Guochang Xu

GNSS navigation and positioning for the GEOHALO experiment in Italy

Abstract GEOHALO is a joint experiment of several German institutes for atmospheric research and earth observation where exploring airborne gravimetry over Italy using the High Altitude and LOng Range (HALO) aircraft data is one of the major goals. The kinematic positioning of the aircraft, on which all remote sensing instruments are located, by Global Navigation Satellite System (GNSS) is affected by the characteristics of long-distance, long-time duration, and high-platform dynamics which are a key factor for the success of the GEOHALO project. We outline the strategy and method of GNSS data processing which takes into account multiple GNSS systems (GPS and GLONASS), multiple static reference stations including stations from the International GNSS Service (IGS) and the EUropean REFerence network (EUREF), multiple GNSS-receiving equipments mounted on the kinematic platform, geometric relations between multiple antennas, and assumptions of similar characteristic of atmospheric effects within a small area above the aircraft. From this precondition, various data processing methods for kinematic positioning have been developed, applied and compared. It is shown that the proposed method based on multiple reference stations and multiple kinematic stations with a common atmospheric delay parameter can effectively improve the reliability and accuracy of GNSS kinematic positioning.

Applications of GPS Theory and Algorithms

In this chapter, we discuss software development using GPS theory and algorithms, and present a concept of precise kinematic positioning and flight-state monitoring of an airborne remote sensing system.

Regularization and Adjustment

The linear observation equation is usually expressed as

Cycle Slip Detection and Ambiguity Resolution

{\user2{l}} = {\user2{Ax}} + {\user2{e}}

Analytic Orbit Theory

(6.1) where the non-random design matrix \( {\user2{A}} \in R^{m \times n} , \) the vector of unknown parameters \( {\user2{x}} \in R^{n \times 1} , \) the vector of measurements \( {\user2{l}} \in R^{m \times 1} \)and contaminated by random error vector \( {\user2{e}} \) with zero mean and variance–covariance matrix \( \sigma_{0}^{2} {\user2{P}}^{ - 1} , \) where P is the weight matrix and \( \sigma_{0}^{2} \) is the variance of unit weight. If the coefficient matrix A of the observation equation possesses very large condition number, the observation equation is ill-conditioned, which is defined as ill-posed problems by Hadamard (1932). In geodesy ill-posed problems are frequently encountered in satellite gravimetry due to downward continuation, or in geodetic date procession due to the colinearity among parameters that are to be estimated. Most useful and necessary adjustment algorithms for data processing are outlined in the second part of this chapter. The adjustment algorithms discussed here include least squares adjustment, sequential application of least squares adjustment via accumulation, sequential least squares adjustment, conditional least squares adjustment, a sequential application of conditional least squares adjustment, block-wise least squares adjustment, a sequential application of block-wise least squares adjustment, a special application of block-wise least squares adjustment for code-phase combination, an equivalent algorithm to form the eliminated observation equation system and the algorithm to diagonalize the normal equation and equivalent observation equation. A priori constrained adjustment and filtering are discussed for solving the rank deficient problems. After a general discussion on the a priori parameter constraints, a special case of the so-called a priori datum method is given. A quasi-stable datum method is also discussed. A summary is given at the end of this part of the chapter.

Physical Influences of GPS Surveying

After a brief discussion on the dynamic and geometric orbit determinations, the observation model, dynamic model and Kalman filter for a geostationary (GEO) satellite orbit determination are introduced. A robustly adaptive Kalman filter based on variance component estimation is proposed for orbit determination of a maneuvered GEO satellite. The main idea is to use robust estimation to resist the influence of measurement outliers and use an adaptive factor to control the effect of dynamic model errors. Simulations with the Chinese ground tracking network for a maneuvered GEO satellite were conducted to verify the performance of the proposed orbit determination technique. The results show that it can efficiently control both the influence of outliers and that of thrust force, and can provide high and reliable orbit accuracy.

Singularity-Free Orbit Theory

Ambiguity problems can arise during phase measurement when the receiver loses its lock on the signal, and phase measurement must be reinitiated. This phenomenon is called cycle slip, i.e. the cycle count must begin again because of a signal interruption. The consequence of a cycle slip is an observable jump by an integer number of cycles in the adjacent carrier phase, and a new ambiguity parameter is required in the related observation model. Accurate cycle slip detection thus ensures correct ambiguity parameterisation. Here, we begin with a discussion of cycle slip detection, after which we will focus on integer ambiguity resolution, including integer ambiguity search criteria. We also provide an outline and discussion of the historical ambiguity function method.

Parameterisation and Algorithms of GPS Data Processing

The airborne kinematic GNSS positioning in the Antarctic region has different characteristics with those in the internal continent. Comparing with the Asian internal continent (e.g. Wuhan), more satellites are visible so that lower PDOP of the polar regional GNSS positioning can be achieved. The PDOP in the polar region may reduce 22% compared with that of Wuhan. However, the VDOP in the polar region is weaker because of lacking of satellites with high elevation angles. On that basis, the significance of the Beidou Compass system for the Antarctic survey is quantitatively studied. The simulation result shows, comparing with using a single navigation system, that using Compass and GPS combined system may raise the positioning precision up to 43% (in case of the elevation cut-off angle is 15°). Finally, the Antarctic GPS data are processed in different ways and the internal and external precisions are analyzed. Results show that the kinematic GNSS positioning can obtain a precision of cm by using precise point positioning technology.