Vectorial integer bootstrapping: flexible integer estimation with application to GNSS

In this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-block processing of the ambiguities based on a user-chosen partitioning. In this way, flexibility is created, where for specific choices of partitioning, tailored VIB-estimators can be designed. This wide range of possibilities is discussed, supported by numerical simulations and analytical examples. Further guidelines are provided, as well as the possible extension to other classes of estimators.

Automated summary

This paper extends the principle of integer bootstrapping to a vectorial form, introducing the mathematical definition and properties of VIB estimators. The vectorial formulation allows flexible block-by-block processing and tailored design choices for specific partitioning. The wide range of possibilities is supported by numerical simulations and analytical examples, with further guidelines and potential extensions to other estimator classes provided.