Abstract
Mixed integer–real least squares (MIRLS) estimation still has two open scientific problems, i.e., the validation of results and computational efficiency for a large number of satellites. This paper presents and discusses a non-conventional approach to MIRLS estimation, which belongs to the ambiguity function method (AFM) class. Because the solution is searched for in the constant three-dimensional coordinate domain instead of the n-dimensional ambiguity domain, the computational efficiency does not depend as much on the number of satellites as it does in conventional MIRLS estimation. Simple numerical pretests have shown that the reliability and precision of results from the presented approach and the conventional MIRLS estimation are exactly the same. Hence, the presented approach, contrary to AFM, may be treated as MIRLS estimation. Furthermore, the presented approach is a few hundred times faster than AFM and may be considered in (near) real-time GNSS positioning. In light of the above, the new field of research on MIRLS estimation may be opened.
Highlights
Precise GNSS positioning requires resolving the so-called mixed integer–real problem to determine carrier phase integer ambiguities
The performed tests have shown that such an approach significantly increases the probability of determining the coordinates located in the good Voronoi cell and the probability of good solution
We discussed and pretested a non-conventional approach to the Mixed integer–real least squares (MIRLS) estimation which may open the new field of research
Summary
Precise GNSS positioning requires resolving the so-called mixed integer–real problem to determine carrier phase integer ambiguities. Integer aperture (IA) estimators belong to the second class (Teunissen 2003) These estimators unify I-estimation with validation and can adopt both integer and real values. Integer equivariant (IE) estimators constitute the third and most general class (Teunissen 2002) The second category of algorithms includes the very first ambiguity estimation technique developed, namely the ambiguity function method (AFM). This method was first introduced by Counselman and Gourevitch (1981). Remondi (1984, 1990) used this method extensively for GPS static positioning and for pseudokinematic positioning These methods utilize certain properties of the chosen trigonometric functions, which have known values for the integer arguments, without determining ambiguities.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
