New Global Navigation Satellite System Ambiguity Resolution Method Compared to Existing Approaches

Abstract

Integer carrier phase ambiguity resolution is the process of resolving unknown cycle ambiguities of doubledifferenced carrier phase data as integers, and it is a prerequisite for rapid and high-precision global navigation satellite system positioning and navigation. Besides integer estimation, integer ambiguity resolution also involves validation of the integer estimates. In this contribution a new ambiguity resolution method is presented, based on the class of integer aperture estimators, which for the first time reveals an overall approach to the combined problem of integer estimation and validation. Furthermore, it is shown how the different discrimination tests that are currently in use in practice can be cast into the framework of the new approach.

A New Method For DGPS Ambiguity Resolution?

“…Secondly, since the ambiguities are resolved on an individual scalar basis, the absence of a vectorial formulation implies N O. 2 F O R U M that no advantage can be taken of the optimal ILS success rate performance, see Equation (5). It is rather unfortunate, given Piergentili's claim of a new method, that the paper has not properly explored the existing body of knowledge.…”

“…Optimality refers here to the maximization of the probability of correct integer estimation (the success rate) or to the minimization of the mean squared error. The three optimal estimators, one for each class, have been identified in [4][5][6].…”

Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications

“…Previous work (e.g., Verhagen, 2005;Verhagen and Teunissen, 2006) has shown some of the ambiguity validation tests are members of the class of IA-estimators, e.g., RIA, FIA, Difference IA (DIA), PIA. Analogously, W-ratio (Wang et al, 1998) can be categorized as one of the IA estimators, named as WIA.…”

“…A common feature for this type of validation methods is that a critical value, which comes either empirically or is based on the distributions of their statistics (Verhagen, 2004;Li and Wang, 2012), is necessary to determine whether to accept the most likely integer candidate or not. With the introduction of the Integer Aperture (IA) estimator (Teunissen, 2003a), some of these methods can be mathematically expressed as IA estimators (Verhagen, 2005;Verhagen and Teunissen, 2006), and several other IA estimators also have been introduced, such as the Ellipsoidal IA (EIA) estimator, (Teunissen, 2003b), Penalized IA (PIA) estimator (Teunissen, 2004), and a unified theoretical framework has been established. The ambiguity validation is then carried out by a user-defined fail-rate, which performs the same function as the critical value in the traditionally used statistics tests but allows for an explicit and overall probabilistic evaluation of the outcome, to validate the integer ambiguities.…”

GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

“…Examples include the ratiotest, the difference-test and the projection-test [14][15][16][17][18]. All these tests can be cast in the framework of Integer Aperture Estimation (IAE) [19][20][21].The ratio-test is probably one of the most popular. Both the Fixed Critical-value Ratio Test (FC-RT) and the Fixed Failure-rate Ratio Test (FF-RT) are part of the new version of LAMBDA.…”