Slawomir Cellmer

Troposphere modeling for precise GPS rapid static positioning in mountainous areas

In global navigation satellite system precise positioning, double differencing of the observations is the common approach that allows for significant reduction of correlated atmospheric effects. However, with growing distance between the receivers, tropospheric errors decorrelate causing large residual errors affecting the carrier phase ambiguity resolution and positioning quality. This is especially true in the case of height differences between the receivers. In addition, the accuracy achieved by using standard atmosphere models is usually unsatisfactory when the tropospheric conditions at the receiver locations are significantly different from the standard atmosphere. This paper presents an evaluation of three different approaches to troposphere modeling: (a) neglecting the troposphere, (b) using a standard atmosphere model, and (c) estimating tropospheric delays at the reference station network and providing interpolated tropospheric corrections to the user. All these solutions were repeated with various constraints imposed on the tropospheric delays in the least-squares adjustment. The quality of each solution was evaluated by analyzing the residual height errors calculated by comparing the estimated results to the reference coordinates. Several permanent GPS stations of the EUPOS (European Position Determination System) active geodetic network located in the Carpathian Mountains were selected as a test reference network. The distances between the reference stations ranged from 64 to 122 km. KRAW station served as a simulated user receiver located inside the reference network. The user receiver ellipsoidal height is 267 m and the reference station heights range from 277 to 647 m. The results show that regardless of station height differences, it is recommended to model the tropospheric delays at the reference stations and interpolate them to the user receiver location. The most noticeable influence of the residual (unmodeled) tropospheric errors is observed in the station height component. In many cases, mismodeling of the troposphere disrupts ambiguity resolution and, therefore, prevents the user from obtaining an accurate position.

A Graphic Representation of the Necessary Condition for the MAFA Method

The modified ambiguity function approach (MAFA) is one of the integer least square estimation methods. Although it is a simple and efficient method, it has a significant limitation. This limitation is formulated and analyzed in this paper. A graphical representation of the necessary condition for the MAFA method is presented by plots of Voronoi cells and error ellipsoids, along with a detailed procedure for constructing these plots. It is shown that the necessary condition for the MAFA method is not satisfied in some cases. To overcome this problem, a solution is presented in the final section of this paper.

Search procedure for improving modified ambiguity function approach

Abstract The modified ambiguity function approach (MAFA) is a method of GNSS carrier phase data processing. In this method, the functional model of the adjustment problem contains the conditions ensuring the ‘integerness’ of the ambiguities. These conditions are expressed in the form of differentiable function. A prerequisite for obtaining the correct solution is a mechanism ensuring not only the ‘integerness’ of the ambiguities, but also appropriate convergence of the computational process. One of such mechanisms is a cascade adjustment, applying the linear combinations of the L1 and L2 signals with the integer coefficients and various wavelengths. Another method of increasing the efficiency of the MAFA method is based on the application of the integer decorrelation matrix to transform observation equations into equivalent, but better conditioned, observation equations. This paper presents the search procedure as the next technique of improving the MAFA method. This technique together with the decorrelation procedure allows to reduce the number of stages of the cascade adjustment and to obtain correct solution even in the case when a priori position is a few metres away from the actual position. In this paper an example of data processing using the proposed algorithm is given. The results of numerical tests based on real data are presented.

Modified GPS/Pseudolite Navigation Message

One of the issues regarding integrated GPS/pseudolite measurements is how to deliver a pseudolites position to a receiver or to post-processing software and how to manage it. This paper presents a proposed solution to this problem. The standard navigation message is modified in such way that without changing receivers (or post-processing software), the calculated position of a transmitter is fixed at a pseudolites known position. The formulae for modification of standard Ephemeris Data are also derived. This algorithm can be implemented in a transmitters firmware or a navigation data file can be modified for post-processing.

Linearization problem in pseudolite surveys

Abstract GPS augmented with pseudolites (PL), can be used in various engineering surveys. Also pseudolite—only navigation system can be designed and used in any place, even if GPS signal is not available (Kee et al. Development of indoor navigation system using asynchronous pseudolites, 1038–1045, 2000). Especially in engineering surveys, where harsh survey environment is common, pseudolites have a lot of applications. Pseudolites may be used in construction sites, open pit mines, city canyons, GPS and PL baseline processing is similar, although there are few differences that must be taken into account. One of the major issues is linearization problem. The source of the problem is neglecting second terms of Taylor series expansion in GPS baseline processing software. This problem occurs when the pseudolite is relatively close to the receiver, which is the case in PL surveys. In this paper authors presents the algorithm for GPS + PL data processing including, neglected in classical GPS only approach, second terms of Taylor series expansion. The mathematical model of adjustment problem, detailed proposal of application in baseline processing algorithms, and numerical tests are presented.

Validation procedure in the modified ambiguity function approach

Precise coordinates of control points, obtained from GNSS data processing can be utilized in geodynamic research. Periodic surveys allow for determination of displacements. They form a data set for geodynamic interpretation. Of particular importance is permanent monitoring of control points. This mode of measurement requires advanced methods of GNSS data processing. One such method is the Modified Ambiguity Function Approach (MAFA). So far many tests of this method have been performed and the results show it is efficient. It is even possible to obtain a good solution based on GNSS data from a single epoch. In this article, three validation procedures for the MAFA method are proposed. They are based on different principles than the validation methods in classic the approach of precise positioning, in which test statistics are formed from the quadratic forms of residuals associated with the most likely set of integer ambiguities and the second most likely set of integer ambiguities. In the MAFA method the proposed procedures are based on defining the confidence region of the float solution and then testing whether the final solution is included in this region. To test the new validation procedures an experiment was designed and performed. Single epoch solutions for some baselines have been analysed and the results of this research presented in this paper. Finally, some conclusions were drawn based on this analysis. ARTICLE INFO

Some considerations in designing a GPS pseudolite

Some Considerations in Designing a GPS Pseudolite Pseudolites are transmitters of GPS-like signals placed on the ground. Though pseudolites are well known devices and have already been used in the project where visibility to the GNSS satellites is limited, there are still many issues that need enhancement. A prototype of a low-cost pseudolite is being designed and assembled at the University of Warmia and Mazury. This will allow for conducting tests with various codes, signals and software. The goal of the project is to apply the pseudolite as an augmentation to GNSS positioning tasks in geodetic engineering projects. Some practical considerations crucial for the design are discussed in this paper.

Pseudolite signal tests

ABSTRACT Pseudolites are ground based GNSS signal transmitters that have already been used in the project where visibility to the GNSS satellites is limited, however there are still many issues that need enhancement. A prototype of a low-cost pseudolite is being designed and assembled at the University of Warmia and Mazury. The goal of the project is to apply the pseudolite as an augmentation to GNSS positioning tasks in geodetic engineering projects. This paper presents the results of first prototype testing in the area of code generation, carrier frequency and signal power.

Mixed integer–real least squares estimation for precise GNSS positioning using a modified ambiguity function approach

AbstractMixed integer–real least squares (MIRLS) estimation still has two open scientific problems, i.e., the validation of results and computational efficiency for a large number of satellites. This paper presents and discusses a non-conventional approach to MIRLS estimation, which belongs to the ambiguity function method (AFM) class. Because the solution is searched for in the constant three-dimensional coordinate domain instead of the n-dimensional ambiguity domain, the computational efficiency does not depend as much on the number of satellites as it does in conventional MIRLS estimation. Simple numerical pretests have shown that the reliability and precision of results from the presented approach and the conventional MIRLS estimation are exactly the same. Hence, the presented approach, contrary to AFM, may be treated as MIRLS estimation. Furthermore, the presented approach is a few hundred times faster than AFM and may be considered in (near) real-time GNSS positioning. In light of the above, the new field of research on MIRLS estimation may be opened.

New Approach to Arc Fitting for Railway Track Realignment

This article presents a new method of arc fitting for railway track realignment. The theoretical foundations are presented, along with a detailed algorithm of the iterative computational process. This method is based on solving a set of linearized pseudo-observation equations. The formulas of the functional model of the fitting problem were derived, and a special form of objective function is proposed. An iterative method for optimization of objective functions is described, and an analysis of the functional model is presented. Specific conclusions are presented based on the results of this analysis.