Bias-constrained integer least squares estimation: distributional properties and applications in GNSS ambiguity resolution

Abstract

To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer search method of BEAT. In this contribution, we present the probability distributions of a class of estimators to which the proposed bias-constrained integer least squares estimation belongs. Some important interferometric measuring systems, whose estimation problems can be covered by BEAT, are identified. To show the proposed estimator at work, we apply BEAT to the problem of GLONASS single-differenced (SD) ambiguity resolution. Numerical results of several short-baseline datasets are presented to illustrate why one can achieve more accurate positioning solutions when considering between-receiver SD ambiguity resolution for the cases where carrier phase data are captured on frequency-varying signals with bounded SD receiver phase delays.