Integer Ambiguity Resolution by Mixture Kalman Filter for Improved GNSS Precision

Accurate carrier-phase integer ambiguity resolution is fundamental to high-precision global navigation satellite systems (GNSSs). Real-time GNSSs typically resolve the ambiguities by a combination of recursive estimators and integer least-squares solvers, which need to be reset when satellites are added or cycle slip occurs. In this article, we propose a mixture Kalman filter solution to integer ambiguity resolution. By marginalizing out the set of ambiguities and exploiting a likelihood proposal for generating the ambiguities, we can bound the possible values to a tight and dense set of integers. Thus, we extract the state and integer estimates from a mixture Kalman filter. The proposed approach yields an integrated method to detect cycle slip and initialize new satellites. Numerical analysis and experimental results indicate that the proposed method achieves reliable position estimates, repeatedly finds the correct integers in cases when other methods may fail, and is more robust to cycle slip.