q4DIM 2-Dimensional(Q4DIM-2D),is improved from around 1.5 Total Electron Content Units(TECU)to better than 0.5 TECU.In addition,treating Q4DIM as a 4-dimensional matrix in latitude,longitude,elevation,and azimuth,whose sparsity is less than 5%,can result in its feasibility in a bandwidth-sensitive applications,e.g.,satellite-based Precising Point Positioning Real-Time Kinematic(PPP-RTK)service.Finally,the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.

Investigating GNSS PPP-RTK with external ionospheric constraints

Real-Time Kinematic Precise Point Positioning(PPP–RTK)is inextricably linked to external ionospheric information.The PPP-RTK performances vary much with the accuracy of ionospheric information,which is derived from diferent network scales,given diferent prior variances,and obtained under diferent disturbed ionospheric conditions.This study investigates the relationships between the PPP–RTK performances,in terms of precision and convergence time,and the accuracy of external ionospheric information.The statistical results show that The Time to First Fix(TTFF)for the PPP-RTK constrained by Global Ionosphere Map(PPP-RTK-GIM)is about 8–10 min,improved by 20%–50%as compared with that for PPP Ambiguity Resolution(PPP-AR)whose TTFF is about 13–16 min.Additionally,the TTFF of PPP-RTK is 4.4 min,5.2 min,and 6.8 min,respectively,when constrained by the external ionospheric information derived from diferent network scales,e.g.small-,medium-,and large-scale networks,respectively.To analyze the infuences of the optimal prior variances of external ionospheric delay on the PPP–RTK results,the errors of 0.5 Total Electron Content Unit(TECU),1 TECU,3 TECU,and 5 TECU are added to the initial ionospheric delays,respectively.The corresponding convergence time of PPP–RTK is less than 1 min,about 3,5,and 6 min,respectively.After adding the errors,the ionospheric information with a small variance leads to a long convergence time and that with a larger variance leads to the same convergence time as that of PPP-AR.Only when an optimal prior variance is determined for the ionospheric delay in PPP-RTK model,the convergence time for PPP-RTK can be shorten greatly.The impact of Travelling Ionospheric Disturbance(TID)on the PPP-RTK performances is further studied with simulation.It is found that the TIDs increase the errors of ionospheric corrections,thus afecting the convergence time,positioning accuracy,and reliability of PPP-RTK.

Effect of temporal variation rate of cross polar cap potential on the equatorial ionospheric vertical drift: A statistical study

Based on the equatorial vertical ion drift measured by DMSP and cross polar cap potential （Фcpc） from AMIE output during 2001 to 2003, this paper investigates the relationship of Фcpc and its temporal variation rate （△Фcpc） with the disturbed ion velocity （△Vx） which is the difference between the disturbed days （Kp〉4） and quiet days （Kp〈2）. The statistical analysis shows： （1） The △Vx correlates better with AФcpc than with Фcpc, indicating that the electric field penetration is more easily to occur when solar wind input rapidly varies with time. （2） The optimal delay time of electric field penetration from the high-latitude magnetosphere to equatorial ionosphere has local time dependence which is longer on the nightside than on the dayside. It may be due to more complicated electrodynamic process on the nightside. （3） With the linear relationship between △Фcpc and △Vx, it is obtained that the penetration efficiency is about 4.5%-13.9% at day and 31%-42% at night, coinciding well with former studies.

Research on Error Analysis and Correction Technique of Atmospheric Refraction for InSAR Measurement with Distributed Satellites

SAR interferometry with distributed satellites is a technique based on the exploitation of the interference pattern of two SAR images acquired synchronously. The interferogram contains geometric, atmospheric, topographic and land defomation. This paper focuses on atmospheric effects on SAR interferometry, which shows theoretically that the relationship among ionosphere TEC and troposphere parameters such as temperature, relative humitdity and pressure with respect to slant rang changes. An atmospheric correction method is given in the end.

A new unequal-weighted triple-frequency first order ionosphere correction algorithm and its application in COMPASS

As the introduction of triple-frequency signals in GNSS,the multi-frequency ionosphere correction technology has been fast developing.References indicate that the triple-frequency second order ionosphere correction is worse than the dual-frequency first order ionosphere correction because of the larger noise amplification factor.On the assumption that the variances of three frequency pseudoranges were equal,other references presented the triple-frequency first order ionosphere correction,which proved worse or better than the dual-frequency first order correction in different situations.In practice,the PN code rate,carrier-to-noise ratio,parameters of DLL and multipath effect of each frequency are not the same,so three frequency pseudorange variances are unequal.Under this consideration,a new unequal-weighted triple-frequency first order ionosphere correction algorithm,which minimizes the variance of the pseudorange ionosphere-free combination,is proposed in this paper.It is found that conventional dual-frequency first-order correction algorithms and the equal-weighted triple-frequency first order correction algorithm are special cases of the new algorithm.A new pseudorange variance estimation method based on the three carrier combination is also introduced.Theoretical analysis shows that the new algorithm is optimal.The experiment with COMPASS G3 satellite observations demonstrates that the ionosphere-free pseudorange combination variance of the new algorithm is smaller than traditional multi-frequency correction algorithms.

Convergence of neutral type proportional-delayed HCNNs with D operators

This paper is concerned with neutral type high-order cellular neural networks(HCNNs)involving proportional delays and D operators.Some criteria are established for the global exponential convergence of the addressed models by using differential inequality techniques.Moreover,an example and its numerical simulations are employed to illustrate the main results.

Crowdsourcing RTK:a new GNSS positioning framework for building spatial high-resolution atmospheric maps based on massive vehicle GNSS data

High-quality spatial atmospheric delay correction information is essential for achieving fast integer ambiguity resolution(AR)in precise positioning.However,traditional real-time precise positioning frameworks(i.e.,NRTK and PPP-RTK)depend on spatial low-resolution atmospheric delay correction through the expensive and sparsely distributed CORS network.This results in limited public appeal.With the mass production of autonomous driving vehicles,more cost-effective and widespread data sources can be explored to create spatial high-resolution atmospheric maps.In this study,we propose a new GNSS positioning framework that relies on dual base stations,massive vehicle GNSS data,and crowdsourced atmospheric delay correction maps(CAM).The map is easily produced and updated by vehicles equipped with GNSS receivers in a crowd-sourced way.Specifically,the map consists of between-station single-differenced ionospheric and tropospheric delays.We introduce the whole framework of CAM initialization for individual vehicles,on-cloud CAM maintenance,and CAM-augmented user-end positioning.The map data are collected and preprocessed in vehicles.Then,the crowdsourced data are uploaded to a cloud server.The massive data from multiple vehicles are merged in the cloud to update the CAM in time.Finally,the CAM will augment the user positioning performance.This framework forms a beneficial cycle where the CAM’s spatial resolution and the user positioning performance mutually improve each other.We validate the performance of the proposed framework in real-world experiments and the applied potency at different spatial scales.We highlight that this framework is a reliable and practical positioning solution that meets the requirements of ubiquitous high-precision positioning.

Basic performance and future developments of BeiDou global navigation satellite system

The core performance elements of global navigation satellite system include availability,continuity,integrity and accuracy,all of which are particularly important for the developing BeiDou global navigation satellite system(BDS-3).This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning,navigation and timing(PNT)service.The precision of the BDS-3 post-processing orbit can reach centimeter level,the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m.The future possible improvements for the BeiDou navigation system are also discussed.It is suggested to increase the orbital inclination of the inclined geostationary orbit(IGSO)satellites to improve the PNT service in the Arctic region.The IGSO satellite can perform part of the geostationary orbit(GEO)satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere(namely the“south wall effect”).The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver.In addition,high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode,and stability of spatial datum.Furthermore,the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy.Finally,to overcome the vulnerability of satellite navigation system,the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

GNSS vulnerabilities:simulation,verification,and mitigation platform design

This paper introduces the design and construction of global navigation satellite systems(GNSS)vulnerability simulation,verification,and mitigation platform.The platform contains five modules:simulation of the signal-in-space environment,simulation of the vulnerabilities in the space segment,signal quality monitoring and data processing,vulnerability assessment and validation,and integrated control.It provides a set of integrated simulations of different types of interference in the GNSS signal propagation domain,including electromagnetic interference,atmospheric disturbances,multipath,and interference in the inter-satellite link.This paper focuses on the design of the main system modules and testing through an experimental analysis.The results demonstrate both the effectiveness and realism of the modules and overall platform.