Journal of Surveying Engineering

Astronomical positioning and orientation are important components of astronomical geodesy tasks, and they could also be used for real-time celestial navigation. In traditional methods, astronomical positioning and astronomical orientation can only be implemented separately, and all the observations with different levels of precision are given the same weight. To change this, a unified astronomical positioning and orientation model based on robust estimation was developed. First, the problem that the coordinate rotation parameters are difficult to calculate directly was solved by using the Rodrigues matrix. Consequently, the astronomical longitude, latitude, and azimuth can be calculated at the same time. Second, as a result of the introduction of a robust estimation method, specific weight is matched to observations with corresponding precision when calculating the parameters, and thus more accurate astronomical longitude, latitude, and azimuth valuation can be calculated simultaneously. Experiments indicate that the unified model was able not only to achieve astronomical positioning and orientation simultaneously but also improve the accuracy of final results.

In a series of papers in this journal, polynomial solutions of transition curves are introduced for road design, constructed as graphs of polynomial functions. These curves admit a simple expression in nonparametric Bézier form, which facilitates their implementation into commercial software and data exchange. Furthermore, in this Bézier representation, few compact formulas describe all possible cases, and the boundary conditions defining the curves translate into intuitive geometric arrangements of the control points. This is illustrated with several examples, including cases where, at the endpoints, zero curvature and smoothness of the curvature diagram are required. The authors also consider an alternative using a nonparametric B-spline curve of lower degree, but at the cost of a more complex model. Quartic splines, at a minimum, are required to ensure a continuous change of lateral acceleration along the transition.

Pseudorange multipath and noise are still considered the major sources of error in precise point positioning (PPP) solutions. If multipath and noise were correctly mitigated from the pseudoranges, the accurate estimation of float ambiguities could be achieved rapidly; thus, a reduction in PPP convergence time would be realized. In this study, three different methods were used: (1) the known multipath linear combination using the postprocessed (PP) average; (2) the multipath linear combination with the moving average by translation, editing, and quality check (TEQC) software; and (3) the modified stochastic modeling or weights based on the multipath linear combination. TEQC software is one of the most famous tools used to solve the preprocessing problems for global navigation satellite system (GNSS) data. TEQC software was used to provide multipath corrections according to a multipath linear combination that depends on the moving average algorithm for a seven-day data set from 75 international global positioning system service stations. The improvements were computed by comparing the proposed methods with the traditional PPP solution for which all pseudorange measurements are equally weighted. The results of this study indicate that the improvements of the convergence time were achieved for 32 and 41.5% of the data set using the postprocessed multipath linear combination and the modified weighting scheme derived from a TEQC multipath linear combination, respectively. Also, the results indicate that only the traditional PPP enhanced by the TEQC multipath linear combination and the traditional PPP have the same convergence performances.

The real-time kinematic precise point positioning (PPP-RTK) technique enables integer ambiguity resolution by providing single-receiver users with information on the satellite phase biases next to the standard PPP corrections. Using undifferenced and uncombined observations, rank deficiencies existing in the design matrix need to be eliminated to form estimable parameters. In this contribution, the estimability of the parameters was studied in single-frequency ionosphere-weighted scenario, given a dynamic satellite-clock model in the network Kalman filter. In case of latency of the network corrections, the estimable satellite clocks, satellite phase biases, and ionospheric delays need to be predicted over short time spans. With and without satellite-clock models incorporated in the network Kalman filter, different approaches were used to predict the network corrections. This contribution shows how the predicted network corrections responded to the presence and absence of satellite-clock models. These differences in the predicted network corrections were also reflected in the user positioning results. Using three different 1-Hz global positioning system (GPS) single-frequency data sets, two user stations in one small-scale network were used to compute the positioning results, applying predicted network corrections. The latency of the network products ranges from 3 to 10 s. It was observed that applying strong satellite-clock constraints in the network Kalman filter (i.e., with the process noise of 1 or 0.5 mm per square root of second) reduced the root-mean squares (RMS) of the user positioning results to centimeters in the horizontal directions and decimeters in the vertical direction for latencies larger than 6 s, compared to the cases without a satellite-clock model.

Real-time networks (RTNs) have become popular for global navigation satellite system (GNSS) surveys because highly accurate positions can be derived in seconds to a few minutes compared with the many minutes and hours required with postprocessed static sessions. To evaluate the accuracy of these shorter-duration RTN GNSS observations and their potential for use as a source for establishing geodetic control, data collected from two National Geodetic Survey (NGS) surveys in South Carolina and Oregon were studied in detail. This article explores the horizontal and vertical accuracy of real-time observations as a function of observation duration, examines the influence of the inclusion of Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS) observables, compares results from real-time kinematic (RTK) positioning using a single base station versus a network of base stations, and assesses the effect of baseline length on accuracy. Thirty-eight passive marks were repeatedly observed with GNSS using a RTN in the two study areas for a variety of different observation times, ranging from 5 s to 15 min. An optimal real-time observation duration was found in the range of 180 to 300 s. The real-time data acquired using a network of base stations tended to be more accurate and precise than single-base RTK data, especially vertically. Further, the addition of GLONASS observables helped obtain more fixed solutions at longer baseline lengths than solutions based solely on global positioning system (GPS) observables and showed a slight improvement in accuracy, particularly for stations with poorer satellite visibility.

This technical note presents alternative derivations for the weighted total least-squares (WTLS) problem subject to weighted and hard constraints. The derivations do not take into account the Lagrange multipliers, and the final results are shown to be identical to those presented by a recently published article in the same journal. The final WTLS estimates are formulated by the standard least-squares theory. The method, which is formulated using the Gauss–Newton method, provides an alternative to the Newton method. The formulation is generally presented for the weighted linear(ized) constraints. As a by-product, hard constraints turn out to be a special case of the general formulation of the weighted constraints. An alternative derivation is presented for the WTLS problem subjected only to hard constraints. For this purpose, the parametric representation of the hard constraints is used, the general solution of which is obtained as the sum of a particular solution and the homogeneous solution. As a special case, the WTLS formulation (without the constraints) can also directly be followed.