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In this paper, the problems of three carrier phase ambiguity resolution (TCAR) and position estimation (PE) are generalised 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, generalised 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.

The L1/E1 band will soon be populated with four different signals, namely the GPS L1 CA code, L1C code, Galileo E1B code and E1C code. The frequency domain receiver, which can provide parallel correlation and process all the signals in a common structure, becomes a promising solution for multi-code and multi-modulation processing. However, the conventional frequency domain receivers require quite high computational capacity to perform the FFT and IFFT operations, especially when the receivers operate at a high sampling rate. The high computational complexity would exert a negative effect on the size, power consumption, and cost of the receiver.To reduce the computational complexities of the frequency domain receiver, a new correlation method with signal down sampling in the frequency domain is proposed in this paper. The down sampling is achieved by pruning the high frequency parts of the signal spectrum and then performing IFFT in a smaller size. The correlation gain loss will be small because the pruned spectrums contain little energy. The results show that the correlation gain losses of BPSK (1) and BOC (1,1) are less than 0.4dB with a sampling rate of 16.384MHz, while the operations in the IFFTs can be reduced to 40% of the conventional method with original sampling rate of 40MHz. And because the IFFTs are the most computationally consuming parts in the frequency domain receiver, the new method can significantly reduce the computational load by reducing the IFFT size.In addition, because the closed code delay tracking loop cannot be applied in the frequency domain receivers directly, a correlation interpolation method, which can produce the EPL correlation as in the time domain receiver, is then usually applied in the existing frequency domain receivers. But the interpolation method will lead to extra operations. In this paper, a novel open loop code delay estimation method without correlation interpolation is also proposed. The method first obtains the integer parts of the code delay by the correlation peak detection, then gets the residual errors by code delay discrimination and finally obtains the precise estimation by post filtering. The results indicate that this new method not only reduces the complexity, but also improves the tracking sensitivity comparing to the conventional closed tracking loops.

The ever-increasing demand on GPS to perform in challenging environments is the main motivation behind this research. With the existence of these challenging environments, more research is directed towards enhancing the tracking capabilities. Several solutions have been proposed to enable high sensitivity tracking using only one signal. However, new GPS signals are now available, in addition to the conventional L1 signal. Being transmitted from the same space vehicle through the same environment, the errors between these signals are correlated. Hence, an increase in tracking sensitivity can be achieved by combining two or more of these signals. This paper proposes the idea of combining the L1 and L5 signals using one Kalman filter, where the correlator outputs of the two signals are used to estimate the tracking errors. The performance of this combined Kalman filter is compared to a similar Kalman filter that is used separately for tracking each of the two signals. The performance of both filters is compared in environments suffering urban canyon multipath, moderate ionospheric errors, in addition to a motion model of a typical vehicle. The combined Kalman filter is shown to outperform the separate Kalman filter, both in the tracking errors and in the filter statistics.

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.

In the past years, several regional error models for the network RTK (NRTK) approach have been proposed, investigated and used. Most of the studies are based on one single model to test the model’s performance in a reference network or a few reference networks. Very limited research has been conducted to evaluate performance differences of different error models in the same network using the same test dataset. It is difficulty to predict which of the models will outperform the others for a specific network since different reference networks have different error characteristics. For example, the multipath effect (or the station specific error), the spatial atmospheric pattern, and the scale of the ionospheric disturbance may be different in different networks. These factors may cause differences in performance among different error models.Among the existing error models for NRTK, the linear interpolation model (LIM) and the low-order surface model (LSM) are typical and most often discussed/used. In this paper, the difference in the accuracies of the interpolated residuals in GPSnet from the two models are compared using several test cases with three different observation sessions combined with various network configurations. The snapshots of the fitting surface planes derived from the two models at the same epochs are also compared as well. Test results indicate that the LSM in some cases performed significantly poorer than the LIM. In this case, the snapshots of the two fitting surface planes from the two models present the error’s correlation trend significantly different.

Ionospheric conditions for South American low- and mid-latitude scenarios are simulated. The performance of an ionospheric correction algorithm on positioning is analysed for this region. This correction is of similar nature to the Satellite Based Augmentation System (SBAS) type algorithm. The mismodelling produced by each ionospheric simulated approximation can be separately quantified: 1) the single layer shell representation of the ionosphere and 2) the simple geometric mapping function. The effects of both components on positioning are evaluated and discussed for periods with different levels of ionospheric activity: winter, summer, and austral spring equinox. The results show that the mapping function is the most important contributor to the ionospheric error. Its effect on the height component is the most important. Besides, on north and east components, the principal error contributor is the Vertical Total Electron Content (VTEC) mismodelling. The application was also tested on real data during a spring equinox of a mid-low solar activity year (2005) and the results are similar and coherent with those obtained using simulated data.

Due to their fast operation, Fast Fourier Transform (FFT)-based coarse signal synchronization methods are an attractive option for Global Navigation Satellite System (GNSS) receiver baseband signal processing. However, there are several reasons why the utility of FFT-based methods is dependent on understanding the trade-off between synchronization speed and the required processing power. Firstly, the new signals of the GNSS family, for instance Galileo and GPS modernization, employ longer period Pseudo Random Noise (PRN) codes and higher signal bandwidths, which demand FFTs of large transform lengths. Secondly, to gain an advantage in positioning performance, next generation receivers target multiple GNSS signals, and since each signal has its own code length (and hence a minimum sampling frequency), the receiver should accommodate FFT blocks of varying lengths. This paper discusses the requirements of FFT-based algorithms for such a multi-band receiver and analyzes the application of prime-factor and mixed-radix FFT algorithms. A novel way of factorizing different transform lengths into smaller transforms and then combining these smaller-point FFTs to compute the larger required FFTs is described. It is shown that the use of the proposed architecture reduces the computational load (or processor cycles) and increases the re-usability of the acquisition search engine to process different signals.

Discussed in this paper are the sigma point-based filter and smoother for a generic discrete-time nonlinear system model. The sigma-point filter is treated as an approximation of the generic nonlinear Kalman filter equations, which extends the chapter on nonlinear Kalman filter theory in Gelb (1974). The implementation of the square-root sigma-point filter is addressed in detail with the necessary numerical tools so that it can easily be used for practical use. The Rauch-Tung-Striebel (RTS) formulation of the sigma-point smoother is derived by combining the statistical linear regression and the optimization criteria given in Rauch et al. (1965). The notes can be used as a supplementary reading material in an introductory nonlinear estimationcourse.