On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data

Abstract

On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data On-the-fly ambiguity resolution (OTF AR) is based on a small data set, obtained from a very short observation session or even from a single epoch observation. In these cases, a classical approach to ambiguity resolution (e.g. the Lambda method) can meet some numerical problems. The basis of the Lambda method is an integer decorrelation of the positive definite ambiguity covariance matrix (ACM). The necessary condition for the proper performing of this procedure is a positive definiteness of ACM. However, this condition is not satisfied in cases of very short observation sessions or single epoch positioning if phase-only observations are used. The subject of this contribution is such a case where phase-only observations are used in the final part of the computational process. The modification of ACM is proposed in order to ensure its positive definiteness. An estimator of modified ACM is a good ACM approximation for the purpose of performing the LAMBDA method. Another problem of short sessions (or a single epoch) positioning is the poor quality of the float solution. In this paper, a cascade adjustment with wide-lane combinations of signals L1 and L2 as a method of solving this problem is presented.