A New Method of Integer Parameter Estimation in Linear Models With Applications to GNSS High Precision Positioning

Abstract

The high precision positioning of global navigation satellite systems (GNSS), which essentially corresponds to solving the integer least-squares (ILS) problem in the integer phase ambiguity estimation, has emerged as a key problem for the development of industrial internet-of-things (IIoT). In this paper, a novel paradigm for solving the ILS problem is introduced to the integer phase ambiguity estimation. Different from the traditional paradigm of ILS which only involves one parameter to characterize the trade-off between performance and complexity, the proposed ILS paradigm entails two parameters named as the initial searching size K ≥ 1 and the standard deviation σ > 0, thus introducing extra degrees of freedom to facilitate the system trade-off. Based on it, explicit analysis can be carried out for a mathematically tractable trade-off, where great potentials could be further exploited for the high precision positioning of GNSS. The equivalent searching algorithm (ESA) is proposed, which achieves the same performance as the classic Fincke-Pohst strategy in sphere decoding (SD) but with tractable complexity measured by the number of visited nodes in the searching stage. Moreover, the candidate protection mechanism is given to further upgrade the equivalent searching algorithm, which makes it not only an optimal but also a sub-optimal ILS estimator given the flexible setup of K.