Rough Integer Mapping and the GNSS Integer Ambiguity Estimation

Paper number

IAC-08.B2.2.7

Author

Mr. Chen Xiaoping, University of electronic science and technology of China, China

Year

2008

Abstract

With the invention and development of the GNSS (Global Navigation Satellite System), huge economic and social benefits have been generated in various application fields. There are a lot of models used for measurement, positioning and navigation, but the integer ambiguity estimation is the most important difficulty for all of those models using carrier phase measurement. In this paper, based on the analysis of the traditional GNSS carrier phase measurement model and the rule of the integer ambiguity estimation, get the quality of the normal integer mapping, then, educe the theory of the rough integer mapping, solve the question of the GNSS integer ambiguity estimation, improve the searching efficiency of the integer ambiguity, deal with the problem of the GNSS carrier phase measurement perfectly.

1. Rough integer mapping

	We can extent the definition of the normal mapping, and define the rough integer mapping that uses mathematical language to describe.

Now, we assume that: there is equivalence relation to compartmentalize set V. Quotient set V/R marks the set which includes all the equivalence sets. Then define another set B to mark the equivalence sets that include elements.
Define two sets which are named the down-approximate set, and the up-approximate set. So we can define the equivalence relation and the rough set.

The integer mapping maps the vector of real number to the vector of integer set. When the set is the rough set for the equivalence relation, we define the mapping as rough integer mapping.

2. With the traditional methods of the ambiguity estimation of GNSS, we design the approach of the ambiguity estimation algorithm using rough integer mapping.

1) Create the model of the carrier phase measurement, and estimate the floating point values and the covariance matrix of the ambiguity using Least-squares.

2) Drop covariance matrix associated with the region to search for conversion using LAMBDA.
3) Transform the vector which is the real number of ambiguity to the rough set using rough integer mapping.

4) Search for the ambiguity using the down-approximate set or up-approximate set.

5) Assurance the result of the ambiguity estimation.

3. Rough integer mapping, which changes the searching topology in the region on the ambiguity, obviously improves the searching efficiency. The method of counting the ambiguity assessment of the correctness is another direction to study.

Abstract document

IAC-08.B2.2.7.pdf

Manuscript document

IAC-08.B2.2.7.pdf (🔒 authorized access only).

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