The Volume of the GPS Ambiguity Search Space and its Relevance for Integer Ambiguity Resolution

Abstract

In the theory of integer least-squares ambiguity estimation and validation, a central role is played by the ambiguity search space. In this contribution, the significance of the volume of the ambiguity search space is discussed and analyzed. It is shown how the volume can be used as an estimate for the number of grid points inside the GPS ambiguity search space. This is done for various measurement scenarios, each characterized by the use of different types of data redundancies. For these measurement scenarios, it is also shown how the volume can be used to appropriately scale the size of the ambiguity search space. This analysis is presented in the context of the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. In particular the low correlation and high precision of the transformed ambiguities as provided by the LAMBDA method, allow an appropriate down scaling of the search space. As a result, only a few candidate grid points are left in the ambiguity search space. 1....