This contribution reviews a few basic concepts of optimization and design of a geodetic network. Proper assessment and analysis of networks is an important task in many geodetic-surveying projects. Appropriate quality-control measures should be defined, and an optimal design should be sought. The quality of a geodetic network is characterized by precision, reliability, and cost. The aim is to present a few case studies that have been designed to meet optimal precision and reliability criteria. Though the case studies may be of interest to the geodetic community in their own right, the aim is to gain insight into the general optimization problem of a geodetic network. This is also potentially of interest for educational purposes. The case studies include a zeroth-order design to improve the precision of the network points in a traverse network and a first-order design to meet the high reliability and maximum precision criteria in a geodetic network. It is shown that not only the configuration of th...

To achieve the best linear unbiased estimation of unknown parameters in geodetic data processing a realistic stochastic model for observables is required. This work is a follow-up to work carried out recently in which the geometry-free observation model (GFOM) was used. Here, least-squares variance component estimation is applied to global positioning system (GPS) observables using the geometry-based observation model (GBOM). The benefit of using GBOM, rather than GFOM, is highlighted in the present contribution. An appropriate stochastic model for GPS observables should include different variances for each observation type, the correlation between different observables, the satellite elevation dependence of the observables’ precision, and the temporal correlation of the GPS observables. Unlike the GFOM, in the GBOM two separate variances along with their corresponding covariances are simultaneously estimated for the phase observations of the L1 and L2 frequencies. The numerical results for two re...

In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of ω _i = 2πi are modulated with the annual signal harmonics of ω _j = 2πj/365.25 as ω _ijM = 2πi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.