Contribution of ionospheric irregularities to the error of dual-frequency GNSS positioning

This paper investigates the third-order residual range error in the dual-frequency correction of ionospheric effects on satellite navigation. We solve the two-point trajectory problem using the perturbation method to derive second-approximation formulas for the phase path of the wave propagating through an inhomogeneous ionosphere. It is shown that these formulas are consistent with the results derived from applying perturbation theory directly to the eikonal equation. The resulting expression for the phase path is used in calculating the residual range error of dual-frequency global positioning system (GPS) observations, in view of second- and third-order terms. The third-order correction includes not only the quadratic correction of the refractive index but also the correction for ray bending in an inhomogeneous ionosphere. Our calculations took into consideration that the ionosphere has regular large-scale irregularities, as well as smaller-scale random irregularities. Numerical examples show that geomagnetic field effects, which constitute a second-order correction, typically exceed the effects of the quadratic correction and the regular ionospheric inhomogeneity. The contribution from random irregularities can compare with or exceed that made by the second-order correction. Therefore, random ionospheric irregularities can make a significant (sometimes dominant) contribution to the residual range error.     

Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.     

Geomagnetic field effect on the ionospheric contribution to the error of navigation satellite systems

When using global navigation satellite systems (GNSSs) for high-precision measurements, one should consider high-order errors. The ionospheric second-order error caused by the geomagnetic field is approximately proportional to the total electron content. Therefore, this error can be taken into account by modifying the coefficients in an “ionosphere-free” combination of GNSS measurements at two frequencies. This study checks the approximations underlying this modification. We reveal that these approximations are valid and the results depend weakly on the accuracy of ionospheric parameters used a priori for calculating the coefficients of the modified two-frequency formula. In addition, we investigate how the choice of a model of the Earth’s magnetic field affects the second-order ionospheric error.     

Comments on “Effects of Strong Regular Refraction in the Solar Radio Pulse Structure in Spike Events” by Afanasiev and Altyntsev and “Mathematical Modeling of the Formation of Type IIId Solar Decameter Radio Bursts with Echo Components” by Afanasiev

Presented are some comments on the papers by Afanasiev and Altyntsev (Solar Phys. 234, 151, 2006) and by Afanasiev (Solar Phys. 238, 87, 2006) devoted to the study of the influence of solar corona inhomogeneities on the form of radio bursts. It is pointed out that in these papers incorrect use is made of methods used previously in investigations into radio wave propagation through a randomly inhomogeneous ionosphere.     

Diagnosing the effective parameters of the ionospheric fine structure from statistical characteristics of radio waves in the vicinity of a regular caustic

This paper is concerned with the oblique propagation of decametric radio waves in the ionosphere with random electron density irregularities. Effective parameters are introduced for calculating the influence of irregularities on the wave field structure. A technique is proposed for determining these parameters from measurements of statistical characteristics of the signal in the vicinity of a regular caustic. The technique uses asymptotic expressions obtained using the interference integral method and perturbation theory, as well as matching them to the numerical solution on the basis of the method of characteristics. A global semi-empirical model that is updated for current ionospheric conditions is used to specify the background medium. The proposed technique has been tested using data from a number of mid-latitude paths. Results obtained in this study testify that the technique deserves a practical implementation.     

Effect of Anisotropy of Ionospheric Inhomogeneities in the Detection of Faults in Phase GNSS Measurements

Geomagnetism and Aeronomy - Phase and amplitude fluctuations (scintillations) are recorded when a signal of the global navigation satellite system (GNSS) passes through the anisotropic, randomly...     

Effect of ionospheric irregularities on accuracy of dual-frequency GPS systems

The residual error of the ionospheric correction of signals from dual frequency GPS systems, related to a ray deviation in random ionospheric irregularities, is studied. The formulas taking into account ray deviation from a straight line in an inhomogeneous ionosphere have been obtained based on the disturbance theory when solving the ray equations. These formulas have been used to estimate the extreme accuracy of a dual frequency GPS method. The algorithm for correcting this ionospheric error of the second order using three-frequency reception has been proposed.     

The association of the residual error of dual-frequency Global Navigation Satellite Systems with ionospheric turbulence parameters

The effects of ionospheric scintillation on the residual error of the dual-frequency Global Navigation Satellite System are investigated. For the ordinary and extraordinary waves the scalar wave equations are obtained to a high-frequency approximation from the Maxwell equations. The solution for these scalar equations to the second-order Rytov approximation made it possible to determine the residual error up to the third order taking into account the ionospheric anisotropy and diffraction effects appearing when the signal is propagating through a turbulent ionospheric plasma. It is shown that the third-order effects, associated with scintillation, that is, with the propagation of the signal through a randomly inhomogeneous ionosphere, can be dominant and exceed second-order effects associated with the influence of the geomagnetic field. We investigate the association of the residual error with such parameters of ionospheric turbulence as the variance, and the inner and outer scales.