Instantaneous Ambiguity Resolved GLONASS FDMA Attitude Determination

<p><strong>G1 – Geodetic Theory and Algorithms</strong></p><p><strong>G1.3 High-precision GNSS: methods, open problems and Geoscience applications</strong></p><p><strong> </strong></p><p><strong>Instantaneous Ambiguity Resolved GLONASS FDMA Attitude Determination</strong></p><p><strong> </strong></p><p>PJG Teunissen<sup>1,2</sup>, A. Khodabandeh<sup>3</sup>, S. Zaminpardaz<sup>4</sup></p><p><sup>1</sup>GNSS Research Centre, Curtin University, Perth, Australia</p><p><sup>2</sup>Geoscience and Remote Sensing, Delft University of Technology, The Netherlands</p><p><sup>3</sup>University of Melbourne, Melbourne, Australia</p><p><sup>4</sup>RMIT University, Melbourne, Australia</p><p> </p><p>In [1] a new formulation of the double-differenced (DD) GLONASS FDMA model was introduced. It closely resembles that of CDMA-based systems and it guarantees the estimability of the newly defined GLONASS ambiguities. The close resemblance between the new GLONASS FDMA model and the standard CDMA-models implies that available CDMA-based GNSS software is easily modified [2] and that existing methods of integer ambiguity resolution can be directly applied. Due to its general applicability, we believe that the new model opens up a whole variety of carrier-phase based GNSS applications that have hitherto been a challenge for GLONASS ambiguity resolution [3]</p><p>We provide insight into the ambiguity resolution capabilities of the new GLONASS FDMA model, combine it with next-generation GLONASS CDMA signals [4] and demonstrate it for remote sensing platforms that require single-epoch, high-precision direction finding. This demonstration will be done with four different, instantaneous baseline estimators: (a) unconstrained, ambiguity-float baseline, (b) length-constrained, ambiguity-float baseline, (c) unconstrained, ambiguity-fixed baseline, and (d) length-constrained, ambiguity-fixed baseline. The unconstrained solutions are computed with the LAMBDA method, while the constrained ambiguity solutions with the C-LAMBDA method, thereby using the numerically efficient bounding-function formulation of [5]. The results will demonstrate that with the new model, GLONASS-only direction finding is instantaneously possible and that the model and associated method therefore holds great potential for array-based attitude determination and array-based precise point positioning.</p><p> </p><p>[1] P.J.G. Teunissen (2019): A New GLONASS FDMA Model, GPS Solutions, 2019, Art 100.</p><p>[2] A. Khodabandeh and P.J.G. Teunissen (2019): GLONASS-L. MATLAB code archived in GPSTOOLBOX:</p><p>https://www.ngs.noaa.gov/gps-toolbox/GLONASS-L.htm</p><p>[3] R. Langley (2017): GLONASS: Past, present and future. GPS World November 2017, 44-48.</p><p>[4] S. Zaminpardaz, P.J.G. Teunissen and N. Nadarajah (2017): GLONASS CDMA L3 ambiguity resolution</p><p>and positioning, GPS Solutions, 2017, 21(2), 535-549.</p><p>[5] P.J.G. Teunissen PJG (2010): Integer least-squares theory for the GNSS compass. Journal of Geodesy, 84:433–447</p><p> </p><p><strong>Keywords: </strong>GNSS, GLONASS, FDMA, CDMA model, Instantaneous Attitude Determination, Integer Ambiguity Resolution</p>

A Triple Checked Partial Ambiguity Resolution for GPS/BDS RTK Positioning

Reliable and accurate carrier phase ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning and application. With the fast development of modern GNSS, the increased number of satellites and ambiguities makes it hard to fix all ambiguities completely and correctly. The partial ambiguity fixing technique, which selects a suitable subset of high-dimensional ambiguities to fix, is beneficial for improving the fixed success rate and reliability of ambiguity resolution. In this contribution, the bootstrapping success rate, bounded fixed-failure ratio test, and the new defined baseline precision defect are used for the selection of the ambiguity subset. Then a model and data dual-driven partial ambiguity resolution method is proposed with the above three checks imposed on it, which is named the Triple Checked Partial Ambiguity Resolution (TC-PAR). The comprehensive performance of TC-PAR compared to the full-fixed LAMBDA method is also analyzed based on several criteria including the fixed rate, the fixed success rate and correct fixed rate of ambiguity as well as the precision defect and RMS of the baseline solution. The results show that TC-PAR could significantly improve the fixed success rate of ambiguity, and it has a comparable baseline precision to the LAMBDA method, both of which are at centimeter level after ambiguities are fixed.

Performance Analysis of Positioning Solution Using Low-Cost Single-Frequency U-Blox Receiver Based on Baseline Length Constraint

With the rapid development of the satellite navigation industry, low-cost and high-precision Global Navigation Satellite System (GNSS) positioning has recently become a research hotspot. The traditional application of GNSS may be further extended thanks to the low cost of measuring instruments, but effective methods are also desperately needed due to the low quality of the data obtained using these instruments. Thus, in this paper, we propose the analysis and evaluation of the ambiguity fixed-rate and positioning accuracy of single-frequency Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) data, collected from a low-cost u-blox receiver, based on the Constrained LAMBDA (CLAMBDA) method with a baseline length constraint, instead of the classical LAMBDA method. Three sets of experiments in different observation environments, including two sets of static short-baseline experiments and a set of dynamic vehicle experiments, are adopted in this paper. The experiment results show that, compared to classical LAMBDA method, the CLAMBDA method can significantly improve the success rate of the GNSS ambiguity resolution. When the ambiguity is fixed correctly, the baseline solution accuracy reaches 0.5 and 1 cm in a static scenario, and 1 and 2 cm on a dynamic platform.

Multivariate Constrained GNSS Real-time Full Attitude Determination Based on Attitude Domain Search

A priori attitude information can improve the success rate and reliability of Global Navigation Satellite System (GNSS) multi-antennae attitude determination. However, a priori attitude information is nonlinear, and integrating a priori information into the objective function rigorously will increase the complexity of an ambiguity domain search, such as the Multivariate Constrained-Least-squares Ambiguity Decorrelation Adjustment (MC-LAMBDA) method. In this paper, a new method based on attitude domain search is presented to make use of the a priori attitude angle information with high efficiency. First, the a priori information of pitch and roll is integrated into the search process to derive the analytic search step for attitude angle, and the integer candidates are determined by traversal search in the three-dimensional attitude domain. Then, the objective function is parameterised with Euler angles, and a non-iterative approximate method is utilised to simplify the iterative computation in calculating objective function values. Experimental results reveal that compared to the MC-LAMBDA method, our new method has the same success rate and reliability, but higher efficiency in making use of a priori attitude information.

Optimization of a Grid of Candidates in the Search Procedure of the MAFA Method

Precise, carrier phase-based positioning requires a search procedure for “fixed solution” i.e. a solution, that takes into account the integer nature of ambiguities. In the classical approach (the Lambda method) the search for a fixed solution is conducted in the ambiguity domain. The computational load in this case depends on a number of satellites (the dimension of an ambiguity space amounts to: the number of satellites minus one). Conversely, in the MAFA method the search procedure is conducted in the coordinate-domain, (i.e. in three-dimensional space). It considerably reduces the computational load. In the article the search procedure in the coordinate domain is described. The technique of forming the optimized grid of candidates is presented, and the results of the tests are presented and analyzed.

On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data

On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data On-the-fly ambiguity resolution (OTF AR) is based on a small data set, obtained from a very short observation session or even from a single epoch observation. In these cases, a classical approach to ambiguity resolution (e.g. the Lambda method) can meet some numerical problems. The basis of the Lambda method is an integer decorrelation of the positive definite ambiguity covariance matrix (ACM). The necessary condition for the proper performing of this procedure is a positive definiteness of ACM. However, this condition is not satisfied in cases of very short observation sessions or single epoch positioning if phase-only observations are used. The subject of this contribution is such a case where phase-only observations are used in the final part of the computational process. The modification of ACM is proposed in order to ensure its positive definiteness. An estimator of modified ACM is a good ACM approximation for the purpose of performing the LAMBDA method. Another problem of short sessions (or a single epoch) positioning is the poor quality of the float solution. In this paper, a cascade adjustment with wide-lane combinations of signals L1 and L2 as a method of solving this problem is presented.