Three Carrier Ambiguity Resolutions : Generalised problems, models and solutions

In this paper, the problems of three carrier phase ambiguity resolution (TCAR) and position estimation (PE) are generalized as real time GNSS data processing problems for a continuously observing network on large scale. In order to describe these problems, a general linear equation system is presented to uniform various geometry-free, geometry-based and geometry-constrained TCAR models, along with state transition questions between observation times. With this general formulation, generalized TCAR solutions are given to cover different real time GNSS data processing scenarios, and various simplified integer solutions, such as geometry-free rounding and geometry-based LAMBDA solutions with single and multiple-epoch measurements. In fact, various ambiguity resolution (AR) solutions differ in the floating ambiguity estimation and integer ambiguity search processes, but their theoretical equivalence remains under the same observational systems models and statistical assumptions. TCAR performance benefits as outlined from the data analyses in some recent literatures are reviewed, showing profound implications for the future GNSS development from both technology and application perspectives.

Achieving high reliability for ambiguity resolutions with multiple GNSS constellations

Global Navigation Satellite Systems (GNSS)-based observation systems can provide high precision positioning and navigation solutions in real time, in the order of subcentimetre if we make use of carrier phase measurements in the differential mode and deal with all the bias and noise terms well. However, these carrier phase measurements are ambiguous due to unknown, integer numbers of cycles. One key challenge in the differential carrier phase mode is to fix the integer ambiguities correctly. On the other hand, in the safety of life or liability-critical applications, such as for vehicle safety positioning and aviation, not only is high accuracy required, but also the reliability requirement is important. This PhD research studies to achieve high reliability for ambiguity resolution (AR) in a multi-GNSS environment. GNSS ambiguity estimation and validation problems are the focus of the research effort. Particularly, we study the case of multiple constellations that include initial to full operations of foreseeable Galileo, GLONASS and Compass and QZSS navigation systems from next few years to the end of the decade. Since real observation data is only available from GPS and GLONASS systems, the simulation method named Virtual Galileo Constellation (VGC) is applied to generate observational data from another constellation in the data analysis. In addition, both full ambiguity resolution (FAR) and partial ambiguity resolution (PAR) algorithms are used in processing single and dual constellation data. Firstly, a brief overview of related work on AR methods and reliability theory is given. Next, a modified inverse integer Cholesky decorrelation method and its performance on AR are presented. Subsequently, a new measure of decorrelation performance called orthogonality defect is introduced and compared with other measures. Furthermore, a new AR scheme considering the ambiguity validation requirement in the control of the search space size is proposed to improve the search efficiency. With respect to the reliability of AR, we also discuss the computation of the ambiguity success rate (ASR) and confirm that the success rate computed with the integer bootstrapping method is quite a sharp approximation to the actual integer least-squares (ILS) method success rate. The advantages of multi-GNSS constellations are examined in terms of the PAR technique involving the predefined ASR. Finally, a novel satellite selection algorithm for reliable ambiguity resolution called SARA is developed. In summary, the study demonstrats that when the ASR is close to one, the reliability of AR can be guaranteed and the ambiguity validation is effective. The work then focuses on new strategies to improve the ASR, including a partial ambiguity resolution procedure with a predefined success rate and a novel satellite selection strategy with a high success rate. The proposed strategies bring significant benefits of multi-GNSS signals to real-time high precision and high reliability positioning services.

Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines

Carrier phase ambiguity resolution over long baselines is challenging in BDS data processing. This is partially due to the variations of the hardware biases in BDS code signals and its dependence on elevation angles. We present an assessment of satellite-induced code bias variations in BDS triple-frequency signals and the ambiguity resolutions procedures involving both geometry-free and geometry-based models. First, since the elevation of a GEO satellite remains unchanged, we propose to model the single-differenced fractional cycle bias with widespread ground stations. Second, the effects of code bias variations induced by GEO, IGSO and MEO satellites on ambiguity resolution of extra-wide-lane, wide-lane and narrow-lane combinations are analyzed. Third, together with the IGSO and MEO code bias variations models, the effects of code bias variations on ambiguity resolution are examined using 30-day data collected over the baselines ranging from 500 to 2600 km in 2014. The results suggest that although the effect of code bias variations on the extra-wide-lane integer solution is almost ignorable due to its long wavelength, the wide-lane integer solutions are rather sensitive to the code bias variations. Wide-lane ambiguity resolution success rates are evidently improved when code bias variations are corrected. However, the improvement of narrow-lane ambiguity resolution is not obvious since it is based on geometry-based model and there is only an indirect impact on the narrow-lane ambiguity solutions.

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.

Real-time kinematic positioning over long baselines using triple-frequency BeiDou signals

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the rea- -time kinematic solutions are improved to centimeter level for all three coordinate components.

Extended GNSS ambiguity resolution models with regularization criterion and constraints

This paper firstly presents an extended ambiguity resolution model that deals with an ill-posed problem and constraints among the estimated parameters. In the extended model, the regularization criterion is used instead of the traditional least squares in order to estimate the float ambiguities better. The existing models can be derived from the general model. Secondly, the paper examines the existing ambiguity searching methods from four aspects: exclusion of nuisance integer candidates based on the available integer constraints; integer rounding; integer bootstrapping and integer least squares estimations. Finally, this paper systematically addresses the similarities and differences between the generalized TCAR and decorrelation methods from both theoretical and practical aspects.

Short-termism : challenges and resolutions

The global financial crisis has highlighted the vulnerability of our economy to systemic risks. While its causes are numerous and relate to complex problems deeply embedded in capital markets, ‘short-termism’ (excessive focus on short-term outcomes at the expense of long-term wealth creation and sustainability) has frequently been flagged as a major contributor to this crisis. Although short-termism is not new, the global financial crisis has highlighted the presence of short-termism among institutional investors, and the failure of global markets and regulators to deal with such perverse and destructive behaviour (Guyatt 2009). Solutions are clearly needed. Although there is a body of research that provides evidence of the presence of short-termism in capital markets and the consequences of short-term decision-making on the financial wellbeing of both individuals and organisations, there is no consensus on mitigating solutions to short-termism. What emerges from the literature is the need to take a broad interdisciplinary perspective in seeking solutions to the problem.

Effect of representation size and visual ambiguity on RatSLAM system performance

RatSLAM is a vision-based SLAM system based on extended models of the rodent hippocampus. RatSLAM creates environment representations that can be processed by the experience mapping algorithm to produce maps suitable for goal recall. The experience mapping algorithm also allows RatSLAM to map environments many times larger than could be achieved with a one to one correspondence between the map and environment, by reusing the RatSLAM maps to represent multiple sections of the environment. This paper describes experiments investigating the effects of the environment-representation size ratio and visual ambiguity on mapping and goal navigation performance. The experiments demonstrate that system performance is weakly dependent on either parameter in isolation, but strongly dependent on their joint values.

A Modified inverse integer Cholesky decorrelation method and the performance on ambiguity resolution

One of the research focuses in the integer least squares problem is the decorrelation technique to reduce the number of integer parameter search candidates and improve the efficiency of the integer parameter search method. It remains as a challenging issue for determining carrier phase ambiguities and plays a critical role in the future of GNSS high precise positioning area. Currently, there are three main decorrelation techniques being employed: the integer Gaussian decorrelation, the Lenstra–Lenstra–Lovász (LLL) algorithm and the inverse integer Cholesky decorrelation (IICD) method. Although the performance of these three state-of-the-art methods have been proved and demonstrated, there is still a potential for further improvements. To measure the performance of decorrelation techniques, the condition number is usually used as the criterion. Additionally, the number of grid points in the search space can be directly utilized as a performance measure as it denotes the size of search space. However, a smaller initial volume of the search ellipsoid does not always represent a smaller number of candidates. This research has proposed a modified inverse integer Cholesky decorrelation (MIICD) method which improves the decorrelation performance over the other three techniques. The decorrelation performance of these methods was evaluated based on the condition number of the decorrelation matrix, the number of search candidates and the initial volume of search space. Additionally, the success rate of decorrelated ambiguities was calculated for all different methods to investigate the performance of ambiguity validation. The performance of different decorrelation methods was tested and compared using both simulation and real data. The simulation experiment scenarios employ the isotropic probabilistic model using a predetermined eigenvalue and without any geometry or weighting system constraints. MIICD method outperformed other three methods with conditioning improvements over LAMBDA method by 78.33% and 81.67% without and with eigenvalue constraint respectively. The real data experiment scenarios involve both the single constellation system case and dual constellations system case. Experimental results demonstrate that by comparing with LAMBDA, MIICD method can significantly improve the efficiency of reducing the condition number by 78.65% and 97.78% in the case of single constellation and dual constellations respectively. It also shows improvements in the number of search candidate points by 98.92% and 100% in single constellation case and dual constellations case.