High Dimensional Integer Ambiguity Resolution: A First Comparison between LAMBDA and Bernese

Abstract

The LAMBDA method for integer least-squares ambiguity resolution has been widely used in a great variety of Global Navigation Satellite System (GNSS) applications. The popularity of this method stems from its numerical efficiency and its guaranteed optimality in the sense of maximizing the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used for the cases where the number of ambiguities was generally less than several tens. With the advent of denser network processing and the availability of multi-frequency, multi-GNSS systems, it is important to understand LAMBDA's performance in high dimensional spaces. In this contribution, we will address this issue using real GPS data based on the Bernese software. We have embedded the LAMBDA method into the Bernese software and compared their ambiguity resolution performances. The 12-day dual-frequency GPS with a sampling interval of 30 s was used in the experiment, which was collected from a network of 19 stations in the Perth area of Western Australia with an average baseline length of 380 km. Different experimental scenarios were examined and tested with different observation spans, which represent the different ambiguity dimensions. The results showed that LAMBDA is still efficient even when the number of ambiguities is more than 100, and the baseline repeatabilities obtained with the ambiguities resolved from LAMBDA method agreed well with that of Bernese. Therefore, for the future's dense network processing, the easy-to-use LAMBDA method should be considered as an alternative to baseline-per-baseline methods as those used in e.g. the Bernese software. KEY WORDS1. LAMBDA method. 2. Bernese software. 3. High-dimensional integer space. 4. Ambiguity resolution.

Introduction of the Double-Differenced Ambiguity Resolution into Precise Point Positioning

“…According to Equation (6), the float DD NL ambiguities can be computed and their integer values can be fixed based on LAMBDA method [29][30][31]. The ambiguity fixing of the PPP user is realized by introducing an SD PPP ambiguity from other users and fixing the DD WL and NL AR.…”

Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications

“…The ILS pull-in region is defined by: For more information on the LAMBDA method and its wide-spread applications see e.g. (Teunissen, 1993(Teunissen, , 1995bLi and Teunissen, 2011;Chang et al, 2005; De Jonge and Tiberius, 1996; Hofmann-Wellenhof et Teunissen and Kleusberg, 1998;Leick, 2004;Strang and Borre, 1997;Misra and Enge, 2001).…”

“…As a first example, we mention the GNSS Real-Time Kinematic (RTK) technique, (Odijk, 2002;Li and Teunissen, 2011;Euler et al, 2004;Takac and Zelzer, 2008). It is widely used for mapping, geodetic surveying and network applications, (Blewitt, 1989;Bock, 1996;Strang and Borre, 1997;Leick, 2004;Hofmann-Wellenhof et al, 2008;Teunissen and Kleusberg, 1998).…”

QIF-based GPS Long-baseline Ambiguity Resolution with the Aid of Atmospheric Delays Determined by PPP

“…Up to now, the long-baseline setup has been adopted across a broad range of applications such as relative positioning (Eckl et al, 2001; Schüler, 2006), time transfer (Lee et al, 2008; Petit and Jiang, 2008) and atmosphere sensing (Jin et al, 2010; Pacione and Vespe, 2003). To maximise the efficiency and accuracy of these applications, fast and successful Integer Ambiguity Resolution (IAR) is always essential, so that the very precise Double-Differenced (DD) carrier-phase data can be fully exploited (Blewitt, 1989; Bock et al, 1985; Li and Teunissen, 2011). Unfortunately, GPS long-baseline IAR is not a trivial task, since it has to tackle the non-negligible atmospheric delays underlying the DD data (Jin et al, 2010; Schüler, 2006; Teunissen, 1998a).…”