Phase Ambiguity Estimation Research Articles

Precise point positioning with GPS and Galileo broadcast ephemerides

For more than 20 years, precise point positioning (PPP) has been a well-established technique for carrier phase-based navigation. Traditionally, it relies on precise orbit and clock products to achieve accuracies in the order of centimeters. With the modernization of legacy GNSS constellations and the introduction of new systems such as Galileo, a continued reduction in the signal-in-space range error (SISRE) can be observed. Supported by this fact, we analyze the feasibility and performance of PPP with broadcast ephemerides and observations of Galileo and GPS. Two different functional models for compensation of SISREs are assessed: process noise in the ambiguity states and the explicit estimation of a SISRE state for each channel. Tests performed with permanent reference stations show that the position can be estimated in kinematic conditions with an average three-dimensional (3D) root mean square (RMS) error of 29 cm for Galileo and 63 cm for GPS. Dual-constellation solutions can further improve the accuracy to 25 cm. Compared to standard algorithms without SISRE compensation, the proposed PPP approaches offer a 40% performance improvement for Galileo and 70% for GPS when working with broadcast ephemerides. An additional test with observations taken on a boat ride yielded 3D RMS accuracy of 39 cm for Galileo, 41 cm for GPS, and 27 cm for dual-constellation processing compared to a real-time kinematic reference solution. Compared to the use of process noise in the phase ambiguity estimation, the explicit estimation of SISRE states yields a slightly improved robustness and accuracy at the expense of increased algorithmic complexity. Overall, the test results demonstrate that the application of broadcast ephemerides in a PPP model is feasible with modern GNSS constellations and able to reach accuracies in the order of few decimeters when using proper SISRE compensation techniques.

A New Method of Integer Parameter Estimation in Linear Models With Applications to GNSS High Precision Positioning

The high precision positioning of global navigation satellite systems (GNSS), which essentially corresponds to solving the integer least-squares (ILS) problem in the integer phase ambiguity estimation, has emerged as a key problem for the development of industrial internet-of-things (IIoT). In this paper, a novel paradigm for solving the ILS problem is introduced to the integer phase ambiguity estimation. Different from the traditional paradigm of ILS which only involves one parameter to characterize the trade-off between performance and complexity, the proposed ILS paradigm entails two parameters named as the initial searching size K ≥ 1 and the standard deviation σ > 0, thus introducing extra degrees of freedom to facilitate the system trade-off. Based on it, explicit analysis can be carried out for a mathematically tractable trade-off, where great potentials could be further exploited for the high precision positioning of GNSS. The equivalent searching algorithm (ESA) is proposed, which achieves the same performance as the classic Fincke-Pohst strategy in sphere decoding (SD) but with tractable complexity measured by the number of visited nodes in the searching stage. Moreover, the candidate protection mechanism is given to further upgrade the equivalent searching algorithm, which makes it not only an optimal but also a sub-optimal ILS estimator given the flexible setup of K.

A GPS relative positioning quality control algorithm considering both code and phase observation errors

GPS relative positioning performance highly relies on the quality control algorithm. Previous efforts were mainly made with emphasis on the phase cycle slip detection in the preprocessing stage and the posterior residual check to re-weight observations. Very limited work focused on the code observation error and its effect on GPS relative positioning. This paper proposes a GPS relative positioning quality control algorithm that considers both code and phase errors of dual-frequency observations for geodetic and navigation receivers. In addition to the phase cycle slip detection in the preprocessing stage, a posterior code residual check is developed that has priority over the posterior phase residual check. If the posterior code residual check fails, no posterior phase residual check is needed. In this sense, the effect of code observation error on the phase ambiguity estimation and subsequently high-precision positioning can be investigated. Three dedicated static and kinematic experiments were carried out to assess the proposed method in terms of the ambiguity and positioning solutions, respectively. As for Experiment #1 under good observation environment, the proposed method provided a similar performance as the conventional method not taking the code observation error into account. However, Experiment #2 characterized by the tree-surrounded observation environment and Experiment #3 for kinematic positioning above the lake surface indicated that the proposed method could provide significant improvements over the conventional method. The ignorance of code observation error would deteriorate the phase ambiguity estimation and subsequently lead to worse positioning convergence and precision.

An arc-clustering-based phase ambiguity estimation method for persistent scatterer interferometry

ABSTRACTThe reliability of persistent scatterer interferometry (PSI) is directly related to the accurate phase unwrapping (PU) of the 3-D (2-D space and time) sparse data stack. Phase ambiguities estimated using temporal phase unwrapping (TPU) are crucially exploited in most 3-D PU algorithms. However, most TPU methods are not noise-robust owing to the independent processing of each arc in the persistent scatterer network. To solve this problem, the cluster-analysis-based PU method for digital elevation model (DEM) construction is adapted to the phase ambiguity estimation problem for PSI in this letter. First, for each arc, the interior relation among phase ambiguities in multiple interferograms is derived to be linear and can be represented by an intercept vector. Subsequently, arcs with the same ambiguities are clustered according to their intercept vectors because arcs with identical phase ambiguities are verified to have the same intercept vectors. Moreover, a more reliable intercept vector can be calculated for each arc cluster by combining the intercept vectors within the cluster. Finally, more precise phase differences are estimated for each cluster using the corresponding intercept vector so that all the arcs are better unwrapped. Both the simulated and real experiments indicate the effectiveness and superiority of the proposed algorithm.

Artificial neural network for detecting incorrectly fixed phase ambiguities for L1 mass-market receivers

One of the main challenges in global navigation satellite systems (GNSS) network real-time kinematic positioning is phase ambiguity estimation. We describe methods that predict false fixing (FF) of phase ambiguities in mass-market receivers. In this work, FF is defined to occur when the differences between 3D coordinates estimated in real-time differ by more than 20 cm with respect to the reference coordinates. Phase ambiguity FF events occur for many reasons, such as wrong estimation of phase ambiguities by the network software, noise in the corrections, and the environment of the rover. Moreover, one of the main reasons for phase ambiguity FF is the high level of noise and the low redundancy of observation by receivers that track L1 frequencies only. We develop and analyze a specific tool utilizing an artificial neural network that, when trained, tested, and refined specifically for GNSS mass-market receivers, can predict and detect FF. This tool comprises three inputs for all epochs, the Horizontal Dilution of Precision index, the latency of the differential correction, and the number of satellites with fixed phase ambiguities seen by the rover. It provides as output an index consisting of values 0 or 1, i.e., 0 for no FF and 1 for FF. A description of the training and validating phases is provided. The results of tests show that the algorithm has a 99.7% probability of detecting phase ambiguity FF in these cases.

Performance analysis of a novel antenna array calibration approach for direction finding systems

This paper addresses the problem of the direction of arrival (DoA) estimation in the presence of an uncalibrated array, i.e. when phase offset, carrier frequency offset and phase noise occur among the array signals. The method that we propose consists in the use of a particular antenna array that comprises the elements for the DoA estimation and a common antenna that is shared with a splitter among the receivers. The signal that impinges on the common antenna is acquired by every receiver and allows the estimation of the phase ambiguity. After the calibration step is performed, analogue switches select the array elements for the DoA estimation. A method that enables the phase ambiguity estimation is presented, and several simulated performance results are illustrated. Furthermore, we show the effect on calibration due to the presence of different carrier frequency offsets among the receivers and propose an approach for their compensation. The presence of phase noise is also considered and its effect is analysed.Copyright © 2012 John Wiley & Sons, Ltd.

Enhanced algorithm based on persistent scatterer interferometry for the estimation of high-rate land subsidence

Persistent scatterer interferometry (PSI) techniques using amplitude analysis and considering a temporal deformation model for PS pixel selection are unable to identify PS pixels in rural areas lacking human-made structures. In contrast, high rates of land subsidence lead to significant phase-unwrapping errors in a recently developed PSI algorithm (StaMPS) that applies phase stability and amplitude analysis to select the PS pixels in rural areas. The objective of this paper is to present an enhanced algorithm based on PSI to estimate the deformation rate in rural areas undergoing high and nearly constant rates of deformation. The proposed approach integrates the strengths of all of the existing PSI algorithms in PS pixel selection and phase unwrapping. PS pixels are first selected based on the amplitude information and phase-stability estimation as performed in StaMPS. The phase-unwrapping step, including the deformation rate and phase-ambiguity estimation, is then performed using least-squares ambiguity decorrelation adjustment (LAMBDA). The atmospheric phase screen (APS) and nonlinear deformation contribution to the phase are estimated by applying a high-pass temporal filter to the residuals derived from the LAMBDA method. The final deformation rate and the ambiguity parameter are re-estimated after subtracting the APS and the nonlinear deformation from that of the initial phase. The proposed method is applied to 22 ENVISAT ASAR images of southwestern Tehran basin captured between 2003 and 2008. A quantitative comparison with the results obtained with leveling and GPS measurements demonstrates the significant improvement of the PSI technique.

The GPS integer least-squares statistics

Successful integer least-squares carrier phase ambiguity estimation is the key to fast and high precision GPS kinematic positioning. In order to describe the quality of the positioning results rigorously, one needs to know the probability distributions of both the integer and noninteger parameters in the GPS model. In this contribution these distributions are presented and discussed. The probability mass function of the integer least-squares ambiguities is needed to evaluate the ambiguity success rate and the joint distribution of the GPS baseline and atmospheric delays is needed to evaluate the relevant confidence regions.