Success rate improvement of single epoch integer least-squares estimator for the GNSS attitude/short baseline applications with common clock scheme

Abstract

The sub-centimeter level relative positioning can be accomplished anytime and anywhere on Earth, provided that the integer ambiguities of the very precise Global Navigation Satellite System (GNSS) carrier-phase observables are correctly resolved. The Integer Least-Squares (ILS) estimator is known to be efficient and optimal for Integer Ambiguity Resolution (IAR) of the unconstrained GNSS model, and the stronger the model strength, the higher the success rate. In this contribution, we investigate the model strength of the common clock scheme, in which the two receivers of the short baseline feed a common clock and the cables have the same delay and many GNSS-based attitude/short baseline applications benefit from this approach. For this scheme, the clock biases between two receivers will be zero and can be omitted, and thus it has a stronger model strength and a higher success rate, compared with the non-common clock scheme. In this contribution, the well-known Ambiguity Dilution of Precision (ADOP), which captures the main characteristics of the ambiguity precision, is utilized to assess the model strengthening when the perfectly synchronized receivers are employed. The mathematical expression of the single epoch ADOP is deduced by the given design parameters, and thus the ADOP-based approximate ILS success rate can be easily computed with the specified measurement set-up which includes the number of available satellites and frequencies and the precision of observation. We focus on the success rate assessment of the common clock scheme for stand-alone, unaided, single-frequency, single epoch observation with only five visible satellites, since it is the most challenging case of GNSS relative positioning and in this case the performance of the employed ambiguity resolution method can be investigated effectively. Thus, one can predict whether or not the required performance will be obtained for the worst case.

Performance Evaluation of QZSS Augmenting GPS and BDS Single-Frequency Single-Epoch Positioning with Actual Data in Asia-Pacific Region

“…Based on the ambiguity estimator theory, the success rate of ambiguity resolution is determined by computing the numerical integration of the probability density function of float ambiguities in the 'pull-in region', which is very rigorous in theory [26]. However, it is difficult to describe the 'pull-in region' so the integration process is very complex and the success rate cannot be calculated directly.…”

Performance improvement for GPS single frequency kinematic relative positioning under poor satellite visibility

“…The ADOP, or Ambiguity Dilution of Precision, is given by , which is a diagnostic that captures the main characteristics of ambiguity precision (Teunissen and Odijk 1997 ). When the ambiguities are completely decorrelated, the ADOP equals the geometric mean of the standard deviations of the ambiguities, hence it can be considered as a measure of the average ambiguity precision (Verhagen et al 2013 ).The success rate of ambiguity resolution is determined by the strength of the underlying GNSS model; the stronger the model, the higher the success rate (Verhagen 2005 ; Teunissen 2010 ; Buist 2013 ; Chen and Li 2014 ). In order to improve the strength of the single frequency model, the float solution should be estimated with data from more epochs.…”

Double-parameter iterative Tikhonov regularization of weak single-epoch GNSS mathematical models

“…However, some researchers have attempted to deal with this limitation, e.g. Chen and Li (2014), Deng et al (2014), Lau et al (2015). Supplementing a single-epoch data set with carrier-phase measurements of other GNSS systems will not eliminate the rank deficiency problem because of new unknown double-differenced (DD) ambiguities.…”